67. Tutorial#

In questo notebook esamineremo il tutorial proposto da Sijtsma and van der Ark [SvdA17], i quali usano un campione (N = 541; 68 donne e 473 uomini) con un’età compresa tra i 23 e gli 89 anni (M = 58.7). I partecipanti erano pazienti affetti da lieve malattia coronarica, a cui è stata somministrata una batteria di questionari, tra cui il DS14, un questionario di 14 item che misura la personalità di Tipo D (Denollet, 2005). Sette item misurano l’affettività negativa (NA) e gli altri sette item misurano l’inibizione sociale (SI).

La somma dei punteggi dei 14 item, denominata punteggio DS14, misura la personalità di Tipo D. Gli item consistono in un’affermazione seguita da una scala di valutazione a cinque punti, da 0 a 4.

  1. I make contact easily when I meet people

  2. I often make a fuss about unimportant things

  3. I often talk to strangers

  4. I often feel unhappy

  5. I am often irritated

  6. I often feel inhibited in social interactions

  7. I take a gloomy view of things

  8. I find it hard to start a conversation

  9. I am often in a bad mood

  10. I am a closed kind of person

  11. I would rather keep other people at a distance

  12. I often find myself worrying about something

  13. I am often down in the dumps

  14. When socializing, I don’t find the right things to talk about

suppressPackageStartupMessages({
    library("mokken")
    library("tidyverse")
    library("mice")
})
data(DS14)
head(DS14)
A matrix: 6 × 16 of type dbl
MaleAgeSi1*Na2Si3*Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
15923222233222424
15420300202024302
15013111222222111
15223200102131101
15922122233232313
05843412010200420
# Define Male, Age, and item scores,
male <- DS14[, "Male"]
age <- DS14[, "Age"]
itemScores <- DS14[, 3:16] |> as.data.frame()
# Define
# N = sample size,
# J = number of items
# m = highest item score,
# Na = items in Na scale
# Si = items in Si scale
N <- nrow(itemScores)
J <- ncol(itemScores)
m <- 4
Na <- c(2, 4, 5, 7, 9, 12, 13)
Si <- c(1, 3, 6, 8, 10, 11, 14)

67.1. Dieci passi per l’analisi di una scala Mokken#

Descriviamo le tre fasi contenenti dieci passi per eseguire un’analisi di scala Mokken (MSA):

i. Esame dei dati. Analizzare i dati e adottare misure appropriate quando si verificano particolari problemi con i dati (passi 1–3).

itemsScores <- as.data.frame(itemScores)
colnames(itemsScores) <- c(
    'Si1','Na2','Si3','Na4','Na5','Si6','Na7','Si8','Na9','Si10','Si11','Na12','Na13','Si14'
)

head(itemsScores)
A data.frame: 6 × 14
Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
123222233222424
220300202024302
313111222222111
423200102131101
522122233232313
643412010200420

67.2. Step 1#

  1. Ricodifica. Ricodificare i punteggi degli item che sono formulati negativamente rispetto all’attributo di interesse, in modo che per tutti gli item punteggi più alti indichino una posizione più elevata sulla scala dell’attributo.

itemsScores$Si1 <- 4 - itemsScores$Si1 
itemsScores$Si3 <- 4 - itemsScores$Si3
head(itemsScores)
A data.frame: 6 × 14
Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
<dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl><dbl>
123222233222424
220100202024302
333311222222111
423200102131101
522322233232313
603012010200420

67.3. Step 2#

  1. Punteggi inammissibili e dati mancanti. Trattare i punteggi inammissibili come valori mancanti. Determinare la percentuale totale di punteggi mancanti nel set di dati e i rispondenti che hanno lasciato un numero irragionevole di risposte incomplete. Impostare i punteggi degli item mancanti utilizzando un qualche procedura di imputazione.

# STEP 2: INADMISSIBLE SCORES AND MISSING DATA
# No inadmissible scores
summary(male)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  1.0000  1.0000  0.8743  1.0000  1.0000 
summary(age)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  23.00   51.00   59.00   58.67   66.00   89.00 
summary(itemsScores)
      Si1            Na2             Si3             Na4        
 Min.   :0.00   Min.   :0.000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.00   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:0.0000  
 Median :1.00   Median :2.000   Median :2.000   Median :0.0000  
 Mean   :1.28   Mean   :1.871   Mean   :1.809   Mean   :0.8965  
 3rd Qu.:2.00   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:2.0000  
 Max.   :4.00   Max.   :4.000   Max.   :4.000   Max.   :4.0000  
 NA's   :1      NA's   :5       NA's   :1                       
      Na5             Si6             Na7             Si8            Na9       
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.00   Min.   :0.000  
 1st Qu.:1.000   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.00   1st Qu.:0.000  
 Median :2.000   Median :1.000   Median :0.000   Median :1.00   Median :1.000  
 Mean   :1.671   Mean   :1.213   Mean   :0.963   Mean   :1.27   Mean   :0.939  
 3rd Qu.:3.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.00   3rd Qu.:2.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.00   Max.   :4.000  
                                                 NA's   :1                     
      Si10            Si11            Na12            Na13       
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:0.0000  
 Median :1.000   Median :2.000   Median :2.000   Median :0.0000  
 Mean   :1.457   Mean   :1.565   Mean   :1.824   Mean   :0.8706  
 3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:3.000   3rd Qu.:2.0000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.0000  
 NA's   :1       NA's   :1                                       
      Si14      
 Min.   :0.000  
 1st Qu.:0.000  
 Median :1.000  
 Mean   :1.177  
 3rd Qu.:2.000  
 Max.   :4.000  
                

Eseguiamo l’imputazione multipla.

# Deterministic regression imputation
imp <- mice(itemsScores, method = "norm.predict", m = 1) # Impute data
 iter imp variable
  1   1  Si1  Na2  Si3  Si8  Si10  Si11
  2   1  Si1  Na2  Si3  Si8  Si10  Si11
  3   1  Si1  Na2  Si3  Si8  Si10  Si11
  4   1  Si1  Na2  Si3  Si8  Si10  Si11
  5   1  Si1  Na2  Si3  Si8  Si10  Si11
itemsScores <- complete(imp)
summary(itemsScores)
      Si1             Na2             Si3             Na4        
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:0.0000  
 Median :1.000   Median :2.000   Median :2.000   Median :0.0000  
 Mean   :1.284   Mean   :1.868   Mean   :1.811   Mean   :0.8965  
 3rd Qu.:2.000   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:2.0000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.0000  
      Na5             Si6             Na7             Si8       
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
 1st Qu.:1.000   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000  
 Median :2.000   Median :1.000   Median :0.000   Median :1.000  
 Mean   :1.671   Mean   :1.213   Mean   :0.963   Mean   :1.272  
 3rd Qu.:3.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.000  
      Na9             Si10            Si11            Na12      
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
 1st Qu.:0.000   1st Qu.:0.000   1st Qu.:1.000   1st Qu.:1.000  
 Median :1.000   Median :1.000   Median :2.000   Median :2.000  
 Mean   :0.939   Mean   :1.457   Mean   :1.564   Mean   :1.824  
 3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:3.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.000  
      Na13             Si14      
 Min.   :0.0000   Min.   :0.000  
 1st Qu.:0.0000   1st Qu.:0.000  
 Median :0.0000   Median :1.000  
 Mean   :0.8706   Mean   :1.177  
 3rd Qu.:2.0000   3rd Qu.:2.000  
 Max.   :4.0000   Max.   :4.000  

Trasformare i dati in numeri interi.

itemsScores[] <- lapply(itemsScores, function(x) {
    if (is.numeric(x)) as.integer(round(x)) else x
})
summary(itemsScores)
      Si1             Na2             Si3             Na4        
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.0000  
 1st Qu.:0.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:0.0000  
 Median :1.000   Median :2.000   Median :2.000   Median :0.0000  
 Mean   :1.285   Mean   :1.867   Mean   :1.811   Mean   :0.8965  
 3rd Qu.:2.000   3rd Qu.:3.000   3rd Qu.:3.000   3rd Qu.:2.0000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.0000  
      Na5             Si6             Na7             Si8       
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
 1st Qu.:1.000   1st Qu.:0.000   1st Qu.:0.000   1st Qu.:0.000  
 Median :2.000   Median :1.000   Median :0.000   Median :1.000  
 Mean   :1.671   Mean   :1.213   Mean   :0.963   Mean   :1.272  
 3rd Qu.:3.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.000  
      Na9             Si10            Si11            Na12      
 Min.   :0.000   Min.   :0.000   Min.   :0.000   Min.   :0.000  
 1st Qu.:0.000   1st Qu.:0.000   1st Qu.:1.000   1st Qu.:1.000  
 Median :1.000   Median :1.000   Median :2.000   Median :2.000  
 Mean   :0.939   Mean   :1.457   Mean   :1.564   Mean   :1.824  
 3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:3.000  
 Max.   :4.000   Max.   :4.000   Max.   :4.000   Max.   :4.000  
      Na13             Si14      
 Min.   :0.0000   Min.   :0.000  
 1st Qu.:0.0000   1st Qu.:0.000  
 Median :0.0000   Median :1.000  
 Mean   :0.8706   Mean   :1.177  
 3rd Qu.:2.0000   3rd Qu.:2.000  
 Max.   :4.0000   Max.   :4.000  

67.4. Step 3#

  1. Outlier. Identificare se particolari schemi di punteggi degli item si qualificano come outlier.

# STEP 3: OUTLIERS
# Outlier score G+ and two criterion values g1 and g2
outliers <- check.errors(itemsScores)
gPlus <- outliers$Gplus
g1 <- outliers$UGplus$U1Gplus
g2 <- outliers$UGplus$U2Gplus

# Number of outliers
nOutliers <- sum(gPlus > g1)
nOutliers
round(nOutliers * 100 / N, 1)
30
5.5
hist(gPlus, breaks = 50)
abline(v = g1, col = "orange")
abline(v = g2, col = "red")
../_images/0c01df91215c726ef87050eb7a9c30458dabb099b22abfa41732f92774a34a1f.png
# Correlation of G+ with X+, X+ ()
xPlus <- rowSums(itemsScores)
xPlusNa <- rowSums(itemsScores[, Na])
xPlusSi <- rowSums(itemsScores[, Si])
cor(cbind(gPlus, xPlus, xPlusNa, xPlusSi))
A matrix: 4 × 4 of type dbl
gPlusxPlusxPlusNaxPlusSi
gPlus1.00000000.28266750.32247550.1416448
xPlus0.28266751.00000000.81946330.8211281
xPlusNa0.32247550.81946331.00000000.3457729
xPlusSi0.14164480.82112810.34577291.0000000

ii. Identificazione della scala. Identificare una o più scale che soddisfino il modello di omogeneità monotona e, se ritenuto appropriato, verificare se le scale soddisfano anche il modello più esigente di monotonia doppia (passi 4–7).

67.5. Step 4#

  1. Scalabilità. Calcolare i coefficienti Hjk, Hj e H per le scale complete. Se ritenuto appropriato, controlliamo se le scale soddisfano anche il modello più esigente di doppia monotonicità.

L’inclusione degli outlier ha mostrato un impatto minimo sulla scalabilità dei risultati; pertanto, tali osservazioni sono state mantenute nell’analisi.

# Scalability coefficients
coefH(itemsScores[, Na])
$Hij
     Na2     se      Na4     se      Na5     se      Na7     se      Na9    
Na2                   0.391  (0.048)  0.522  (0.039)  0.465  (0.045)  0.468 
Na4   0.391  (0.048)                  0.439  (0.047)  0.661  (0.039)  0.503 
Na5   0.522  (0.039)  0.439  (0.047)                  0.499  (0.040)  0.581 
Na7   0.465  (0.045)  0.661  (0.039)  0.499  (0.040)                  0.555 
Na9   0.468  (0.045)  0.503  (0.045)  0.581  (0.038)  0.555  (0.043)        
Na12  0.532  (0.035)  0.616  (0.040)  0.475  (0.040)  0.648  (0.036)  0.440 
Na13  0.493  (0.040)  0.725  (0.033)  0.508  (0.042)  0.722  (0.031)  0.548 
     se      Na12    se      Na13    se     
Na2  (0.045)  0.532  (0.035)  0.493  (0.040)
Na4  (0.045)  0.616  (0.040)  0.725  (0.033)
Na5  (0.038)  0.475  (0.040)  0.508  (0.042)
Na7  (0.043)  0.648  (0.036)  0.722  (0.031)
Na9           0.440  (0.045)  0.548  (0.041)
Na12 (0.045)                  0.685  (0.031)
Na13 (0.041)  0.685  (0.031)                

$Hi
     Item H  se     
Na2    0.483 (0.028)
Na4    0.557 (0.030)
Na5    0.503 (0.028)
Na7    0.591 (0.026)
Na9    0.515 (0.029)
Na12   0.562 (0.025)
Na13   0.616 (0.024)

$H
Scale H      se 
  0.546 (0.022) 
coefH(itemsScores[, Si])
$Hij
     Si1     se      Si3     se      Si6     se      Si8     se      Si10   
Si1                   0.671  (0.036)  0.515  (0.043)  0.566  (0.040)  0.588 
Si3   0.671  (0.036)                  0.277  (0.049)  0.469  (0.044)  0.468 
Si6   0.515  (0.043)  0.277  (0.049)                  0.595  (0.039)  0.551 
Si8   0.566  (0.040)  0.469  (0.044)  0.595  (0.039)                  0.611 
Si10  0.588  (0.039)  0.468  (0.042)  0.551  (0.040)  0.611  (0.034)        
Si11  0.543  (0.040)  0.403  (0.044)  0.493  (0.043)  0.516  (0.041)  0.554 
Si14  0.506  (0.041)  0.410  (0.044)  0.526  (0.040)  0.680  (0.033)  0.523 
     se      Si11    se      Si14    se     
Si1  (0.039)  0.543  (0.040)  0.506  (0.041)
Si3  (0.042)  0.403  (0.044)  0.410  (0.044)
Si6  (0.040)  0.493  (0.043)  0.526  (0.040)
Si8  (0.034)  0.516  (0.041)  0.680  (0.033)
Si10          0.554  (0.038)  0.523  (0.039)
Si11 (0.038)                  0.451  (0.045)
Si14 (0.039)  0.451  (0.045)                

$Hi
     Item H  se     
Si1    0.566 (0.026)
Si3    0.451 (0.031)
Si6    0.494 (0.031)
Si8    0.573 (0.025)
Si10   0.549 (0.024)
Si11   0.494 (0.029)
Si14   0.518 (0.028)

$H
Scale H      se 
  0.521 (0.022) 
coefH(itemsScores)
$Hij
     Si1     se      Na2      se      Si3      se      Na4     se      Na5     
Si1                    0.050  (0.049)   0.671  (0.036)  0.219  (0.051)   0.092 
Na2   0.050  (0.049)                   -0.062  (0.047)  0.391  (0.048)   0.522 
Si3   0.671  (0.036)  -0.062  (0.047)                   0.097  (0.053)  -0.059 
Na4   0.219  (0.051)   0.391  (0.048)   0.097  (0.053)                   0.439 
Na5   0.092  (0.049)   0.522  (0.039)  -0.059  (0.046)  0.439  (0.047)         
Si6   0.515  (0.043)   0.270  (0.048)   0.277  (0.049)  0.450  (0.044)   0.368 
Na7   0.211  (0.050)   0.465  (0.045)   0.114  (0.049)  0.661  (0.039)   0.499 
Si8   0.566  (0.040)   0.176  (0.048)   0.469  (0.044)  0.318  (0.048)   0.165 
Na9   0.112  (0.050)   0.468  (0.045)   0.033  (0.050)  0.503  (0.045)   0.581 
Si10  0.588  (0.039)   0.156  (0.048)   0.468  (0.042)  0.242  (0.048)   0.172 
Si11  0.543  (0.040)   0.129  (0.050)   0.403  (0.044)  0.225  (0.051)   0.188 
Na12  0.172  (0.048)   0.532  (0.035)   0.042  (0.047)  0.616  (0.040)   0.475 
Na13  0.212  (0.052)   0.493  (0.040)   0.091  (0.052)  0.725  (0.033)   0.508 
Si14  0.506  (0.041)   0.104  (0.049)   0.410  (0.044)  0.337  (0.047)   0.148 
     se      Si6     se      Na7     se      Si8     se      Na9     se     
Si1  (0.049)  0.515  (0.043)  0.211  (0.050)  0.566  (0.040)  0.112  (0.050)
Na2  (0.039)  0.270  (0.048)  0.465  (0.045)  0.176  (0.048)  0.468  (0.045)
Si3  (0.046)  0.277  (0.049)  0.114  (0.049)  0.469  (0.044)  0.033  (0.050)
Na4  (0.047)  0.450  (0.044)  0.661  (0.039)  0.318  (0.048)  0.503  (0.045)
Na5           0.368  (0.047)  0.499  (0.040)  0.165  (0.049)  0.581  (0.038)
Si6  (0.047)                  0.468  (0.044)  0.595  (0.039)  0.392  (0.046)
Na7  (0.040)  0.468  (0.044)                  0.355  (0.046)  0.555  (0.043)
Si8  (0.049)  0.595  (0.039)  0.355  (0.046)                  0.277  (0.049)
Na9  (0.038)  0.392  (0.046)  0.555  (0.043)  0.277  (0.049)                
Si10 (0.046)  0.551  (0.040)  0.314  (0.047)  0.611  (0.034)  0.230  (0.048)
Si11 (0.047)  0.493  (0.043)  0.260  (0.049)  0.516  (0.041)  0.181  (0.049)
Na12 (0.040)  0.357  (0.043)  0.648  (0.036)  0.249  (0.045)  0.440  (0.045)
Na13 (0.042)  0.413  (0.045)  0.722  (0.031)  0.315  (0.047)  0.548  (0.041)
Si14 (0.048)  0.526  (0.040)  0.356  (0.046)  0.680  (0.033)  0.273  (0.049)
     Si10    se      Si11    se      Na12    se      Na13    se      Si14   
Si1   0.588  (0.039)  0.543  (0.040)  0.172  (0.048)  0.212  (0.052)  0.506 
Na2   0.156  (0.048)  0.129  (0.050)  0.532  (0.035)  0.493  (0.040)  0.104 
Si3   0.468  (0.042)  0.403  (0.044)  0.042  (0.047)  0.091  (0.052)  0.410 
Na4   0.242  (0.048)  0.225  (0.051)  0.616  (0.040)  0.725  (0.033)  0.337 
Na5   0.172  (0.046)  0.188  (0.047)  0.475  (0.040)  0.508  (0.042)  0.148 
Si6   0.551  (0.040)  0.493  (0.043)  0.357  (0.043)  0.413  (0.045)  0.526 
Na7   0.314  (0.047)  0.260  (0.049)  0.648  (0.036)  0.722  (0.031)  0.356 
Si8   0.611  (0.034)  0.516  (0.041)  0.249  (0.045)  0.315  (0.047)  0.680 
Na9   0.230  (0.048)  0.181  (0.049)  0.440  (0.045)  0.548  (0.041)  0.273 
Si10                  0.554  (0.038)  0.230  (0.046)  0.224  (0.048)  0.523 
Si11  0.554  (0.038)                  0.197  (0.046)  0.236  (0.053)  0.451 
Na12  0.230  (0.046)  0.197  (0.046)                  0.685  (0.031)  0.245 
Na13  0.224  (0.048)  0.236  (0.053)  0.685  (0.031)                  0.310 
Si14  0.523  (0.039)  0.451  (0.045)  0.245  (0.045)  0.310  (0.046)        
     se     
Si1  (0.041)
Na2  (0.049)
Si3  (0.044)
Na4  (0.047)
Na5  (0.048)
Si6  (0.040)
Na7  (0.046)
Si8  (0.033)
Na9  (0.049)
Si10 (0.039)
Si11 (0.045)
Na12 (0.045)
Na13 (0.046)
Si14        

$Hi
     Item H  se     
Si1    0.347 (0.026)
Na2    0.280 (0.028)
Si3    0.225 (0.029)
Na4    0.403 (0.026)
Na5    0.310 (0.027)
Si6    0.437 (0.024)
Na7    0.433 (0.024)
Si8    0.409 (0.024)
Na9    0.354 (0.026)
Si10   0.374 (0.024)
Si11   0.338 (0.026)
Na12   0.367 (0.024)
Na13   0.423 (0.024)
Si14   0.376 (0.024)

$H
Scale H      se 
  0.361 (0.018) 

Riguardo agli item NA, per coppie di item con una scalabilità di .41 < Hjk < .73 (con un errore standard, SE, compreso tra .03 e .05) e per singoli item con .49 < Hj < .62 (.02 < SE < .03), è stata evidenziata una forte coerenza nella scala (H = .55, SE = .02).

Per gli item SI, le coppie mostrano una scalabilità di .40 < Hjk < .67 (.03 < SE < .05), mentre i singoli item si attestano tra .45 < Hj < .57 (.02 < SE < .03).

La scala complessiva per gli item SI registra un H = .52 (SE = .02); tuttavia, l’ampiezza dell’errore standard impedisce di affermare con certezza che nella popolazione H sia maggiore di .5, suggerendo così una forza media della scala.

Per quanto riguarda i 14 item del DS14, è stato ottenuto un H = .36 (SE = .02), ma questi non formano una scala Mokken debole, dato che i coefficienti H2,3 e H3,5 risultano negativi, in violazione del criterio per la definizione di scala. Altri coefficienti di scalabilità per coppie di item non hanno mostrato significatività superiore a zero. Tenendo conto degli errori standard, i coefficienti di scalabilità per gli item H2, H5 e H11 superano significativamente il limite inferiore convenzionale di .3.

  1. Indipendenza locale. Investigare l’indipendenza locale utilizzando la procedura di associazione condizionale (Straat et al., in stampa). La procedura di associazione condizionale coinvolge due indici W1 e W3 che segnalano coppie di item dipendenti localmente.

# STEP 5: LOCAL INDEPENDENCE
# Results from CA procedure
check.ca(itemsScores[, Na], TRUE)
$InScale
    1. TRUE
    2. TRUE
    3. TRUE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
$Index
  1. $W1
    A matrix: 7 × 7 of type dbl
    Na2Na4Na5Na7Na9Na12Na13
    Na2 NA0.61796971.20666791.3798871.09183643.59959942.164015
    Na40.4210748 NA0.84148101.7531251.05501882.63994193.698480
    Na50.55068750.8513984 NA1.8830611.68987031.13053482.105468
    Na70.12197970.54475780.2169763 NA0.75273971.60904711.404433
    Na90.75671350.90766061.15584421.629162 NA0.22448191.904042
    Na120.84733970.62949610.29113381.8610600.8821990 NA2.135409
    Na130.12002160.34721910.23349701.1010580.32923021.9645768 NA
    $W2
    A matrix: 1 × 7 of type dbl
    46.0590439.5975143.6594436.3604544.0564436.0818939.60723
    $W3
    A matrix: 7 × 7 of type dbl
    Na2Na4Na5Na7Na9Na12Na13
    Na2 NA12.289372 3.24324710.058823 6.395469 3.91829910.153830
    Na412.289372 NA 9.886621 3.011686 7.617531 4.007542 2.784763
    Na5 3.243247 9.886621 NA 9.606688 2.424949 6.98806811.509870
    Na710.058823 3.011686 9.606688 NA 6.554529 4.415711 2.713013
    Na9 6.395469 7.617531 2.424949 6.554529 NA12.685237 8.378724
    Na12 3.918299 4.007542 6.988068 4.41571112.685237 NA 4.067033
    Na1310.153830 2.78476311.509870 2.713013 8.378724 4.067033 NA
$Flagged
  1. $F1
    A matrix: 7 × 7 of type dbl
    Na2Na4Na5Na7Na9Na12Na13
    Na20000000
    Na40000000
    Na50000000
    Na70000000
    Na90000000
    Na120000000
    Na130000000
    $F2
    A matrix: 1 × 7 of type dbl
    0000000
    $F3
    A matrix: 7 × 7 of type dbl
    Na2Na4Na5Na7Na9Na12Na13
    Na20000000
    Na40000000
    Na50000000
    Na70000000
    Na90000000
    Na120000000
    Na130000000
check.ca(itemsScores[, Si], TRUE)
$InScale
    1. TRUE
    2. TRUE
    3. TRUE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
    1. TRUE
    2. FALSE
    3. TRUE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
    1. TRUE
    2. FALSE
    3. TRUE
    4. TRUE
    5. TRUE
    6. TRUE
    7. FALSE
$Index
  1. $W1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NA0.610802750.132332000.38648780.32141380.390273500.2545415
    Si37.4940537 NA0.147883693.34043132.29405951.626892791.9854466
    Si63.23838930.02665348 NA3.01482243.07859041.699013402.0204872
    Si80.88870820.141691550.07253119 NA0.37751190.096349220.4288780
    Si101.59603510.086813540.132810540.8860611 NA0.830189180.2547350
    Si111.68891980.275933650.274920050.83758711.0178655 NA0.1092758
    Si141.56307120.162512260.537819902.55121661.36772660.16834674 NA
    $W2
    A matrix: 1 × 7 of type dbl
    39.5030945.6588845.3855234.3325137.1993942.1562140.21989
    $W3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NA 1.235175 6.8769408.9534526.1792797.3085608.949681
    Si31.235175 NA14.9536178.1532766.2687066.9726698.075439
    Si66.87694014.953617 NA3.8617047.0522176.7619275.879112
    Si88.953452 8.153276 3.861704 NA5.1551776.7992791.409627
    Si106.179279 6.268706 7.0522175.155177 NA5.4758737.068136
    Si117.308560 6.972669 6.7619276.7992795.475873 NA8.837899
    Si148.949681 8.075439 5.8791121.4096277.0681368.837899 NA
  2. $W1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NANA0.132332000.38648490.32140110.382464170.25232684
    Si3 NANA NA NA NA NA NA
    Si60.14118765NA NA0.61308081.11225100.445491430.26424484
    Si80.07884079NA0.06649432 NA0.25906590.061085220.25906970
    Si100.33580780NA0.124440400.7630631 NA0.617723740.21501398
    Si110.38493217NA0.259413310.68620650.8826178 NA0.09181554
    Si140.54030147NA0.419849981.88690841.29371280.05051468 NA
    $W2
    A matrix: 1 × 7 of type dbl
    20.21876NA24.3426718.7075422.293825.9312424.02858
    $W3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NANA4.9174334.0999432.7604073.5945244.846455
    Si3 NANA NA NA NA NA NA
    Si64.917433NA NA3.0228265.6922705.8357544.874390
    Si84.099943NA3.022826 NA4.3641696.0503611.170238
    Si102.760407NA5.6922704.364169 NA3.3950296.081922
    Si113.594524NA5.8357546.0503613.395029 NA7.055575
    Si144.846455NA4.8743901.1702386.0819227.055575 NA
  3. $W1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NANA0.047492830.100018910.27064520.36325565NA
    Si3 NANA NA NA NA NANA
    Si60.06539702NA NA0.255632750.32069860.43438917NA
    Si80.07880992NA0.06644315 NA0.25893590.06108031NA
    Si100.06804149NA0.013014360.04022932 NA0.59752476NA
    Si110.18821851NA0.035879700.166045950.4313432 NANA
    Si14 NANA NA NA NA NANA
    $W2
    A matrix: 1 × 7 of type dbl
    11.14005NA13.200449.15061411.4744612.69603NA
    $W3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 NANA3.5997362.1857172.6399042.714694NA
    Si3 NANA NA NA NA NANA
    Si63.599736NA NA1.3308154.8172933.452590NA
    Si82.185717NA1.330815 NA1.5613024.072780NA
    Si102.639904NA4.8172931.561302 NA2.455961NA
    Si112.714694NA3.4525904.0727802.455961 NANA
    Si14 NANA NA NA NA NANA
$Flagged
  1. $F1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si10000000
    Si31000000
    Si60000000
    Si80000000
    Si100000000
    Si110000000
    Si140000000
    $F2
    A matrix: 1 × 7 of type dbl
    0000000
    $F3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si10000000
    Si30010000
    Si60100000
    Si80000000
    Si100000000
    Si110000000
    Si140000000
  2. $F1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 0NA 0 0 0 0 0
    Si3NANANANANANANA
    Si6 0NA 0 0 0 0 0
    Si8 0NA 0 0 0 0 0
    Si10 0NA 0 0 0 0 0
    Si11 0NA 0 0 0 0 0
    Si14 0NA 0 1 0 0 0
    $F2
    A matrix: 1 × 7 of type dbl
    0NA00000
    $F3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 0NA 0 0 0 0 0
    Si3NANANANANANANA
    Si6 0NA 0 0 0 0 0
    Si8 0NA 0 0 0 0 0
    Si10 0NA 0 0 0 0 0
    Si11 0NA 0 0 0 0 0
    Si14 0NA 0 0 0 0 0
  3. $F1
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 0NA 0 0 0 0NA
    Si3NANANANANANANA
    Si6 0NA 0 0 0 0NA
    Si8 0NA 0 0 0 0NA
    Si10 0NA 0 0 0 0NA
    Si11 0NA 0 0 0 0NA
    Si14NANANANANANANA
    $F2
    A matrix: 1 × 7 of type dbl
    0NA0000NA
    $F3
    A matrix: 7 × 7 of type dbl
    Si1Si3Si6Si8Si10Si11Si14
    Si1 0NA 0 0 0 0NA
    Si3NANANANANANANA
    Si6 0NA 0 0 0 0NA
    Si8 0NA 0 0 0 0NA
    Si10 0NA 0 0 0 0NA
    Si11 0NA 0 0 0 0NA
    Si14NANANANANANANA
check.ca(itemsScores, TRUE)
$InScale
    1. TRUE
    2. TRUE
    3. TRUE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
    8. TRUE
    9. TRUE
    10. TRUE
    11. TRUE
    12. TRUE
    13. TRUE
    14. TRUE
    1. TRUE
    2. TRUE
    3. FALSE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
    8. TRUE
    9. TRUE
    10. TRUE
    11. TRUE
    12. TRUE
    13. TRUE
    14. TRUE
    1. FALSE
    2. TRUE
    3. FALSE
    4. TRUE
    5. TRUE
    6. TRUE
    7. TRUE
    8. TRUE
    9. TRUE
    10. TRUE
    11. TRUE
    12. TRUE
    13. TRUE
    14. TRUE
$Index
  1. $W1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 NA3.76567595.395036112.763969 5.39221522.2782313.8911018.465576 7.96706516.55115113.99093410.17001413.62174015.756574
    Na2 9.338788 NA3.133963416.35783113.14726317.6070519.8100514.05057715.86521013.16994412.45978221.20956020.67221312.380653
    Si331.4676958.3767345 NA16.654163 7.65440823.6454418.9342127.58042014.43288027.33803023.13323314.69445417.39752826.568026
    Na4 5.8496912.08942631.9303778 NA 3.34281713.9356011.92809 9.399139 5.810212 6.290490 6.446997 8.58362611.018004 8.642545
    Na510.0143769.05001662.969715816.619004 NA21.9028320.6184611.17209415.29691511.74634413.84489813.65001317.80503911.374531
    Si6 5.4092960.84886750.2330259 5.003882 2.895776 NA 6.80852 5.595272 6.359225 3.790967 3.408145 2.813723 7.055205 4.341929
    Na7 6.8069451.49468571.4407670 8.238079 1.90550111.80435 NA 8.795147 3.962045 7.965476 5.593104 8.210832 8.798303 8.797831
    Si8 6.8595122.31983551.5996206 9.563978 1.52046414.9669411.04066 NA 8.590548 5.904984 5.125885 5.524485 9.223541 7.712751
    Na9 7.8981934.66579592.092016211.162755 7.14769617.4986812.9441012.835822 NA 9.737938 7.423739 8.34790011.67263911.733514
    Si10 8.4653902.28607362.4677840 8.180382 3.33884614.9274813.2713312.138669 7.431532 NA 9.332409 7.344684 8.27297510.098650
    Si11 9.4803362.47538823.7213631 9.469153 6.39056815.6979311.2861010.091799 6.31945910.205066 NA 8.83074912.620963 8.874111
    Na12 9.6605314.47438721.303869011.187390 3.99747013.5637614.1618910.886371 6.534872 9.563710 8.738885 NA14.28005610.183019
    Na13 7.5562362.27303201.880182410.161251 2.78303512.0812412.7843310.008027 4.055762 6.292040 6.135067 7.821810 NA 8.712854
    Si1410.2613081.90782472.5234735 9.320444 2.52201412.3092911.6532113.136709 8.191802 8.646156 7.115753 7.669230 9.186305 NA
    $W2
    A matrix: 1 × 14 of type dbl
    199.7975209.1171222.4811196.5573208.3068171.5022184.1062183.4612201.4381196.0021208.553201.7752187.5183200.3439
    $W3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 NA23.583543 1.43990521.02518323.756321 7.99047623.449608 4.69019024.787752 4.642923 7.04389124.94311222.994205 9.450376
    Na223.583543 NA26.43685213.401040 5.59916117.72922410.27895820.919021 7.92997721.57615122.591901 5.733513 8.67914524.658609
    Si3 1.43990526.436852 NA23.00051728.97994614.35010124.146972 5.48149725.389764 8.066076 7.75407224.23761923.679720 9.518100
    Na421.02518313.40104023.000517 NA11.49167215.805479 5.78633721.039569 8.78980123.73477621.745469 6.876545 5.70417818.156704
    Na523.756321 5.59916128.97994611.491672 NA16.944251 8.57598523.184673 5.97776321.66007121.430096 8.312872 8.49845723.895494
    Si6 7.99047617.72922414.35010115.80547916.944251 NA15.115749 6.57014117.411380 7.376653 9.28840217.49721215.955490 9.467630
    Na723.44960810.27895824.146972 5.786337 8.57598515.115749 NA20.015148 7.33879621.78379920.889961 5.418474 3.98570617.320702
    Si8 4.69019020.919021 5.48149721.03956923.184673 6.57014120.015148 NA21.120330 4.503019 8.21748122.85717020.365858 4.497078
    Na924.787752 7.92997725.389764 8.789801 5.97776317.411380 7.33879621.120330 NA19.85248323.50662012.247466 7.80887719.277134
    Si10 4.64292321.576151 8.06607623.73477621.660071 7.37665321.783799 4.50301919.852483 NA 8.43482221.68105823.542237 9.148065
    Si11 7.04389122.591901 7.75407221.74546921.430096 9.28840220.889961 8.21748123.506620 8.434822 NA24.07427221.04596512.530008
    Na1224.943112 5.73351324.237619 6.876545 8.31287217.497212 5.41847422.85717012.24746621.68105824.074272 NA 5.36518222.530682
    Na1322.994205 8.67914523.679720 5.704178 8.49845715.955490 3.98570620.365858 7.80887723.54223721.045965 5.365182 NA19.893302
    Si14 9.45037624.658609 9.51810018.15670423.895494 9.46763017.320702 4.49707819.277134 9.14806512.53000822.53068219.893302 NA
  2. $W1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 NA3.7656759NA12.763803 5.39221122.27822713.89098218.465573 7.80811216.55113813.98312510.17001413.62076315.754359
    Na25.168384 NANA12.82494010.34617013.52523916.005403 9.63989112.308310 8.645005 8.41960517.10183817.080766 8.085127
    Si3 NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na42.9272591.2302787NA NA 2.51342511.102750 9.784654 6.507296 4.532399 3.582967 4.163946 7.334070 9.050631 5.468034
    Na56.1497006.2307747NA13.181291 NA17.41440116.366912 7.56530011.569358 7.454093 9.777547 9.71067814.526032 7.269407
    Si62.3120940.5199761NA 4.835524 2.579262 NA 6.038700 3.193530 4.973205 1.824628 2.154623 2.699062 6.212732 2.585687
    Na73.8689150.9290250NA 6.547796 1.342486 9.087505 NA 5.792234 3.062543 4.845919 3.281795 6.415142 6.926073 5.819706
    Si86.0496442.3196208NA 9.551355 1.51943414.96090510.981691 NA 8.423854 5.786538 5.090621 5.522902 9.166333 7.542943
    Na94.7629543.2093002NA 8.249070 5.81136513.67246610.287373 8.927097 NA 6.050103 4.225303 6.310433 9.102697 8.056472
    Si107.2051632.2859751NA 8.179009 3.31199914.91910813.11998712.015671 7.276035 NA 9.119943 7.336979 8.23807310.058929
    Si118.1763492.4752589NA 9.466454 6.36709215.68241911.217817 9.940419 6.25530410.069818 NA 8.82993912.611387 8.856651
    Na125.8380512.9750387NA 8.379742 2.84585610.91490811.385362 7.453634 4.717835 5.808480 5.693636 NA11.353235 6.892064
    Na134.4358541.4388142NA 8.081367 2.185438 9.17868810.547555 7.021736 2.926157 3.335403 3.574300 6.383381 NA 5.651557
    Si149.2385381.8945364NA 9.313604 2.51451912.19132511.63717612.472400 8.098654 8.572142 6.997921 7.667735 8.940731 NA
    $W2
    A matrix: 1 × 14 of type dbl
    183.4906181.9844NA165.8003180.8347150.7912164.063174.6936178.8568180.665190.4845171.4054154.802181.3141
    $W3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 NA23.780790NA19.53531622.963098 5.73167022.406986 5.53613923.920166 4.078907 6.20482822.23085220.088205 7.013683
    Na223.780790 NANA13.770937 6.82560016.44453710.38668322.431811 7.77043921.91045921.797842 5.995459 8.19003122.679833
    Si3 NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na419.53531613.770937NA NA11.37451815.656150 4.50870919.85559210.62830121.06965821.264498 8.063787 3.24903716.823782
    Na522.963098 6.825600NA11.374518 NA16.912847 8.92235224.230329 6.12524122.20827920.842778 6.581999 8.18995025.657758
    Si6 5.73167016.444537NA15.65615016.912847 NA17.411490 6.47286916.403934 6.207183 8.17307416.62378215.934809 8.818826
    Na722.40698610.386683NA 4.508709 8.92235217.411490 NA19.508576 8.68541820.63697222.486362 6.005155 4.35822818.746045
    Si8 5.53613922.431811NA19.85559224.230329 6.47286919.508576 NA19.775288 4.532032 6.86483822.76949618.754285 3.962326
    Na923.920166 7.770439NA10.628301 6.12524116.403934 8.68541819.775288 NA20.56754522.10259313.031775 9.47424820.371856
    Si10 4.07890721.910459NA21.06965822.208279 6.20718320.636972 4.53203220.567545 NA 6.79424222.41560822.100840 8.143277
    Si11 6.20482821.797842NA21.26449820.842778 8.17307422.486362 6.86483822.102593 6.794242 NA21.90841421.96616410.078817
    Na1222.230852 5.995459NA 8.063787 6.58199916.623782 6.00515522.76949613.03177522.41560821.908414 NA 4.62872121.150367
    Na1320.088205 8.190031NA 3.249037 8.18995015.934809 4.35822818.754285 9.47424822.10084021.966164 4.628721 NA17.867491
    Si14 7.01368322.679833NA16.82378225.657758 8.81882618.746045 3.96232620.371856 8.14327710.07881721.15036717.867491 NA
  3. $W1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na2NA NANA 9.9119028.045225 9.85255312.864620 6.3297069.953431 5.2933365.69591813.81101713.726837 5.303845
    Si3NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na4NA1.0436371NA NA2.019564 8.209863 8.334766 4.5677754.112617 2.0899802.688691 6.609983 7.594499 3.901180
    Na5NA4.8930832NA10.445484 NA13.71724813.370997 4.8441719.683839 4.6528356.974582 7.44289812.071869 4.792993
    Si6NA0.5155162NA 4.8274662.541566 NA 5.834359 3.1123164.730148 1.6484972.073000 2.697738 6.089226 2.472399
    Na7NA0.6202472NA 4.9351631.035004 6.047585 NA 3.6213322.568974 2.8001661.637648 4.890220 5.374256 3.911354
    Si8NA2.3195831NA 9.4297981.51897414.92725110.942139 NA7.777493 5.7598745.057029 5.522007 9.055772 7.425219
    Na9NA2.0479517NA 5.9654574.564073 9.582883 7.899129 5.621354 NA 3.1659501.952049 4.601055 6.809659 5.044614
    Si10NA2.2859736NA 8.1789333.29571714.91189113.11621412.0072437.141527 NA8.871903 7.335115 8.19365010.058164
    Si11NA2.4752299NA 9.4591876.27217715.67579811.195626 9.9300426.02230410.001968 NA 8.82992212.605660 8.836101
    Na12NA2.5223799NA 6.7087842.279759 8.563978 9.518220 4.9889424.177720 3.7655874.035683 NA 9.321894 5.050960
    Na13NA1.1490103NA 6.7069541.862815 6.775952 8.788081 4.8548212.503683 1.7243802.550900 5.746211 NA 3.735390
    Si14NA1.8703108NA 9.2772222.50996012.10648511.61749612.1859347.663806 8.5213866.978712 7.655978 8.744605 NA
    $W2
    A matrix: 1 × 14 of type dbl
    NA153.0343NA140.2051149.8509137.0658139.9683159.1131152.8541162.9803164.3808144.6456138.9441162.3001
    $W3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na2NA NANA13.368235 7.62887115.829520 9.99027420.042775 8.94783120.81367919.083393 4.915126 9.36911423.045519
    Si3NA NANA NA NA NA NA NA NA NA NA NA NA NA
    Na4NA13.368235NA NA11.81175016.171848 5.02009718.96938310.44775919.62739819.650382 6.201317 2.84371316.093198
    Na5NA 7.628871NA11.811750 NA13.79679210.65421321.916268 5.76597619.50901118.555753 7.74242510.25306122.216814
    Si6NA15.829520NA16.17184813.796792 NA14.896317 5.82550515.893522 5.468681 7.03474416.45794118.247187 7.443786
    Na7NA 9.990274NA 5.02009710.65421314.896317 NA20.044285 9.92365120.21843420.350933 6.509602 6.12755616.232976
    Si8NA20.042775NA18.96938321.916268 5.82550520.044285 NA18.308179 3.873418 5.96818221.51320220.190087 2.461829
    Na9NA 8.947831NA10.447759 5.76597615.893522 9.92365118.308179 NA19.68565720.74100315.384444 8.60459319.151466
    Si10NA20.813679NA19.62739819.509011 5.46868120.218434 3.87341819.685657 NA 4.71325820.62807520.186516 8.256204
    Si11NA19.083393NA19.65038218.555753 7.03474420.350933 5.96818220.741003 4.713258 NA19.61173220.571127 8.100257
    Na12NA 4.915126NA 6.201317 7.74242516.457941 6.50960221.51320215.38444420.62807519.611732 NA 4.46740421.214324
    Na13NA 9.369114NA 2.84371310.25306118.247187 6.12755620.190087 8.60459320.18651620.571127 4.467404 NA18.083776
    Si14NA23.045519NA16.09319822.216814 7.44378616.232976 2.46182919.151466 8.256204 8.10025721.21432418.083776 NA
$Flagged
  1. $F1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si100000000000000
    Na200000000000000
    Si310000001010001
    Na400000000000000
    Na500000000000000
    Si600000000000000
    Na700000000000000
    Si800000000000000
    Na900000000000000
    Si1000000000000000
    Si1100000000000000
    Na1200000000000000
    Na1300000000000000
    Si1400000000000000
    $F2
    A matrix: 1 × 14 of type dbl
    00000000000000
    $F3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si100000000000000
    Na200000000000000
    Si300000000000000
    Na400000000000000
    Na500000000000000
    Si600000000000000
    Na700000000000000
    Si800000000000000
    Na900000000000000
    Si1000000000000000
    Si1100000000000000
    Na1200000000000000
    Na1300000000000000
    Si1400000000000000
  2. $F1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 0 0NA 0 0 1 0 1 0 0 0 0 0 0
    Na2 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si3NANANANANANANANANANANANANANA
    Na4 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na5 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si6 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na7 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si8 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na9 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si10 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si11 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na12 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na13 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si14 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    $F2
    A matrix: 1 × 14 of type dbl
    00NA00000001000
    $F3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na2 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si3NANANANANANANANANANANANANANA
    Na4 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na5 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si6 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na7 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si8 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na9 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si10 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si11 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na12 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na13 0 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si14 0 0NA 0 0 0 0 0 0 0 0 0 0 0
  3. $F1
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1NANANANANANANANANANANANANANA
    Na2NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si3NANANANANANANANANANANANANANA
    Na4NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na5NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si6NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na7NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si8NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na9NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si10NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si11NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na12NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na13NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si14NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    $F2
    A matrix: 1 × 14 of type dbl
    NA0NA00000000000
    $F3
    A matrix: 14 × 14 of type dbl
    Si1Na2Si3Na4Na5Si6Na7Si8Na9Si10Si11Na12Na13Si14
    Si1NANANANANANANANANANANANANANA
    Na2NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si3NANANANANANANANANANANANANANA
    Na4NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na5NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si6NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na7NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si8NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na9NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si10NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si11NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na12NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Na13NA 0NA 0 0 0 0 0 0 0 0 0 0 0
    Si14NA 0NA 0 0 0 0 0 0 0 0 0 0 0

Per gli item NA, la procedura di associazione condizionata utilizzando gli indici W1 e W3 non ha evidenziato alcun item problematico.

Per gli item SI, un elevato indice W1 ha suggerito che gli item formulati negativamente 1 e 3 fossero dipendenti localmente in modo positivo. L’indice W3 ha segnalato la coppia di item (3, 6), suggerendo che questi item potrebbero essere dipendenti localmente in modo negativo.

In conformità con i passi 3 e 4, questo risultato ha suggerito che l’item 3 potrebbe essere rivisto. Senza l’item 3, l’indice W1 ha indicato le coppie di item (8, 14) e (10, 14) come dipendenti localmente in modo positivo. Per l’intero DS14, gli indici hanno identificato gli item 1 e 3 come dipendenti localmente in modo positivo, e presenti in diverse coppie di item dipendenti localmente in modo negativo con altri item. Senza gli item 1 e 3, i dati rimanenti non mostrano evidenze di dipendenza locale.

67.6. Step 6#

  1. Monotonicità. Investigare la monotonia delle funzioni di risposta agli item (IRF) usando un metodo di regressione non parametrico per un punteggio dell’item sul punteggio totale degli altri J-1 item nella stessa scala (Junker & Sijtsma, 2000; Sijtsma & Molenaar, 2002, 2016). L’analisi grafica fornisce un’indicazione del grado in cui una curva osservata può essere considerata monotona, e le deviazioni locali dalla monotonia possono essere testate per significatività statistica.

# Results from manifest monotonicity
resMonNa <- check.monotonicity(itemsScores[, Na])
resMonSi <- check.monotonicity(itemsScores[, Si])
resMonDs <- check.monotonicity(itemsScores)
summary(resMonNa)
A matrix: 7 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#aczmax#zsigcrit
Na20.48 8400.000.000.000.00000.000 0
Na40.5610710.010.040.040.00040.770-1
Na50.50 7910.010.050.050.00070.950 4
Na70.59 7820.030.070.100.00131.020 5
Na90.51 8640.050.080.230.00271.26017
Na120.56 7800.000.000.000.00000.000 0
Na130.62 5900.000.000.000.00000.000 0
summary(resMonSi)
A matrix: 7 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#aczmax#zsigcrit
Si10.5710800.000.000.000.00000.000 0
Si30.4511250.040.080.240.00210.91018
Si60.4910380.080.070.450.00441.76139
Si80.57 8910.010.040.040.00050.920-1
Si100.55 9600.000.000.000.00000.000 0
Si110.49 9760.060.090.380.00401.53026
Si140.52 8930.030.040.100.00121.130 8
summary(resMonDs)
A matrix: 14 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#aczmax#zsigcrit
Si10.35 95 00.000.000.000.00000.000 0
Na20.28144 60.040.140.480.00341.97152
Si30.22112 60.050.070.290.00261.16032
Na40.40 96 10.010.090.090.00090.91013
Na50.31112 30.030.050.130.00120.92018
Si60.44118 60.050.040.250.00211.00017
Na70.43 95110.120.070.410.00431.51033
Si80.41 91 50.050.080.220.00241.06022
Na90.35 83 50.060.050.250.00311.40026
Si100.37129 30.020.100.190.00140.96021
Si110.34131 30.020.080.190.00151.73135
Na120.37105 20.020.060.090.00090.62012
Na130.42 97 10.010.030.030.00030.330 2
Si140.38 90 00.000.000.000.00000.000 0
plot(resMonSi, items = 3, curve = "IRF")
../_images/c3c495f50f96e2194356f360986d59f9411f9738fbbde48f47d22b8e8c5bc914.png
plot(resMonDs, items = 2, curve = "IRF")
../_images/658452e0a9e7eba199f63e2be3901b34cd6990f99189a87c295a18f927a4fef4.png
plot(resMonDs, items = 11, curve = "IRF")
../_images/551abf35e6efbe3bc2deeae1c69817b1a20becad8598926b423c94502d5a0d44.png

Nel caso di NA, l’analisi dei dati ha supportato la monotonia manifesta. Per quanto riguarda SI, un ISRF dell’elemento 6 ha mostrato una significativa diminuzione, ma l’item response function (IRF) risultante non è stato influenzato. Per l’intero DS14, i ISRF degli item 2 e 11 hanno mostrato una significativa diminuzione, ma l’effetto sull’IRF è stato minimo.

67.7. Step 7#

  1. Ordinamento invariante degli item. L’IIO sostiene che l’ordine degli item, basato sulla difficoltà o sulla probabilità di una risposta positiva, dovrebbe rimanere costante indipendentemente dal gruppo di soggetti considerato. Ciò significa che, se un item è generalmente più difficile di un altro in un sottogruppo di soggetti, dovrebbe rimanere più difficile in tutti i sottogruppi.

Per NA, SI e gli item DS14, l’ispezione visiva ha suggerito che diverse IRF fossero quasi identiche, rendendo quindi difficile stabilire un ordinamento degli item invariante. Il metodo più rigoroso per indagare sull’ordinamento degli item invariante (chiamato aumento in trasposizione; Ligtvoet, Van der Ark, Bergsma e Sijtsma, 2011) ha suggerito che solo quattro dei 14 item (NA: 4, 13; SI: 10, 14) non mostrano segni di violazione dell’ordinamento degli item invariante.

# Results from manifest IIO
resIioNa <- check.iio(itemsScores[, Na])
resIioSi <- check.iio(itemsScores[, Si])
resIioDs <- check.iio(itemsScores)
summary(resIioNa)
$method
'MIIO'
$item.summary
A matrix: 7 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#actmax#tsigcrit
Na20.483620.060.240.460.01281.952 70
Na120.563530.090.240.590.01681.952 74
Na50.503610.030.130.130.00360.750 17
Na70.593640.110.160.600.01672.532 71
Na90.523650.140.361.110.03093.133124
Na40.563630.080.280.580.01622.363 86
Na130.623520.060.360.540.01543.132 85
$backward.selection
A matrix: 7 × 4 of type dbl
step 1step 2step 3step 4
Na21 1 1NA
Na121 1 1 0
Na50 0 0 0
Na72 1 0 0
Na93NANANA
Na43 2NANA
Na132 1 0 0
$HT
0.438472566753628
summary(resIioSi)
$method
'MIIO'
$item.summary
A matrix: 7 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#actmax#tsigcrit
Si30.453700.000.000.000.00000.000 0
Si110.493620.060.320.490.01362.95284
Si100.553720.050.320.460.01242.95172
Si10.573820.050.240.400.01061.61042
Si80.573740.110.260.730.01961.76174
Si60.493630.080.260.640.01781.61060
Si140.523710.030.130.130.00361.12018
$backward.selection
A matrix: 7 × 2 of type dbl
step 1step 2
Si30 0
Si112NA
Si101 0
Si10 0
Si81 0
Si60 0
Si140 0
$HT
0.121036422377558
summary(resIioDs)
$method
'MIIO'
$item.summary
A matrix: 14 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#actmax#tsigcrit
Na20.2893 40.040.351.060.01142.251 86
Na120.3794 70.070.582.050.02182.893135
Si30.2296 70.070.582.050.02142.892137
Na50.3193 50.050.251.080.01161.140 60
Si110.3496 40.040.240.790.00821.610 53
Si100.3791 20.020.230.360.00401.610 40
Si10.3595 50.050.391.270.01332.932 99
Si80.4194 40.040.290.870.00932.232 75
Si60.4496 80.080.391.710.01782.932105
Si140.3893 60.060.301.190.01282.252 85
Na70.4396 80.080.401.870.01952.924116
Na90.3597100.100.401.920.01982.493116
Na40.4096 60.060.281.240.01302.924 94
Na130.4294 40.040.280.740.00791.941 64
$backward.selection
A matrix: 14 × 6 of type dbl
step 1step 2step 3step 4step 5step 6
Na21 1 0 0 0 0
Na122 2NANANANA
Si31 1 0 0 0 0
Na50 0 0 0 0 0
Si110 0 0 0 0 0
Si100 0 0 0 0 0
Si12 2 2NANANA
Si82 2 2 1 0 0
Si62 2 2 1 0 0
Si142 2 2 2NANA
Na72 1 1 1 1 0
Na92 1 1 1 1NA
Na43NANANANANA
Na131 0 0 0 0 0
$HT
0.155631246942616
# visual inspection
plot(resIioNa)
../_images/df3f96480224b6c8e4485aaec8b81a3d43ff0d7f738e06e4777ea6d86c83e2dc.png ../_images/30ae753f781de62d75ea44b589f4647ccd6abac496c1390f2c1cc1a30cda719b.png ../_images/4a56ddf13608d47233630be5abb37faf67e7c83065d0f3c19c6e1a53a661f36e.png ../_images/d3f53d84c22b45652aac53d33ab3ce30fa94eb571d9d9db23edbff6e3d4af0ce.png ../_images/77f394a6ca280a46d4e2a3760dff00d3d1828f3c759c0cbf0df62bc91a0b6511.png ../_images/f852f438e49bcf0471781b198b16e3e80619634c3246146873449addc395ee22.png ../_images/0cfdd1c6b9eceb19fb6c475504b144265241c8688d58604d26e1c7984efccc26.png ../_images/ddd03c7cdce859e6f0648d931d1f2b8802b5944aa9888302c1c9525eca24d195.png ../_images/2bcf6bc30daaa5de4f4d22651fcda8ccacbaf923169c7ae2126bf3a9e0b4f16f.png ../_images/12a7849df2a7e9c97192bffc134e58f753ba6aca9c8e67b2a5f9335a506788d8.png ../_images/8e7157f522c5d636a9ff90496887614ee82876fdff184c88f3c9a5801fce938a.png ../_images/a81a6fcfe84d773a63987076833a6198eb726308d6f531581a72ecd7bf18707c.png ../_images/26cc818e2214794c5b2bd5abc94153952e1452fede470cc09f1aac8f21f9ab5b.png ../_images/3c5f01cbe1ee11d9d4e8455656de2816484cc76dd2d647d25edfd72fe3b61af9.png ../_images/32b5fa4825d3db2903cc8f0215a2e67ad7b973cf4948fd925f85aa92fc338639.png ../_images/e8a3ad1fc95e96124ddfbcead8bbf5f4309aa195de74154beee14eb58652a1c2.png ../_images/2c72aaa9ec3c11c733c15afc926da891084e399653441e05e5e1b3724a093a85.png ../_images/c027473d6ed16493d636851a4b8c7e25da4cb450c3bac9a346607d1266e6edb8.png ../_images/cbcdc262a969d0073a4d8193b9c9b3b9efd8906614bf4cc99479fe5392b99ffb.png ../_images/61d013766cb28424c47ece808c84b0232d1f7fe21e11f7d4d804d9308fcaaa33.png ../_images/b71f4316b9f4623ae9abd4362d0521849ddc08667853ad9f8c1a69b39c20f183.png
plot(resIioSi)
../_images/33635663769f3fc164c39e72259286b925a5df7e82c63369b3f2a7edcd989c41.png ../_images/6ebfc6b6bc4ea03ef732e14c86d67d50c1f81474cc1540b3a58a2625fc3cfe08.png ../_images/92a4c41eba42f7872ea7bac5b507a2d2560b07d2f0cdc844a75d65f1cede47e3.png ../_images/931512a83c3fc22818228feaf02531b8e72bc3f98299eaa670916c8ecfa5c622.png ../_images/15eeee07b16930cf8aa537efb555686dcb92b376bf4673dc93e41b502072cc6d.png ../_images/58413c37760b1fb8d9f0ee0e628fb803d05b2be4253538d3a90e70d0a1b18477.png ../_images/47be33ef2a49c55aa19ec3e404f3f5fc7d9f498d1a8e205663511ea6f936aef6.png ../_images/ddb5d69bf9c0efe475eedd59b459df087565fb15cd4a3896c9344e96b59b0d51.png ../_images/2b26f99f493e68aa49ad8246af0672db233c268882a47492f45ec13e0afc293d.png ../_images/3907f33af2e9b3f59f1a0f37a046d135c109923413bdcb12a735d9b54dfc9b58.png ../_images/21dba8862bad50e88161aca7215ee3891efe24c9dc555f4efb588ff20c00aa79.png ../_images/95e1f2b1cf20ea3006a19758796f627ef9674effe4bdf31dbed08285b8ecec86.png ../_images/46b43ce68d3621b9aec5c0e99095598896f2d872868f5bca1514774f5c49d472.png ../_images/b8d960e4bf106d74ad15027d30f08ed279a2269f4d21f97a3f569e58ba719845.png ../_images/56c39d583caf6e4f1c7dd0db4ff0683b64fc115057f3d39796894f07d1076bd8.png ../_images/55887614e4182ba2bb40ea6e69112ac9fb91af1c81c600a46af11e0e94c97f01.png ../_images/8e3888511ff53cf058a25012b3307e0b2f86455edc8c0b00e5ff55cceba4b62e.png ../_images/fcbb0aeb93ce12fc5b4fcc096c288fe0ec6dc39c722bd6f22815b8f7b2be29f2.png ../_images/c8ac21a571b2b421e9a55c994dd3654047ae0f9fcfab46c708cdf9f7f67de9e4.png ../_images/6cc4f3e1ac6d28bdd11355c95120d97bc2657082fefec93931ab22e23315fb6d.png ../_images/8297e994ee8bbd6190e32290a5feb42bca93c3ea52feb5f5e86b2b4f89f1da45.png
# Results from Method IT
resIioDsIt <- check.iio(itemsScores, method = "IT")
summary(resIioDsIt)
$method
'IT'
$item.summary
A matrix: 14 × 10 of type dbl
ItemH#ac#vi#vi/#acmaxvisumsum/#acxmax#xsigcrit
Na20.28930670.070.103.280.00355.00 5 95
Na120.37940680.070.143.920.00427.0010117
Si30.22960650.070.143.440.00367.12 9120
Na50.31930720.080.123.870.00426.00 6106
Si110.34960690.070.143.780.00397.00 9116
Si100.37910840.090.114.120.00457.1212122
Si10.35950650.070.103.370.00356.00 8103
Si80.41940600.060.163.240.00346.00 6101
Si60.44960690.070.143.630.00387.1411115
Si140.38930560.060.132.870.00316.40 6 99
Na70.43960620.060.173.120.00327.14 5104
Na90.35970520.050.173.110.00329.00 9123
Na40.40960380.040.141.780.00189.00 2 93
Na130.42940370.040.091.500.00164.00 2 61
$backward.selection
A matrix: 14 × 10 of type dbl
step 1step 2step 3step 4step 5step 6step 7step 8step 9step 10
Na24 4 4 4 3NANANANANA
Na127 6 5 5NANANANANANA
Si34 4 4 3 2 1 1 1NANA
Na56 6 5NANANANANANANA
Si115 5 5 4 3 2 2NANANA
Si107 6 5 4 3 3 2 1 0 0
Si15 4 3 2 2 2 1 1 1NA
Si84 3 2 2 2 2 2 1 1 0
Si69 8NANANANANANANANA
Si145 4 3 2 1 1 0 0 0 0
Na75 4 3 3 3 3NANANANA
Na99NANANANANANANANANA
Na42 1 0 0 0 0 0 0 0 0
Na132 1 1 1 1 0 0 0 0 0
$HT
0.121597784660984

iii. Proprietà della scala. Determinare le proprietà della scala delle scale identificate nella seconda fase (passi 8–10).

67.8. Step 8#

  1. Affidabilità. Utilizzare il metodo Molenaar–Sijtsma (MS) (Sijtsma & Molenaar, 1987) per stimare l’affidabilità del punteggio del test. Il metodo MS assume il modello di doppia monotonia.

# STEP 8: RELIABILITY
check.reliability(itemsScores[, Na], irc = TRUE)
check.reliability(itemsScores[, Si], irc = TRUE)
check.reliability(itemsScores, irc = TRUE)
check.reliability(itemsScores[, -3])
$MS
0.883119159334185
$alpha
0.873083318798202
$lambda.2
0.875456228510461
$irc
  1. 0.561109330803049
  2. 0.672666349202855
  3. 0.59796006308463
  4. 0.720428543936926
  5. 0.62034425728731
  6. 0.673226022236864
  7. 0.745593733797823
$MS
0.870585822377467
$alpha
0.870525714715513
$lambda.2
0.873002304002601
$irc
  1. 0.719531318297224
  2. 0.53754980794435
  3. 0.616373529957479
  4. 0.732414321605589
  5. 0.689086278309901
  6. 0.595592592863512
  7. 0.645843416546044
$MS
0.881483548710253
$alpha
0.874670545530637
$lambda.2
0.883217093565466
$irc
  1. 0.521684456004778
  2. 0.408601876069594
  3. 0.327122024723764
  4. 0.5960367816755
  5. 0.45848610474584
  6. 0.669154194901804
  7. 0.646226455219469
  8. 0.623158664363801
  9. 0.524777674924687
  10. 0.566485040801581
  11. 0.496087120703027
  12. 0.549426117441985
  13. 0.622125970215216
  14. 0.568115691718221
$MS
0.892032690253982
$alpha
0.877185217828487
$lambda.2
0.884159430531047

Tutte le stime sono molto alte e quindi soddisfacenti.

67.9. Step 9.#

  1. Norme.

Nell’ambito della verifica delle scale Mokken, i ricercatori possono necessitare di tabelle normative per effettuare misurazioni accurate sugli individui. Una soluzione proposta da Oosterhuis, Van der Ark, e Sijtsma (2016) prevede l’utilizzo di una procedura di regressione per stimare le norme e gli intervalli di confidenza relativi a queste norme. Questo metodo consente di avere riferimenti quantitativi chiari e basati sulla statistica per valutare i risultati dei test in un contesto normativo.

Nel contesto della ricerca scientifica, tuttavia, l’uso di norme per interpretare le prestazioni ai test può non essere necessario. In questi casi, la fase di stima delle norme può essere omessa. Questo approccio è particolarmente utile quando l’obiettivo della ricerca è esplorare relazioni teoriche o costrutti piuttosto che valutare le performance individuali rispetto a un gruppo normativo. La decisione di includere o escludere la stima delle norme dipenderà quindi dagli obiettivi specifici dello studio e dal contesto in cui il test viene applicato.

# STEP 9: NORMS
check.norms(xPlusNa[male == 1])$perc
check.norms(xPlusNa[male == 0])$perc
check.norms(xPlusSi[male == 1])$perc
check.norms(xPlusSi[male == 0])$perc
check.norms(xPlus[male == 1])$perc
check.norms(xPlus[male == 0])$perc
   Percentiles SE      lo      up     
0    2.854     (0.533)   1.809   3.900
1    7.822     (1.141)   5.587  10.058
2   14.376     (1.461)  11.514  17.239
3   22.199     (1.815)  18.642  25.756
4   28.224     (2.001)  24.302  32.146
5   34.461     (2.096)  30.352  38.570
6   41.226     (2.188)  36.938  45.515
7   46.934     (2.235)  42.553  51.316
8   51.586     (2.249)  47.178  55.993
9   55.497     (2.243)  51.100  59.893
10  60.465     (2.172)  56.208  64.723
11  66.068     (2.117)  61.918  70.217
12  70.930     (2.025)  66.960  74.900
13  75.053     (1.944)  71.242  78.863
14  78.647     (1.830)  75.060  82.234
15  82.241     (1.706)  78.898  85.584
16  85.412     (1.574)  82.327  88.497
17  88.055     (1.449)  85.214  90.896
18  90.592     (1.287)  88.069  93.115
19  93.129     (1.109)  90.955  95.303
20  95.137     (0.943)  93.290  96.985
21  96.300     (0.848)  94.637  97.963
22  97.252     (0.706)  95.868  98.635
23  98.309     (0.554)  97.223  99.394
24  98.943     (0.446)  98.069  99.817
25  99.471     (0.279)  98.925 100.018
28  99.894     (0.106)  99.687 100.101
   Percentiles SE      lo      up     
0    2.206     (1.245)  -0.235   4.646
1    5.147     (2.577)   0.097  10.197
2    6.618     (2.924)   0.887  12.348
4    9.559     (3.330)   3.031  16.086
5   14.706     (4.035)   6.797  22.615
6   21.324     (4.687)  12.137  30.510
7   31.618     (5.189)  21.446  41.789
8   39.706     (5.842)  28.256  51.156
9   43.382     (5.874)  31.870  54.895
10  48.529     (5.880)  37.005  60.054
11  52.941     (5.963)  41.254  64.628
12  55.147     (5.986)  43.414  66.880
13  60.294     (5.654)  49.213  71.375
14  66.912     (5.562)  56.010  77.813
15  71.324     (5.334)  60.868  81.779
16  77.206     (4.814)  67.770  86.642
17  81.618     (4.639)  72.525  90.711
18  83.824     (4.343)  75.312  92.335
19  86.029     (4.139)  77.916  94.143
20  88.235     (3.766)  80.854  95.617
21  90.441     (3.489)  83.603  97.280
23  91.912     (3.224)  85.593  98.230
24  93.382     (2.924)  87.652  99.113
25  94.853     (2.577)  89.803  99.903
26  97.059     (1.765)  93.599 100.519
27  99.265     (0.730)  97.834 100.695
   Percentiles SE      lo      up     
0    2.854     (0.533)   1.809   3.900
1    7.188     (1.120)   4.993   9.383
2   10.359     (1.336)   7.741  12.978
3   15.433     (1.550)  12.396  18.471
4   21.776     (1.813)  18.222  25.330
5   27.801     (1.980)  23.921  31.682
6   33.298     (2.107)  29.169  37.427
7   38.372     (2.173)  34.114  42.630
8   43.129     (2.228)  38.763  47.495
9   47.569     (2.242)  43.174  51.963
10  52.537     (2.234)  48.158  56.916
11  57.611     (2.215)  53.270  61.952
12  62.896     (2.152)  58.678  67.115
13  67.759     (2.099)  63.645  71.873
14  72.410     (1.986)  68.518  76.303
15  77.061     (1.877)  73.381  80.741
16  81.395     (1.719)  78.026  84.765
17  85.201     (1.584)  82.096  88.306
18  88.372     (1.412)  85.605  91.140
19  91.543     (1.217)  89.159  93.928
20  93.658     (1.090)  91.520  95.795
21  95.032     (0.959)  93.152  96.912
22  95.983     (0.890)  94.238  97.728
23  97.146     (0.697)  95.780  98.512
24  98.414     (0.544)  97.347  99.481
25  98.837     (0.481)  97.894  99.781
26  99.260     (0.349)  98.576  99.944
27  99.789     (0.149)  99.496 100.081
   Percentiles SE      lo      up     
0    1.471     (1.024)  -0.537   3.479
1    5.882     (2.445)   1.090  10.675
2   11.029     (3.579)   4.015  18.044
3   15.441     (4.193)   7.223  23.659
4   23.529     (4.705)  14.308  32.751
5   33.088     (5.464)  22.379  43.798
6   38.971     (5.775)  27.651  50.290
7   44.118     (5.839)  32.673  55.562
8   50.000     (5.882)  38.471  61.529
9   54.412     (5.950)  42.751  66.073
10  58.824     (5.784)  47.486  70.161
11  63.235     (5.754)  51.958  74.513
12  66.912     (5.562)  56.010  77.813
13  74.265     (4.932)  64.599  83.931
14  81.618     (4.521)  72.756  90.479
16  86.029     (4.007)  78.176  93.882
17  89.706     (3.535)  82.777  96.635
18  91.912     (3.224)  85.593  98.230
20  93.382     (2.924)  87.652  99.113
21  94.853     (2.577)  89.803  99.903
24  96.324     (2.160)  92.089 100.558
26  98.529     (1.024)  96.521 100.537
   Percentiles SE      lo      up     
0    0.634     (0.257)   0.130   1.139
1    1.480     (0.535)   0.432   2.528
2    2.326     (0.643)   1.066   3.585
3    4.017     (0.839)   2.373   5.661
4    5.920     (1.043)   3.875   7.964
5    8.140     (1.198)   5.791  10.488
6   10.677     (1.376)   7.980  13.373
7   13.742     (1.518)  10.766  16.718
8   17.548     (1.690)  14.234  20.861
9   20.613     (1.827)  17.033  24.193
10  23.784     (1.903)  20.055  27.514
11  27.061     (2.010)  23.122  31.000
12  30.444     (2.062)  26.402  34.486
13  34.144     (2.142)  29.946  38.341
14  36.998     (2.190)  32.706  41.289
15  40.592     (2.203)  36.274  44.910
16  44.186     (2.254)  39.768  48.604
17  47.357     (2.252)  42.944  51.770
18  51.586     (2.244)  47.188  55.983
19  55.497     (2.248)  51.091  59.903
20  58.774     (2.223)  54.416  63.132
21  61.839     (2.201)  57.526  66.153
22  64.799     (2.157)  60.570  69.028
23  67.442     (2.128)  63.270  71.614
24  69.979     (2.070)  65.922  74.036
25  72.622     (2.020)  68.662  76.581
26  75.159     (1.950)  71.337  78.980
27  77.167     (1.913)  73.418  80.916
28  79.810     (1.787)  76.307  83.313
29  82.770     (1.707)  79.423  86.116
30  85.095     (1.593)  81.974  88.217
31  87.209     (1.510)  84.250  90.169
32  88.584     (1.439)  85.763  91.404
33  90.063     (1.343)  87.432  92.695
34  91.966     (1.204)  89.606  94.327
35  93.446     (1.118)  91.255  95.638
36  94.503     (1.015)  92.513  96.494
37  95.243     (0.973)  93.336  97.150
38  95.877     (0.883)  94.147  97.608
39  96.829     (0.777)  95.305  98.353
40  97.569     (0.684)  96.228  98.910
41  98.097     (0.610)  96.901  99.293
43  98.414     (0.565)  97.308  99.521
44  98.732     (0.492)  97.766  99.697
45  99.154     (0.394)  98.383  99.926
48  99.471     (0.316)  98.852 100.091
51  99.789     (0.149)  99.496 100.081
   Percentiles SE      lo      up     
4    2.206     (1.245)  -0.235   4.646
5    5.147     (2.577)   0.097  10.197
6    6.618     (2.924)   0.887  12.348
7    8.824     (3.279)   2.397  15.250
8   12.500     (3.803)   5.046  19.954
9   16.176     (4.343)   7.665  24.688
10  20.588     (4.678)  11.420  29.756
11  24.265     (5.146)  14.178  34.351
12  25.735     (5.250)  15.445  36.026
13  28.676     (5.334)  18.221  39.132
14  31.618     (5.591)  20.660  42.575
15  33.824     (5.642)  22.765  44.882
16  38.235     (5.707)  27.050  49.420
17  41.912     (5.938)  30.273  53.551
18  44.118     (5.931)  32.493  55.742
20  47.059     (5.963)  35.372  58.746
21  52.206     (5.830)  40.779  63.633
22  58.088     (5.846)  46.629  69.547
23  61.765     (5.801)  50.395  73.134
24  63.971     (5.775)  52.651  75.290
25  66.912     (5.562)  56.010  77.813
26  71.324     (5.334)  60.868  81.779
28  74.265     (5.250)  63.974  84.555
29  76.471     (5.038)  66.597  86.345
30  79.412     (4.792)  70.020  88.804
31  81.618     (4.639)  72.525  90.711
32  84.559     (4.193)  76.341  92.777
33  88.235     (3.766)  80.854  95.617
35  90.441     (3.489)  83.603  97.280
36  91.912     (3.224)  85.593  98.230
37  93.382     (2.924)  87.652  99.113
39  94.853     (2.577)  89.803  99.903
41  96.324     (2.160)  92.089 100.558
42  97.794     (1.622)  94.614 100.974
49  99.265     (0.730)  97.834 100.695
# STEP 10: GROUP COMPARISON
coefH(itemsScores[, Na], group.var = male)
coefH(itemsScores[, Si], group.var = male)
coefH(itemsScores[, ], group.var = male)
$Hij
     Na2     se      Na4     se      Na5     se      Na7     se      Na9    
Na2                   0.391  (0.048)  0.522  (0.039)  0.465  (0.045)  0.468 
Na4   0.391  (0.048)                  0.439  (0.047)  0.661  (0.039)  0.503 
Na5   0.522  (0.039)  0.439  (0.047)                  0.499  (0.040)  0.581 
Na7   0.465  (0.045)  0.661  (0.039)  0.499  (0.040)                  0.555 
Na9   0.468  (0.045)  0.503  (0.045)  0.581  (0.038)  0.555  (0.043)        
Na12  0.532  (0.035)  0.616  (0.040)  0.475  (0.040)  0.648  (0.036)  0.440 
Na13  0.493  (0.040)  0.725  (0.033)  0.508  (0.042)  0.722  (0.031)  0.548 
     se      Na12    se      Na13    se     
Na2  (0.045)  0.532  (0.035)  0.493  (0.040)
Na4  (0.045)  0.616  (0.040)  0.725  (0.033)
Na5  (0.038)  0.475  (0.040)  0.508  (0.042)
Na7  (0.043)  0.648  (0.036)  0.722  (0.031)
Na9           0.440  (0.045)  0.548  (0.041)
Na12 (0.045)                  0.685  (0.031)
Na13 (0.041)  0.685  (0.031)                

$Hi
     Item H  se     
Na2    0.483 (0.028)
Na4    0.557 (0.030)
Na5    0.503 (0.028)
Na7    0.591 (0.026)
Na9    0.515 (0.029)
Na12   0.562 (0.025)
Na13   0.616 (0.024)

$H
Scale H      se 
  0.546 (0.022) 

$covHij
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 0.0022989144 3.556849e-04 0.0010052778 0.0007801401 5.414757e-04
 [2,] 0.0003556849 1.522519e-03 0.0004450386 0.0007497889 3.237255e-04
 [3,] 0.0010052778 4.450386e-04 0.0020145721 0.0008348416 6.037465e-04
 [4,] 0.0007801401 7.497889e-04 0.0008348416 0.0020011917 2.133779e-04
 [5,] 0.0005414757 3.237255e-04 0.0006037465 0.0002133779 1.252743e-03
 [6,] 0.0010327520 4.223827e-04 0.0009859993 0.0007096234 5.688558e-04
 [7,] 0.0009265585 2.924636e-04 0.0005067649 0.0001641998 1.687561e-04
 [8,] 0.0005798666 2.057109e-04 0.0003789838 0.0004366579 2.382688e-05
 [9,] 0.0006313731 2.724419e-05 0.0005297773 0.0003579973 2.259319e-04
[10,] 0.0011515255 1.166517e-04 0.0002853404 0.0004386392 1.252333e-04
[11,] 0.0006354989 1.030805e-04 0.0002116375 0.0002939252 3.066150e-06
[12,] 0.0004848910 4.089064e-04 0.0007576294 0.0003694439 2.548367e-04
[13,] 0.0001304570 3.282199e-04 0.0002764868 0.0006001385 1.110339e-04
[14,] 0.0003022050 6.120800e-04 0.0003822614 0.0004062380 5.161931e-04
[15,] 0.0004406155 4.664556e-04 0.0003028667 0.0003416939 2.205691e-04
[16,] 0.0005615340 2.062509e-04 0.0005319594 0.0004577893 1.855316e-04
[17,] 0.0002657088 1.385843e-04 0.0007070134 0.0003594403 1.705285e-04
[18,] 0.0002539180 2.503942e-05 0.0003831389 0.0001757285 1.111084e-04
[19,] 0.0005975976 3.847111e-04 0.0005597349 0.0009951346 3.942800e-04
[20,] 0.0005391523 2.356209e-04 0.0004123386 0.0006353813 2.340805e-04
[21,] 0.0002714302 1.195848e-04 0.0003704439 0.0002956231 2.230986e-04
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 0.0010327520 0.0009265585 5.798666e-04 6.313731e-04 0.0011515255
 [2,] 0.0004223827 0.0002924636 2.057109e-04 2.724419e-05 0.0001166517
 [3,] 0.0009859993 0.0005067649 3.789838e-04 5.297773e-04 0.0002853404
 [4,] 0.0007096234 0.0001641998 4.366579e-04 3.579973e-04 0.0004386392
 [5,] 0.0005688558 0.0001687561 2.382688e-05 2.259319e-04 0.0001252333
 [6,] 0.0015846387 0.0003935561 1.920062e-04 3.838401e-04 0.0002211614
 [7,] 0.0003935561 0.0021757415 6.996295e-04 1.169290e-03 0.0006095637
 [8,] 0.0001920062 0.0006996295 1.498185e-03 6.613515e-04 0.0007660527
 [9,] 0.0003838401 0.0011692901 6.613515e-04 2.069302e-03 0.0004557181
[10,] 0.0002211614 0.0006095637 7.660527e-04 4.557181e-04 0.0015846511
[11,] 0.0001713933 0.0005058242 7.652694e-04 5.736487e-04 0.0007183495
[12,] 0.0002827819 0.0008792980 3.867651e-04 5.449631e-04 0.0003061978
[13,] 0.0002354823 0.0006316330 2.183373e-04 3.339671e-04 0.0001292073
[14,] 0.0003047019 0.0007142048 2.929320e-04 3.818841e-04 0.0003075222
[15,] 0.0006623985 0.0010685493 3.329102e-04 5.349169e-04 0.0001767506
[16,] 0.0003197038 0.0005806718 5.702923e-04 8.745371e-04 0.0003711308
[17,] 0.0003423557 0.0003033842 4.373767e-04 3.304571e-04 0.0005130346
[18,] 0.0003252324 0.0003000955 5.448684e-04 3.037242e-04 0.0002086832
[19,] 0.0004934985 0.0004892996 4.631575e-04 7.818722e-04 0.0006107260
[20,] 0.0005399889 0.0005728860 4.015112e-04 1.064776e-03 0.0003366808
[21,] 0.0005161993 0.0001559809 2.597643e-04 2.100049e-04 0.0005114014
             [,11]        [,12]        [,13]        [,14]        [,15]
 [1,] 6.354989e-04 4.848910e-04 0.0001304570 3.022050e-04 4.406155e-04
 [2,] 1.030805e-04 4.089064e-04 0.0003282199 6.120800e-04 4.664556e-04
 [3,] 2.116375e-04 7.576294e-04 0.0002764868 3.822614e-04 3.028667e-04
 [4,] 2.939252e-04 3.694439e-04 0.0006001385 4.062380e-04 3.416939e-04
 [5,] 3.066150e-06 2.548367e-04 0.0001110339 5.161931e-04 2.205691e-04
 [6,] 1.713933e-04 2.827819e-04 0.0002354823 3.047019e-04 6.623985e-04
 [7,] 5.058242e-04 8.792980e-04 0.0006316330 7.142048e-04 1.068549e-03
 [8,] 7.652694e-04 3.867651e-04 0.0002183373 2.929320e-04 3.329102e-04
 [9,] 5.736487e-04 5.449631e-04 0.0003339671 3.818841e-04 5.349169e-04
[10,] 7.183495e-04 3.061978e-04 0.0001292073 3.075222e-04 1.767506e-04
[11,] 1.095457e-03 2.360418e-04 0.0001053015 1.287099e-04 2.507401e-04
[12,] 2.360418e-04 1.638270e-03 0.0004761083 8.155179e-04 9.520111e-04
[13,] 1.053015e-04 4.761083e-04 0.0014120850 2.918993e-04 5.221017e-04
[14,] 1.287099e-04 8.155179e-04 0.0002918993 1.601433e-03 7.607755e-04
[15,] 2.507401e-04 9.520111e-04 0.0005221017 7.607755e-04 1.728808e-03
[16,] 3.259419e-04 8.933070e-04 0.0003351606 4.722255e-04 6.352700e-04
[17,] 2.258234e-04 3.189966e-04 0.0001774220 3.426430e-04 8.507645e-05
[18,] 3.412301e-04 3.520174e-04 0.0002307829 3.587954e-05 3.314236e-04
[19,] 3.483552e-04 5.709602e-04 0.0002905545 9.107817e-04 5.868172e-04
[20,] 4.162964e-04 6.569933e-04 0.0003601311 5.128423e-04 8.315401e-04
[21,] 3.203275e-04 8.104277e-05 0.0001796005 2.713080e-04 3.432581e-04
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 5.615340e-04 2.657088e-04 2.539180e-04 0.0005975976 0.0005391523
 [2,] 2.062509e-04 1.385843e-04 2.503942e-05 0.0003847111 0.0002356209
 [3,] 5.319594e-04 7.070134e-04 3.831389e-04 0.0005597349 0.0004123386
 [4,] 4.577893e-04 3.594403e-04 1.757285e-04 0.0009951346 0.0006353813
 [5,] 1.855316e-04 1.705285e-04 1.111084e-04 0.0003942800 0.0002340805
 [6,] 3.197038e-04 3.423557e-04 3.252324e-04 0.0004934985 0.0005399889
 [7,] 5.806718e-04 3.033842e-04 3.000955e-04 0.0004892996 0.0005728860
 [8,] 5.702923e-04 4.373767e-04 5.448684e-04 0.0004631575 0.0004015112
 [9,] 8.745371e-04 3.304571e-04 3.037242e-04 0.0007818722 0.0010647764
[10,] 3.711308e-04 5.130346e-04 2.086832e-04 0.0006107260 0.0003366808
[11,] 3.259419e-04 2.258234e-04 3.412301e-04 0.0003483552 0.0004162964
[12,] 8.933070e-04 3.189966e-04 3.520174e-04 0.0005709602 0.0006569933
[13,] 3.351606e-04 1.774220e-04 2.307829e-04 0.0002905545 0.0003601311
[14,] 4.722255e-04 3.426430e-04 3.587954e-05 0.0009107817 0.0005128423
[15,] 6.352700e-04 8.507645e-05 3.314236e-04 0.0005868172 0.0008315401
[16,] 1.815778e-03 1.593929e-04 4.435823e-04 0.0008161650 0.0010984076
[17,] 1.593929e-04 1.284653e-03 3.534202e-04 0.0006703988 0.0001603725
[18,] 4.435823e-04 3.534202e-04 9.484849e-04 0.0001866630 0.0004338891
[19,] 8.161650e-04 6.703988e-04 1.866630e-04 0.0020466051 0.0010073351
[20,] 1.098408e-03 1.603725e-04 4.338891e-04 0.0010073351 0.0016866111
[21,] 5.837058e-05 5.632637e-04 3.272104e-04 0.0004892206 0.0002115278
             [,21]
 [1,] 2.714302e-04
 [2,] 1.195848e-04
 [3,] 3.704439e-04
 [4,] 2.956231e-04
 [5,] 2.230986e-04
 [6,] 5.161993e-04
 [7,] 1.559809e-04
 [8,] 2.597643e-04
 [9,] 2.100049e-04
[10,] 5.114014e-04
[11,] 3.203275e-04
[12,] 8.104277e-05
[13,] 1.796005e-04
[14,] 2.713080e-04
[15,] 3.432581e-04
[16,] 5.837058e-05
[17,] 5.632637e-04
[18,] 3.272104e-04
[19,] 4.892206e-04
[20,] 2.115278e-04
[21,] 9.677864e-04

$covHi
             [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 0.0007936386 0.0004303348 0.0004343871 0.0004279487 0.0004653750
[2,] 0.0004303348 0.0009277628 0.0004418741 0.0005147918 0.0005365340
[3,] 0.0004343871 0.0004418741 0.0007830148 0.0004287359 0.0005138697
[4,] 0.0004279487 0.0005147918 0.0004287359 0.0006750199 0.0005097711
[5,] 0.0004653750 0.0005365340 0.0005138697 0.0005097711 0.0008657743
[6,] 0.0004398289 0.0004324170 0.0003986552 0.0004105594 0.0004411029
[7,] 0.0003926113 0.0004640153 0.0003907992 0.0004252847 0.0004690683
             [,6]         [,7]
[1,] 0.0004398289 0.0003926113
[2,] 0.0004324170 0.0004640153
[3,] 0.0003986552 0.0003907992
[4,] 0.0004105594 0.0004252847
[5,] 0.0004411029 0.0004690683
[6,] 0.0006177435 0.0003637520
[7,] 0.0003637520 0.0005604125

$covH
             [,1]
[1,] 0.0004901546

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Na2     0% ci   Na4     0% ci   Na5     0% ci   Na7     0% ci   Na9    
Na2                   0.441  (0.117)  0.508  (0.114)  0.543  (0.092)  0.518 
Na4   0.441  (0.117)                  0.371  (0.106)  0.720  (0.088)  0.552 
Na5   0.508  (0.114)  0.371  (0.106)                  0.401  (0.123)  0.599 
Na7   0.543  (0.092)  0.720  (0.088)  0.401  (0.123)                  0.512 
Na9   0.518  (0.110)  0.552  (0.116)  0.599  (0.087)  0.512  (0.111)        
Na12  0.569  (0.091)  0.581  (0.106)  0.430  (0.109)  0.603  (0.081)  0.345 
Na13  0.588  (0.079)  0.779  (0.058)  0.404  (0.098)  0.809  (0.047)  0.598 
     0% ci   Na12    0% ci   Na13    0% ci  
Na2  (0.110)  0.569  (0.091)  0.588  (0.079)
Na4  (0.116)  0.581  (0.106)  0.779  (0.058)
Na5  (0.087)  0.430  (0.109)  0.404  (0.098)
Na7  (0.111)  0.603  (0.081)  0.809  (0.047)
Na9           0.345  (0.122)  0.598  (0.111)
Na12 (0.122)                  0.710  (0.075)
Na13 (0.111)  0.710  (0.075)                

$Groups$`0`$Hi
     Item H  se     
Na2    0.530 (0.065)
Na4    0.583 (0.067)
Na5    0.449 (0.084)
Na7    0.608 (0.058)
Na9    0.527 (0.084)
Na12   0.544 (0.065)
Na13   0.648 (0.049)

$Groups$`0`$H
 Scale H se     
   0.557 (0.057)


$Groups$`1`
$Groups$`1`$Hij
     Na2     0% ci   Na4     0% ci   Na5     0% ci   Na7     0% ci   Na9    
Na2                   0.373  (0.052)  0.523  (0.041)  0.445  (0.050)  0.456 
Na4   0.373  (0.052)                  0.451  (0.052)  0.647  (0.043)  0.490 
Na5   0.523  (0.041)  0.451  (0.052)                  0.514  (0.042)  0.578 
Na7   0.445  (0.050)  0.647  (0.043)  0.514  (0.042)                  0.560 
Na9   0.456  (0.048)  0.490  (0.049)  0.578  (0.041)  0.560  (0.046)        
Na12  0.513  (0.039)  0.612  (0.043)  0.482  (0.042)  0.646  (0.040)  0.444 
Na13  0.461  (0.045)  0.708  (0.038)  0.531  (0.045)  0.699  (0.036)  0.532 
     0% ci   Na12    0% ci   Na13    0% ci  
Na2  (0.048)  0.513  (0.039)  0.461  (0.045)
Na4  (0.049)  0.612  (0.043)  0.708  (0.038)
Na5  (0.041)  0.482  (0.042)  0.531  (0.045)
Na7  (0.046)  0.646  (0.040)  0.699  (0.036)
Na9           0.444  (0.048)  0.532  (0.043)
Na12 (0.048)                  0.666  (0.035)
Na13 (0.043)  0.666  (0.035)                

$Groups$`1`$Hi
     Item H  se     
Na2    0.467 (0.031)
Na4    0.547 (0.034)
Na5    0.512 (0.029)
Na7    0.583 (0.029)
Na9    0.509 (0.031)
Na12   0.555 (0.027)
Na13   0.601 (0.027)

$Groups$`1`$H
 Scale H se     
   0.538 (0.024)
$Hij
     Si1     se      Si3     se      Si6     se      Si8     se      Si10   
Si1                   0.671  (0.036)  0.515  (0.043)  0.566  (0.040)  0.588 
Si3   0.671  (0.036)                  0.277  (0.049)  0.469  (0.044)  0.468 
Si6   0.515  (0.043)  0.277  (0.049)                  0.595  (0.039)  0.551 
Si8   0.566  (0.040)  0.469  (0.044)  0.595  (0.039)                  0.611 
Si10  0.588  (0.039)  0.468  (0.042)  0.551  (0.040)  0.611  (0.034)        
Si11  0.543  (0.040)  0.403  (0.044)  0.493  (0.043)  0.516  (0.041)  0.554 
Si14  0.506  (0.041)  0.410  (0.044)  0.526  (0.040)  0.680  (0.033)  0.523 
     se      Si11    se      Si14    se     
Si1  (0.039)  0.543  (0.040)  0.506  (0.041)
Si3  (0.042)  0.403  (0.044)  0.410  (0.044)
Si6  (0.040)  0.493  (0.043)  0.526  (0.040)
Si8  (0.034)  0.516  (0.041)  0.680  (0.033)
Si10          0.554  (0.038)  0.523  (0.039)
Si11 (0.038)                  0.451  (0.045)
Si14 (0.039)  0.451  (0.045)                

$Hi
     Item H  se     
Si1    0.566 (0.026)
Si3    0.451 (0.031)
Si6    0.494 (0.031)
Si8    0.573 (0.025)
Si10   0.549 (0.024)
Si11   0.494 (0.029)
Si14   0.518 (0.028)

$H
Scale H      se 
  0.521 (0.022) 

$covHij
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 1.326234e-03 3.148230e-05 0.0003423128 0.0003894712 0.0004268642
 [2,] 3.148230e-05 1.822688e-03 0.0007018545 0.0005715538 0.0004868289
 [3,] 3.423128e-04 7.018545e-04 0.0015823404 0.0008274935 0.0004407275
 [4,] 3.894712e-04 5.715538e-04 0.0008274935 0.0014996080 0.0005850977
 [5,] 4.268642e-04 4.868289e-04 0.0004407275 0.0005850977 0.0016027152
 [6,] 2.387396e-04 5.128700e-04 0.0008772929 0.0006510906 0.0003378176
 [7,] 7.331617e-04 1.451832e-03 0.0006355201 0.0005320106 0.0004183089
 [8,] 5.533883e-04 4.994686e-04 0.0009478469 0.0005276416 0.0001007506
 [9,] 5.041181e-04 4.236027e-04 0.0005162177 0.0008249585 0.0002356199
[10,] 6.626651e-04 2.863598e-04 0.0001412691 0.0002272101 0.0008740511
[11,] 5.745834e-04 3.584135e-04 0.0005068683 0.0004482119 0.0001233220
[12,] 1.370246e-04 8.228506e-04 0.0004681540 0.0003085023 0.0002401868
[13,] 1.395707e-04 8.293709e-04 0.0003388724 0.0003648660 0.0001140969
[14,] 4.144024e-05 8.137073e-04 0.0003217256 0.0001090130 0.0005304653
[15,] 1.065186e-04 6.932608e-04 0.0003275542 0.0003227576 0.0003272020
[16,] 1.929262e-04 3.007363e-04 0.0004967575 0.0003867450 0.0001979057
[17,] 2.143675e-05 3.543813e-04 0.0007628287 0.0003646496 0.0006124136
[18,] 7.494426e-05 2.210940e-04 0.0003861432 0.0001951433 0.0001821352
[19,] 3.410130e-05 7.432037e-05 0.0002758960 0.0004158360 0.0005040973
[20,] 1.856760e-04 3.876625e-04 0.0003531423 0.0003934886 0.0002614172
[21,] 8.913423e-06 4.811298e-04 0.0004626634 0.0003652616 0.0006662474
              [,6]         [,7]         [,8]          [,9]         [,10]
 [1,] 0.0002387396 0.0007331617 5.533883e-04  5.041181e-04  6.626651e-04
 [2,] 0.0005128700 0.0014518319 4.994686e-04  4.236027e-04  2.863598e-04
 [3,] 0.0008772929 0.0006355201 9.478469e-04  5.162177e-04  1.412691e-04
 [4,] 0.0006510906 0.0005320106 5.276416e-04  8.249585e-04  2.272101e-04
 [5,] 0.0003378176 0.0004183089 1.007506e-04  2.356199e-04  8.740511e-04
 [6,] 0.0016939188 0.0004890351 4.983521e-04  4.158569e-04  1.352208e-04
 [7,] 0.0004890351 0.0024468732 1.108801e-03  8.892630e-04  9.209044e-04
 [8,] 0.0004983521 0.0011088006 1.939729e-03  8.865508e-04  6.959694e-04
 [9,] 0.0004158569 0.0008892630 8.865508e-04  1.769998e-03  7.871405e-04
[10,] 0.0001352208 0.0009209044 6.959694e-04  7.871405e-04  1.962134e-03
[11,] 0.0009287999 0.0009070149 1.138977e-03  7.359981e-04  6.945996e-04
[12,] 0.0002803957 0.0008456847 1.058809e-04  1.867356e-04  1.212024e-04
[13,] 0.0003489007 0.0008222433 2.101908e-04  3.210863e-06 -5.547986e-05
[14,] 0.0003795883 0.0008492032 2.005457e-04 -7.892562e-05  1.296154e-04
[15,] 0.0005283547 0.0006696172 4.552146e-05  1.926017e-04  1.761486e-04
[16,] 0.0003371062 0.0003824320 3.805428e-04  3.653072e-04  2.514581e-04
[17,] 0.0004406999 0.0003950374 5.975313e-04  3.519937e-04  5.951065e-04
[18,] 0.0004454892 0.0002034270 3.908572e-04  1.849098e-04  1.161549e-04
[19,] 0.0002515276 0.0001121089 2.721215e-04  3.210100e-04  5.052162e-04
[20,] 0.0007914413 0.0003963630 3.066623e-04  3.802799e-04  3.333191e-04
[21,] 0.0007611678 0.0004232794 2.941310e-04  3.603859e-04  5.613659e-04
             [,11]        [,12]         [,13]         [,14]        [,15]
 [1,] 5.745834e-04 1.370246e-04  1.395707e-04  4.144024e-05 1.065186e-04
 [2,] 3.584135e-04 8.228506e-04  8.293709e-04  8.137073e-04 6.932608e-04
 [3,] 5.068683e-04 4.681540e-04  3.388724e-04  3.217256e-04 3.275542e-04
 [4,] 4.482119e-04 3.085023e-04  3.648660e-04  1.090130e-04 3.227576e-04
 [5,] 1.233220e-04 2.401868e-04  1.140969e-04  5.304653e-04 3.272020e-04
 [6,] 9.287999e-04 2.803957e-04  3.489007e-04  3.795883e-04 5.283547e-04
 [7,] 9.070149e-04 8.456847e-04  8.222433e-04  8.492032e-04 6.696172e-04
 [8,] 1.138977e-03 1.058809e-04  2.101908e-04  2.005457e-04 4.552146e-05
 [9,] 7.359981e-04 1.867356e-04  3.210863e-06 -7.892562e-05 1.926017e-04
[10,] 6.945996e-04 1.212024e-04 -5.547986e-05  1.296154e-04 1.761486e-04
[11,] 1.918183e-03 4.847524e-05  2.123517e-04  2.278268e-04 1.062812e-04
[12,] 4.847524e-05 1.552705e-03  7.503131e-04  6.928588e-04 8.604778e-04
[13,] 2.123517e-04 7.503131e-04  1.589336e-03  8.930087e-04 4.930575e-04
[14,] 2.278268e-04 6.928588e-04  8.930087e-04  1.867909e-03 3.592243e-04
[15,] 1.062812e-04 8.604778e-04  4.930575e-04  3.592243e-04 1.594745e-03
[16,] 2.805824e-04 4.085177e-04  4.861942e-04  2.032543e-04 2.278487e-04
[17,] 3.219529e-04 3.801083e-04  2.342123e-04  6.915337e-04 1.881575e-04
[18,] 3.939816e-04 3.522066e-04  1.303340e-04  8.959822e-05 5.339055e-04
[19,] 3.241841e-04 9.995056e-05  3.974028e-04  5.274966e-04 5.290067e-05
[20,] 5.817733e-04 2.659919e-04  3.289984e-04  1.601106e-04 6.777408e-04
[21,] 5.490426e-04 2.610918e-04  2.200481e-04  7.613368e-04 6.030693e-04
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 0.0001929262 2.143675e-05 7.494426e-05 3.410130e-05 0.0001856760
 [2,] 0.0003007363 3.543813e-04 2.210940e-04 7.432037e-05 0.0003876625
 [3,] 0.0004967575 7.628287e-04 3.861432e-04 2.758960e-04 0.0003531423
 [4,] 0.0003867450 3.646496e-04 1.951433e-04 4.158360e-04 0.0003934886
 [5,] 0.0001979057 6.124136e-04 1.821352e-04 5.040973e-04 0.0002614172
 [6,] 0.0003371062 4.406999e-04 4.454892e-04 2.515276e-04 0.0007914413
 [7,] 0.0003824320 3.950374e-04 2.034270e-04 1.121089e-04 0.0003963630
 [8,] 0.0003805428 5.975313e-04 3.908572e-04 2.721215e-04 0.0003066623
 [9,] 0.0003653072 3.519937e-04 1.849098e-04 3.210100e-04 0.0003802799
[10,] 0.0002514581 5.951065e-04 1.161549e-04 5.052162e-04 0.0003333191
[11,] 0.0002805824 3.219529e-04 3.939816e-04 3.241841e-04 0.0005817733
[12,] 0.0004085177 3.801083e-04 3.522066e-04 9.995056e-05 0.0002659919
[13,] 0.0004861942 2.342123e-04 1.303340e-04 3.974028e-04 0.0003289984
[14,] 0.0002032543 6.915337e-04 8.959822e-05 5.274966e-04 0.0001601106
[15,] 0.0002278487 1.881575e-04 5.339055e-04 5.290067e-05 0.0006777408
[16,] 0.0011319410 6.597845e-04 3.378432e-04 2.733794e-04 0.0005961831
[17,] 0.0006597845 1.709023e-03 3.148906e-04 7.107327e-04 0.0004110028
[18,] 0.0003378432 3.148906e-04 1.121554e-03 1.553415e-04 0.0005613125
[19,] 0.0002733794 7.107327e-04 1.553415e-04 1.477243e-03 0.0002347616
[20,] 0.0005961831 4.110028e-04 5.613125e-04 2.347616e-04 0.0015446835
[21,] 0.0004232531 1.089428e-03 4.414152e-04 6.733900e-04 0.0008475472
             [,21]
 [1,] 8.913423e-06
 [2,] 4.811298e-04
 [3,] 4.626634e-04
 [4,] 3.652616e-04
 [5,] 6.662474e-04
 [6,] 7.611678e-04
 [7,] 4.232794e-04
 [8,] 2.941310e-04
 [9,] 3.603859e-04
[10,] 5.613659e-04
[11,] 5.490426e-04
[12,] 2.610918e-04
[13,] 2.200481e-04
[14,] 7.613368e-04
[15,] 6.030693e-04
[16,] 4.232531e-04
[17,] 1.089428e-03
[18,] 4.414152e-04
[19,] 6.733900e-04
[20,] 8.475472e-04
[21,] 1.985525e-03

$covHi
             [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 0.0006807785 0.0005123966 0.0004796531 0.0004503299 0.0004347937
[2,] 0.0005123966 0.0009839775 0.0004356884 0.0004590853 0.0004434675
[3,] 0.0004796531 0.0004356884 0.0009666859 0.0004585805 0.0004173673
[4,] 0.0004503299 0.0004590853 0.0004585805 0.0006409695 0.0004226465
[5,] 0.0004347937 0.0004434675 0.0004173673 0.0004226465 0.0005748214
[6,] 0.0004140468 0.0004309778 0.0004171204 0.0004103270 0.0004028547
[7,] 0.0004442039 0.0004375897 0.0004333364 0.0004463414 0.0004259015
             [,6]         [,7]
[1,] 0.0004140468 0.0004442039
[2,] 0.0004309778 0.0004375897
[3,] 0.0004171204 0.0004333364
[4,] 0.0004103270 0.0004463414
[5,] 0.0004028547 0.0004259015
[6,] 0.0008178897 0.0004142683
[7,] 0.0004142683 0.0007626027

$covH
             [,1]
[1,] 0.0004876375

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Si1     0% ci   Si3      0% ci   Si6      0% ci   Si8     0% ci   Si10   
Si1                    0.598  (0.119)   0.354  (0.122)  0.512  (0.114)  0.627 
Si3   0.598  (0.119)                   -0.058  (0.149)  0.215  (0.142)  0.195 
Si6   0.354  (0.122)  -0.058  (0.149)                   0.571  (0.117)  0.556 
Si8   0.512  (0.114)   0.215  (0.142)   0.571  (0.117)                  0.671 
Si10  0.627  (0.094)   0.195  (0.133)   0.556  (0.115)  0.671  (0.083)        
Si11  0.563  (0.102)   0.173  (0.134)   0.400  (0.139)  0.514  (0.114)  0.696 
Si14  0.347  (0.117)   0.137  (0.146)   0.471  (0.125)  0.641  (0.096)  0.411 
     0% ci   Si11    0% ci   Si14    0% ci  
Si1  (0.094)  0.563  (0.102)  0.347  (0.117)
Si3  (0.133)  0.173  (0.134)  0.137  (0.146)
Si6  (0.115)  0.400  (0.139)  0.471  (0.125)
Si8  (0.083)  0.514  (0.114)  0.641  (0.096)
Si10          0.696  (0.094)  0.411  (0.109)
Si11 (0.094)                  0.413  (0.134)
Si14 (0.109)  0.413  (0.134)                

$Groups$`0`$Hi
     Item H  se     
Si1    0.498 (0.076)
Si3    0.205 (0.113)
Si6    0.388 (0.096)
Si8    0.523 (0.065)
Si10   0.526 (0.063)
Si11   0.462 (0.087)
Si14   0.404 (0.084)

$Groups$`0`$H
 Scale H se     
   0.431 (0.070)


$Groups$`1`
$Groups$`1`$Hij
     Si1     0% ci   Si3     0% ci   Si6     0% ci   Si8     0% ci   Si10   
Si1                   0.681  (0.038)  0.547  (0.044)  0.574  (0.042)  0.580 
Si3   0.681  (0.038)                  0.337  (0.050)  0.510  (0.045)  0.511 
Si6   0.547  (0.044)  0.337  (0.050)                  0.599  (0.041)  0.551 
Si8   0.574  (0.042)  0.510  (0.045)  0.599  (0.041)                  0.601 
Si10  0.580  (0.043)  0.511  (0.043)  0.551  (0.042)  0.601  (0.037)        
Si11  0.537  (0.044)  0.438  (0.046)  0.512  (0.043)  0.517  (0.044)  0.529 
Si14  0.532  (0.043)  0.449  (0.044)  0.534  (0.042)  0.685  (0.036)  0.542 
     0% ci   Si11    0% ci   Si14    0% ci  
Si1  (0.043)  0.537  (0.044)  0.532  (0.043)
Si3  (0.043)  0.438  (0.046)  0.449  (0.044)
Si6  (0.042)  0.512  (0.043)  0.534  (0.042)
Si8  (0.037)  0.517  (0.044)  0.685  (0.036)
Si10          0.529  (0.042)  0.542  (0.042)
Si11 (0.042)                  0.457  (0.047)
Si14 (0.042)  0.457  (0.047)                

$Groups$`1`$Hi
     Item H  se     
Si1    0.576 (0.028)
Si3    0.489 (0.031)
Si6    0.514 (0.032)
Si8    0.581 (0.027)
Si10   0.552 (0.026)
Si11   0.498 (0.030)
Si14   0.535 (0.029)

$Groups$`1`$H
 Scale H se     
   0.536 (0.023)
$Hij
     Si1     se      Na2      se      Si3      se      Na4     se      Na5     
Si1                    0.050  (0.049)   0.671  (0.036)  0.219  (0.051)   0.092 
Na2   0.050  (0.049)                   -0.062  (0.047)  0.391  (0.048)   0.522 
Si3   0.671  (0.036)  -0.062  (0.047)                   0.097  (0.053)  -0.059 
Na4   0.219  (0.051)   0.391  (0.048)   0.097  (0.053)                   0.439 
Na5   0.092  (0.049)   0.522  (0.039)  -0.059  (0.046)  0.439  (0.047)         
Si6   0.515  (0.043)   0.270  (0.048)   0.277  (0.049)  0.450  (0.044)   0.368 
Na7   0.211  (0.050)   0.465  (0.045)   0.114  (0.049)  0.661  (0.039)   0.499 
Si8   0.566  (0.040)   0.176  (0.048)   0.469  (0.044)  0.318  (0.048)   0.165 
Na9   0.112  (0.050)   0.468  (0.045)   0.033  (0.050)  0.503  (0.045)   0.581 
Si10  0.588  (0.039)   0.156  (0.048)   0.468  (0.042)  0.242  (0.048)   0.172 
Si11  0.543  (0.040)   0.129  (0.050)   0.403  (0.044)  0.225  (0.051)   0.188 
Na12  0.172  (0.048)   0.532  (0.035)   0.042  (0.047)  0.616  (0.040)   0.475 
Na13  0.212  (0.052)   0.493  (0.040)   0.091  (0.052)  0.725  (0.033)   0.508 
Si14  0.506  (0.041)   0.104  (0.049)   0.410  (0.044)  0.337  (0.047)   0.148 
     se      Si6     se      Na7     se      Si8     se      Na9     se     
Si1  (0.049)  0.515  (0.043)  0.211  (0.050)  0.566  (0.040)  0.112  (0.050)
Na2  (0.039)  0.270  (0.048)  0.465  (0.045)  0.176  (0.048)  0.468  (0.045)
Si3  (0.046)  0.277  (0.049)  0.114  (0.049)  0.469  (0.044)  0.033  (0.050)
Na4  (0.047)  0.450  (0.044)  0.661  (0.039)  0.318  (0.048)  0.503  (0.045)
Na5           0.368  (0.047)  0.499  (0.040)  0.165  (0.049)  0.581  (0.038)
Si6  (0.047)                  0.468  (0.044)  0.595  (0.039)  0.392  (0.046)
Na7  (0.040)  0.468  (0.044)                  0.355  (0.046)  0.555  (0.043)
Si8  (0.049)  0.595  (0.039)  0.355  (0.046)                  0.277  (0.049)
Na9  (0.038)  0.392  (0.046)  0.555  (0.043)  0.277  (0.049)                
Si10 (0.046)  0.551  (0.040)  0.314  (0.047)  0.611  (0.034)  0.230  (0.048)
Si11 (0.047)  0.493  (0.043)  0.260  (0.049)  0.516  (0.041)  0.181  (0.049)
Na12 (0.040)  0.357  (0.043)  0.648  (0.036)  0.249  (0.045)  0.440  (0.045)
Na13 (0.042)  0.413  (0.045)  0.722  (0.031)  0.315  (0.047)  0.548  (0.041)
Si14 (0.048)  0.526  (0.040)  0.356  (0.046)  0.680  (0.033)  0.273  (0.049)
     Si10    se      Si11    se      Na12    se      Na13    se      Si14   
Si1   0.588  (0.039)  0.543  (0.040)  0.172  (0.048)  0.212  (0.052)  0.506 
Na2   0.156  (0.048)  0.129  (0.050)  0.532  (0.035)  0.493  (0.040)  0.104 
Si3   0.468  (0.042)  0.403  (0.044)  0.042  (0.047)  0.091  (0.052)  0.410 
Na4   0.242  (0.048)  0.225  (0.051)  0.616  (0.040)  0.725  (0.033)  0.337 
Na5   0.172  (0.046)  0.188  (0.047)  0.475  (0.040)  0.508  (0.042)  0.148 
Si6   0.551  (0.040)  0.493  (0.043)  0.357  (0.043)  0.413  (0.045)  0.526 
Na7   0.314  (0.047)  0.260  (0.049)  0.648  (0.036)  0.722  (0.031)  0.356 
Si8   0.611  (0.034)  0.516  (0.041)  0.249  (0.045)  0.315  (0.047)  0.680 
Na9   0.230  (0.048)  0.181  (0.049)  0.440  (0.045)  0.548  (0.041)  0.273 
Si10                  0.554  (0.038)  0.230  (0.046)  0.224  (0.048)  0.523 
Si11  0.554  (0.038)                  0.197  (0.046)  0.236  (0.053)  0.451 
Na12  0.230  (0.046)  0.197  (0.046)                  0.685  (0.031)  0.245 
Na13  0.224  (0.048)  0.236  (0.053)  0.685  (0.031)                  0.310 
Si14  0.523  (0.039)  0.451  (0.045)  0.245  (0.045)  0.310  (0.046)        
     se     
Si1  (0.041)
Na2  (0.049)
Si3  (0.044)
Na4  (0.047)
Na5  (0.048)
Si6  (0.040)
Na7  (0.046)
Si8  (0.033)
Na9  (0.049)
Si10 (0.039)
Si11 (0.045)
Na12 (0.045)
Na13 (0.046)
Si14        

$Hi
     Item H  se     
Si1    0.347 (0.026)
Na2    0.280 (0.028)
Si3    0.225 (0.029)
Na4    0.403 (0.026)
Na5    0.310 (0.027)
Si6    0.437 (0.024)
Na7    0.433 (0.024)
Si8    0.409 (0.024)
Na9    0.354 (0.026)
Si10   0.374 (0.024)
Si11   0.338 (0.026)
Na12   0.367 (0.024)
Na13   0.423 (0.024)
Si14   0.376 (0.024)

$H
Scale H      se 
  0.361 (0.018) 

$covHij
               [,1]          [,2]          [,3]          [,4]          [,5]
 [1,]  2.434238e-03 -1.495269e-04  8.594139e-04  1.257516e-03  4.151211e-04
 [2,] -1.495269e-04  1.326234e-03 -6.211550e-06 -3.789549e-04  3.148230e-05
 [3,]  8.594139e-04 -6.211550e-06  2.622031e-03  7.594278e-04  7.551575e-04
 [4,]  1.257516e-03 -3.789549e-04  7.594278e-04  2.433117e-03  4.008195e-04
 [5,]  4.151211e-04  3.148230e-05  7.551575e-04  4.008195e-04  1.822688e-03
 [6,]  8.610112e-04 -1.630711e-05  1.566734e-03  8.526865e-04  7.492925e-04
 [7,]  2.709405e-04  3.423128e-04  5.212472e-04  9.950627e-05  7.018545e-04
 [8,]  1.103668e-03 -1.706341e-04  1.228477e-03  1.402898e-03  6.821965e-04
 [9,]  2.110546e-04  3.894712e-04  3.677207e-04  3.772704e-05  5.715538e-04
[10,]  3.702751e-05  4.268642e-04  2.485208e-04 -1.191778e-05  4.868289e-04
[11,]  1.151212e-03 -9.101252e-05  1.181871e-03  9.432152e-04  3.951396e-04
[12,]  1.040878e-03 -3.500551e-05  1.877626e-03  1.022770e-03  6.377324e-04
[13,]  1.772294e-04  2.387396e-04  5.810354e-04  1.084298e-04  5.128700e-04
[14,]  1.505274e-03  2.103932e-04  4.141674e-04  6.282812e-04  2.144128e-04
[15,]  5.245784e-04 -1.249220e-04 -1.451571e-04  3.953097e-04  2.473014e-05
[16,]  1.356779e-04 -1.063259e-04  1.104419e-04  8.579419e-05 -7.437012e-06
[17,]  1.050261e-03 -1.487516e-04  3.614334e-04  5.303926e-04 -2.722630e-05
[18,]  3.542381e-04 -1.054809e-04  7.103924e-06  2.698007e-04 -5.128920e-05
[19,]  1.307711e-03  5.072716e-05  2.642618e-04  5.563795e-04  1.209411e-04
[20,]  2.656278e-04 -6.468823e-05  1.936449e-04  1.125675e-04 -3.852466e-05
[21,]  1.337394e-03  7.973286e-06  5.521338e-04  5.820986e-04  1.927765e-04
[22,]  1.353143e-03 -3.549755e-05  3.516577e-04  6.938719e-04  2.531976e-05
[23,]  3.145673e-04 -1.649429e-04  5.109162e-05  3.531082e-04 -5.732922e-05
[24,]  4.183864e-04 -1.253598e-04 -8.004636e-06  3.629808e-04 -5.859445e-05
[25,]  1.055036e-03 -3.216684e-05  2.348789e-04  4.484452e-04  1.243449e-04
[26,]  4.028604e-04  4.239013e-04  1.741616e-03  3.539726e-04  4.566631e-04
[27,]  6.384266e-04  3.417927e-04  3.878872e-04  1.353818e-03  1.786841e-04
[28,]  1.478353e-04  7.331617e-04  4.631666e-04  1.152104e-05  1.451832e-03
[29,]  4.424294e-04  4.109802e-04  8.953324e-04  4.008604e-04  4.969152e-04
[30,]  1.777531e-04  5.533883e-04  2.843017e-04 -9.110099e-05  4.994686e-04
[31,]  5.617561e-04  1.688257e-04  5.601073e-04  7.549291e-04  4.328453e-04
[32,]  8.691149e-05  5.041181e-04  2.096599e-04 -7.374291e-05  4.236027e-04
[33,]  5.693732e-05  6.626651e-04  2.950461e-05 -5.335879e-05  2.863598e-04
[34,]  5.785526e-04  3.079035e-04  7.451123e-04  5.072114e-04  2.968744e-04
[35,]  5.504606e-04  3.785055e-04  1.172784e-03  4.600633e-04  4.481258e-04
[36,]  5.825737e-06  5.745834e-04  3.454125e-04 -1.464405e-04  3.584135e-04
[37,]  3.648446e-04 -1.474616e-04 -2.473914e-04  6.153476e-04  4.206993e-05
[38,]  4.423817e-04 -8.222259e-05  1.075266e-03  4.703075e-04  3.387502e-04
[39,]  2.160853e-04 -5.427949e-05  3.127918e-05  3.459440e-04  1.558594e-04
[40,]  2.938853e-04  3.974018e-05  1.082763e-03  2.722079e-04  2.399818e-04
[41,]  3.590014e-04 -1.211744e-04 -7.827564e-05  3.729310e-04  8.423477e-06
[42,]  5.881346e-04  1.068661e-04  1.535035e-03  4.164136e-04  5.262943e-04
[43,]  3.819032e-04 -3.591748e-05  1.484208e-03  4.278047e-04  4.092308e-04
[44,]  2.610635e-04 -3.475434e-06  1.397773e-04  2.243270e-04  1.645992e-04
[45,]  1.540091e-04 -1.788314e-05  4.454794e-05  1.066920e-04  8.508835e-05
[46,]  2.496438e-04  6.629115e-05  1.133468e-03  1.877287e-04  9.014975e-05
[47,]  5.162332e-04 -3.077021e-04  3.339470e-04  1.143457e-03 -1.196333e-04
[48,]  2.686081e-04 -1.773492e-04  1.087970e-04  3.553610e-04  8.517616e-05
[49,]  5.627835e-04 -1.539524e-04  2.285180e-04  1.348592e-03  3.714875e-04
[50,]  1.017129e-04 -4.104462e-05  9.834629e-05  1.807792e-04  2.407260e-05
[51,]  5.826099e-04 -1.216401e-04  3.796085e-04  1.171845e-03  3.023066e-04
[52,]  6.603283e-04 -1.604907e-04  3.766725e-04  1.138396e-03  1.936556e-04
[53,]  3.834807e-04 -5.440377e-05  5.268493e-05  4.424806e-04  3.230096e-05
[54,]  3.763377e-04 -1.991902e-04 -7.556787e-05  5.514414e-04  5.227489e-05
[55,]  4.500508e-04 -1.925890e-04  1.529525e-04  1.127649e-03  1.785393e-04
[56,]  3.282473e-04 -9.166534e-05  5.897628e-04  3.641356e-04  1.232471e-04
[57,]  2.096189e-04  1.370246e-04  3.034857e-04  3.954278e-04  8.228506e-04
[58,]  4.225693e-04 -1.174585e-04  3.133533e-04  6.270530e-04 -1.915143e-04
[59,]  2.973053e-04  1.395707e-04  5.007641e-04  3.355178e-04  8.293709e-04
[60,]  5.614288e-05  4.144024e-05  3.508089e-04  2.384237e-04  8.137073e-04
[61,]  4.578122e-04 -3.688540e-05  7.242965e-04  4.236678e-04  2.216164e-04
[62,]  3.703761e-04 -8.945349e-05  7.075276e-04  4.110976e-04  2.115934e-04
[63,]  2.159809e-04  1.065186e-04  2.532768e-04  2.393660e-04  6.932608e-04
[64,]  3.927272e-04  3.091324e-05  6.009505e-04  3.275164e-04  2.235335e-04
[65,]  2.736992e-04 -1.559309e-04  6.225207e-05  2.659073e-04 -5.897097e-06
[66,]  4.145575e-04  9.274789e-05  8.202686e-04  3.890856e-04  1.050143e-04
[67,]  4.243077e-04 -3.879917e-05  9.414010e-04  3.886163e-04  1.351608e-04
[68,]  5.739569e-05 -2.081439e-06  1.430015e-04  1.221103e-04  8.960287e-06
[69,]  1.087919e-04 -8.363185e-05  1.756905e-04  1.515136e-04  4.598911e-05
[70,]  2.990100e-04 -1.070358e-05  3.148289e-04  2.271875e-04  8.816004e-05
[71,]  4.070164e-04 -2.024539e-05  2.856767e-04  6.264584e-04  2.508110e-04
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               [,6]          [,7]          [,8]          [,9]         [,10]
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[91,]  4.531404e-04  2.363351e-04  4.256723e-04  2.889718e-04  2.680587e-04
              [,11]         [,12]         [,13]         [,14]         [,15]
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              [,41]         [,42]         [,43]         [,44]         [,45]
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[91,]  3.111628e-04  7.318943e-04  6.099982e-04  2.270404e-04  4.519132e-04
              [,46]         [,47]         [,48]         [,49]         [,50]
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              [,81]         [,82]         [,83]         [,84]         [,85]
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[86,]  1.711231e-04  1.320532e-04  1.101112e-03  8.026137e-04  1.321520e-04
[87,]  4.365098e-04  2.310744e-04  8.753876e-04  1.447706e-03  4.134501e-04
[88,] -3.232509e-05  6.733900e-04  1.284047e-04  4.591989e-04  8.475472e-04
[89,]  7.145716e-05  1.581439e-04  5.860524e-05  1.344561e-04  1.648952e-05
[90,]  8.581590e-04  8.449649e-05  9.303258e-04  6.016369e-04  1.555095e-04
[91,]  1.121718e-03  2.673968e-04  5.909345e-04  1.108497e-03  1.251671e-04
              [,86]         [,87]         [,88]         [,89]        [,90]
 [1,]  5.639359e-04  4.390979e-04  2.107497e-04  2.560965e-04 4.023267e-04
 [2,]  9.609410e-05 -4.869332e-05  8.913423e-06 -1.696488e-05 2.280926e-05
 [3,]  7.017259e-04  1.143457e-03  4.882554e-04  1.537692e-04 5.232473e-04
 [4,]  2.606768e-04  4.871396e-04  3.134183e-04  2.283208e-04 3.191116e-04
 [5,]  9.445223e-05  3.901570e-04  4.811298e-04  3.141594e-05 1.418941e-04
 [6,]  5.509018e-04  9.202240e-04  5.118179e-04  7.414652e-05 6.477588e-04
 [7,]  1.944809e-04  2.754473e-04  4.626634e-04  1.103730e-04 1.879430e-04
 [8,]  3.373056e-04  6.266739e-04  3.342391e-04  1.973514e-04 3.256455e-04
 [9,]  1.213739e-04  2.561741e-04  3.652616e-04  1.571687e-04 2.755797e-04
[10,]  1.462931e-04  3.419183e-04  6.662474e-04 -2.784296e-05 1.765123e-04
[11,]  1.118878e-03  6.926836e-04  2.190328e-04  1.319493e-04 8.869230e-04
[12,]  6.187172e-04  1.432428e-03  4.224989e-04  6.125549e-05 5.812360e-04
[13,]  2.245810e-04  4.456062e-04  7.611678e-04  1.041810e-04 1.489242e-04
[14,]  4.208504e-04  3.878483e-04  8.336977e-05  9.442602e-05 3.179801e-04
[15,]  4.571628e-05  4.345178e-05 -2.748681e-04  2.714302e-04 2.653526e-04
[16,]  2.155394e-04  8.206980e-05 -3.197288e-05  1.195848e-04 2.077740e-04
[17,]  4.490439e-04  3.164239e-04 -4.963832e-05  3.105713e-04 6.102325e-04
[18,]  1.152408e-04  4.329994e-05 -9.117521e-05  3.704439e-04 2.108579e-04
[19,]  5.228230e-04  5.466024e-04  4.004093e-05  1.895252e-04 6.119792e-04
[20,]  2.262251e-04  1.663052e-05 -4.993361e-05  2.956231e-04 2.790703e-04
[21,]  6.651633e-04  5.675823e-04  7.733711e-06  6.084476e-05 3.666044e-04
[22,]  1.094774e-03  9.389819e-04  4.021428e-05  1.749182e-04 3.813936e-04
[23,]  7.983960e-05  1.213915e-04  1.138626e-05  2.230986e-04 4.439672e-05
[24,]  1.567533e-04 -1.100356e-05 -4.718423e-05  5.161993e-04 2.081107e-04
[25,]  3.855760e-04  3.074936e-04  1.686678e-04  2.415462e-04 1.055838e-03
[26,]  6.036796e-04  9.098015e-04  3.942148e-04  1.190678e-05 5.062303e-04
[27,]  2.676166e-04  4.174651e-04  1.607756e-04  1.027392e-04 2.273655e-04
[28,]  3.413324e-05  2.209339e-04  4.232794e-04 -1.817373e-05 1.420552e-04
[29,]  4.535284e-04  7.914253e-04  2.395313e-04 -3.913319e-05 5.985656e-04
[30,]  4.833133e-05  1.061460e-04  2.941310e-04  5.562046e-05 9.093284e-05
[31,]  2.456143e-04  6.050836e-04  1.319280e-04  2.719833e-05 3.635345e-04
[32,] -2.349140e-05 -5.616074e-05  3.603859e-04  1.326604e-04 1.170242e-04
[33,] -5.932680e-05  1.172726e-04  5.613659e-04  7.887696e-06 6.612668e-05
[34,]  8.850351e-04  6.023898e-04  1.181571e-04  1.508571e-05 7.234630e-04
[35,]  5.755967e-04  1.200529e-03  2.521868e-04 -7.102333e-05 5.262495e-04
[36,]  6.438163e-05  1.727030e-04  5.490426e-04  7.486292e-05 4.353834e-05
[37,]  8.649458e-05  1.258978e-04 -6.013667e-05  1.559809e-04 2.274448e-04
[38,]  2.833515e-04  5.003429e-04  5.364458e-05  2.334561e-04 5.854422e-04
[39,] -4.197727e-05  5.827891e-05  7.744525e-05  2.597643e-04 2.620457e-04
[40,]  5.705345e-04  8.438294e-04  1.757668e-04  1.753646e-04 8.118905e-04
[41,]  1.807359e-04  2.724360e-04 -6.210108e-05  2.100049e-04 2.239610e-04
[42,]  5.907224e-04  1.047586e-03  3.713421e-04  1.039656e-04 5.719711e-04
[43,]  1.066626e-03  1.891917e-03  6.745963e-04  1.142515e-04 4.556389e-04
[44,] -2.011577e-05  8.485508e-05 -4.472159e-05  5.114014e-04 3.046093e-04
[45,]  7.753816e-05  7.795931e-05  3.515667e-05  3.203275e-04 2.338855e-04
[46,]  3.633299e-04  5.726758e-04  1.490990e-04  1.266368e-04 1.036658e-03
[47,]  1.899166e-04  2.450604e-04  8.600386e-05  1.325293e-04 5.188465e-04
[48,]  8.741217e-05  7.919810e-05 -1.392898e-05  8.104277e-05 5.567749e-05
[49,]  3.303885e-04  5.687386e-04  2.112492e-04  3.123350e-05 5.502579e-04
[50,]  2.149729e-04  1.081273e-04  1.960649e-04  1.796005e-04 1.773217e-04
[51,]  4.320528e-04  5.472786e-04  4.580620e-05 -4.367419e-05 5.161892e-04
[52,]  7.868502e-04  8.283976e-04  1.084406e-05  6.372826e-05 2.427065e-04
[53,]  1.123444e-04  2.109042e-05 -3.990401e-05  2.713080e-04 1.222138e-04
[54,]  8.782200e-06  4.598597e-05  9.536745e-05  3.432581e-04 3.394664e-05
[55,]  2.468239e-04  4.249628e-04  1.948961e-04  1.044414e-04 8.299097e-04
[56,]  3.032113e-04  2.900979e-04  4.851721e-05  1.616455e-04 3.877097e-04
[57,]  1.134662e-04  3.092622e-04  2.610918e-04  7.571557e-05 1.873570e-04
[58,]  1.099404e-04  1.980149e-04  2.904029e-05  1.589443e-04 2.346815e-04
[59,]  1.666562e-04  4.309239e-04  2.200481e-04 -7.481281e-06 1.656669e-05
[60,]  3.198210e-04  6.340783e-04  7.613368e-04 -5.473477e-05 3.098868e-05
[61,]  8.393937e-04  4.954971e-04  7.225446e-05  3.112669e-04 8.899494e-04
[62,]  3.751557e-04  8.512182e-04  8.223529e-05  2.737952e-04 5.841263e-04
[63,]  8.820622e-05  1.495440e-04  6.030693e-04  1.077436e-04 3.463130e-04
[64,]  4.500416e-04  8.046375e-04  1.367438e-05  2.408385e-06 7.533731e-04
[65,] -3.985342e-05  8.409580e-05 -1.935671e-04  5.837058e-05 8.358989e-05
[66,]  6.728122e-04  8.790662e-04  2.644023e-04 -9.751587e-05 4.732810e-04
[67,]  1.142858e-03  1.597422e-03  5.390912e-04  6.094583e-06 2.974902e-04
[68,]  5.644790e-05  5.024463e-05 -8.136774e-05  5.632637e-04 2.927440e-04
[69,]  3.721265e-05  1.835508e-04  5.014032e-05  3.272104e-04 6.420229e-05
[70,]  2.582237e-04  4.195337e-04  9.678348e-05  2.176245e-05 1.189836e-03
[71,]  2.128118e-04  6.794391e-04  1.198567e-05 -1.583224e-05 5.213375e-04
[72,]  1.278136e-04  2.532863e-04  4.232531e-04  1.588404e-05 7.385284e-05
[73,]  2.370242e-04  5.614170e-04  1.089428e-03  1.747216e-04 1.362191e-04
[74,]  9.142537e-04  8.158659e-04  1.198249e-04  1.976989e-04 1.216450e-03
[75,]  7.217318e-04  1.213255e-03  1.907056e-04  2.265633e-04 7.029389e-04
[76,]  1.359326e-04  2.041961e-04  4.414152e-04 -6.687589e-06 2.102799e-04
[77,]  4.741888e-04  6.954948e-04  2.441315e-04 -2.637973e-05 3.193672e-04
[78,]  7.517876e-04  1.096577e-03  4.981847e-04  9.324617e-05 2.123481e-04
[79,]  7.974595e-05  1.170806e-04 -1.260288e-04  4.892206e-04 2.918031e-04
[80,]  1.497727e-04  1.752032e-04  9.691943e-05  2.115278e-04 1.774041e-04
[81,]  1.711231e-04  4.365098e-04 -3.232509e-05  7.145716e-05 8.581590e-04
[82,]  1.320532e-04  2.310744e-04  6.733900e-04  1.581439e-04 8.449649e-05
[83,]  1.101112e-03  8.753876e-04  1.284047e-04  5.860524e-05 9.303258e-04
[84,]  8.026137e-04  1.447706e-03  4.591989e-04  1.344561e-04 6.016369e-04
[85,]  1.321520e-04  4.134501e-04  8.475472e-04  1.648952e-05 1.555095e-04
[86,]  2.152119e-03  1.263604e-03  2.558272e-04  6.998596e-05 6.956986e-04
[87,]  1.263604e-03  2.803276e-03  5.482425e-04  1.608652e-05 5.531150e-04
[88,]  2.558272e-04  5.482425e-04  1.985525e-03  1.135516e-04 4.366036e-05
[89,]  6.998596e-05  1.608652e-05  1.135516e-04  9.677864e-04 2.532856e-04
[90,]  6.956986e-04  5.531150e-04  4.366036e-05  2.532856e-04 1.994875e-03
[91,]  4.982358e-04  7.074153e-04  1.710000e-04  2.127409e-04 1.225077e-03
              [,91]
 [1,]  3.649586e-04
 [2,] -2.568160e-05
 [3,]  6.674159e-04
 [4,]  2.341908e-04
 [5,]  1.614424e-04
 [6,]  4.531404e-04
 [7,]  2.363351e-04
 [8,]  4.256723e-04
 [9,]  2.889718e-04
[10,]  2.680587e-04
[11,]  5.603101e-04
[12,]  8.264530e-04
[13,]  1.112237e-04
[14,]  3.365833e-04
[15,]  1.726714e-04
[16,]  1.991470e-05
[17,]  4.902528e-04
[18,]  2.436524e-04
[19,]  5.217462e-04
[20,]  1.570608e-04
[21,]  3.496910e-04
[22,]  2.698810e-04
[23,]  1.315343e-04
[24,]  1.087335e-04
[25,]  1.002831e-03
[26,]  5.929217e-04
[27,]  1.366522e-04
[28,]  1.469423e-04
[29,]  3.425734e-04
[30,]  9.608099e-06
[31,]  3.929317e-04
[32,]  5.163223e-05
[33,]  8.477411e-05
[34,]  4.794893e-04
[35,]  7.770183e-04
[36,] -7.922301e-06
[37,]  7.105016e-05
[38,]  6.137423e-04
[39,]  3.992040e-04
[40,]  1.026450e-03
[41,]  3.111628e-04
[42,]  7.318943e-04
[43,]  6.099982e-04
[44,]  2.270404e-04
[45,]  4.519132e-04
[46,]  1.482591e-03
[47,]  4.187717e-04
[48,]  1.565582e-04
[49,]  4.468531e-04
[50,]  9.067997e-05
[51,]  5.069319e-04
[52,]  3.520901e-04
[53,]  1.027538e-05
[54,] -4.648232e-05
[55,]  8.964609e-04
[56,]  5.780837e-04
[57,]  3.348009e-04
[58,]  4.385803e-04
[59,]  1.257423e-04
[60,]  4.176451e-05
[61,]  5.992598e-04
[62,]  9.419532e-04
[63,]  5.087419e-04
[64,]  6.810668e-04
[65,]  2.807021e-04
[66,]  5.543583e-04
[67,]  4.066769e-04
[68,]  1.139091e-05
[69,]  3.464130e-04
[70,]  1.242895e-03
[71,]  7.446733e-04
[72,]  9.744722e-05
[73,]  1.450635e-04
[74,]  6.730617e-04
[75,]  1.238819e-03
[76,]  2.484554e-04
[77,]  6.001807e-04
[78,]  4.628824e-04
[79,]  1.426331e-04
[80,]  3.981958e-04
[81,]  1.121718e-03
[82,]  2.673968e-04
[83,]  5.909345e-04
[84,]  1.108497e-03
[85,]  1.251671e-04
[86,]  4.982358e-04
[87,]  7.074153e-04
[88,]  1.710000e-04
[89,]  2.127409e-04
[90,]  1.225077e-03
[91,]  2.161564e-03

$covHi
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 0.0006645838 0.0002304549 4.470618e-04 0.0003266593 2.195585e-04
 [2,] 0.0002304549 0.0007646835 1.152516e-04 0.0003051144 4.120705e-04
 [3,] 0.0004470618 0.0001152516 8.541852e-04 0.0002339629 8.045099e-05
 [4,] 0.0003266593 0.0003051144 2.339629e-04 0.0006913407 3.239688e-04
 [5,] 0.0002195585 0.0004120705 8.045099e-05 0.0003239688 7.396551e-04
 [6,] 0.0003525765 0.0002813870 2.171933e-04 0.0003497003 2.961426e-04
 [7,] 0.0002750415 0.0003006784 2.029810e-04 0.0004041106 2.971901e-04
 [8,] 0.0003661938 0.0002606764 3.237293e-04 0.0003430305 2.411293e-04
 [9,] 0.0002223256 0.0003588539 1.394439e-04 0.0004024452 4.514541e-04
[10,] 0.0004139202 0.0002458037 3.272823e-04 0.0003129578 2.417322e-04
[11,] 0.0003804442 0.0002180598 3.237151e-04 0.0002840287 2.404339e-04
[12,] 0.0002857903 0.0003815629 2.050990e-04 0.0003826860 3.282982e-04
[13,] 0.0003142032 0.0003242748 2.136426e-04 0.0004431976 2.956983e-04
[14,] 0.0003294196 0.0002214053 2.719708e-04 0.0003202643 2.109477e-04
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 0.0003525765 0.0002750415 0.0003661938 0.0002223256 0.0004139202
 [2,] 0.0002813870 0.0003006784 0.0002606764 0.0003588539 0.0002458037
 [3,] 0.0002171933 0.0002029810 0.0003237293 0.0001394439 0.0003272823
 [4,] 0.0003497003 0.0004041106 0.0003430305 0.0004024452 0.0003129578
 [5,] 0.0002961426 0.0002971901 0.0002411293 0.0004514541 0.0002417322
 [6,] 0.0005801617 0.0002818677 0.0003466236 0.0002974021 0.0003349083
 [7,] 0.0002818677 0.0005713878 0.0002915138 0.0003124611 0.0002782050
 [8,] 0.0003466236 0.0002915138 0.0005581007 0.0002982279 0.0003805091
 [9,] 0.0002974021 0.0003124611 0.0002982279 0.0006909820 0.0002750708
[10,] 0.0003349083 0.0002782050 0.0003805091 0.0002750708 0.0005628807
[11,] 0.0002809188 0.0002449153 0.0003475380 0.0002423574 0.0003705075
[12,] 0.0002926391 0.0003291309 0.0002861552 0.0003095475 0.0002922727
[13,] 0.0003074648 0.0003631671 0.0003230056 0.0003660364 0.0003098117
[14,] 0.0003135730 0.0002700939 0.0003807911 0.0002652745 0.0003238305
             [,11]        [,12]        [,13]        [,14]
 [1,] 0.0003804442 0.0002857903 0.0003142032 0.0003294196
 [2,] 0.0002180598 0.0003815629 0.0003242748 0.0002214053
 [3,] 0.0003237151 0.0002050990 0.0002136426 0.0002719708
 [4,] 0.0002840287 0.0003826860 0.0004431976 0.0003202643
 [5,] 0.0002404339 0.0003282982 0.0002956983 0.0002109477
 [6,] 0.0002809188 0.0002926391 0.0003074648 0.0003135730
 [7,] 0.0002449153 0.0003291309 0.0003631671 0.0002700939
 [8,] 0.0003475380 0.0002861552 0.0003230056 0.0003807911
 [9,] 0.0002423574 0.0003095475 0.0003660364 0.0002652745
[10,] 0.0003705075 0.0002922727 0.0003098117 0.0003238305
[11,] 0.0006640774 0.0002533448 0.0002960417 0.0002941563
[12,] 0.0002533448 0.0005523158 0.0003481367 0.0002692463
[13,] 0.0002960417 0.0003481367 0.0005599367 0.0003031403
[14,] 0.0002941563 0.0002692463 0.0003031403 0.0005791888

$covH
             [,1]
[1,] 0.0003288151

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Si1      0% ci   Na2      0% ci   Si3      0% ci   Na4      0% ci  
Si1                    -0.088  (0.110)   0.598  (0.119)   0.038  (0.125)
Na2   -0.088  (0.110)                   -0.221  (0.123)   0.441  (0.117)
Si3    0.598  (0.119)  -0.221  (0.123)                   -0.152  (0.122)
Na4    0.038  (0.125)   0.441  (0.117)  -0.152  (0.122)                 
Na5    0.174  (0.127)   0.508  (0.114)  -0.310  (0.131)   0.371  (0.106)
Si6    0.354  (0.122)   0.210  (0.122)  -0.058  (0.149)   0.347  (0.132)
Na7    0.019  (0.123)   0.543  (0.092)  -0.143  (0.130)   0.720  (0.088)
Si8    0.512  (0.114)   0.161  (0.129)   0.215  (0.142)   0.400  (0.126)
Na9    0.064  (0.117)   0.518  (0.110)  -0.179  (0.128)   0.552  (0.116)
Si10   0.627  (0.094)   0.062  (0.121)   0.195  (0.133)   0.216  (0.125)
Si11   0.563  (0.102)   0.006  (0.132)   0.173  (0.134)   0.235  (0.128)
Na12   0.016  (0.095)   0.569  (0.091)  -0.196  (0.117)   0.581  (0.106)
Na13   0.114  (0.109)   0.588  (0.079)  -0.081  (0.124)   0.779  (0.058)
Si14   0.347  (0.117)   0.172  (0.117)   0.137  (0.146)   0.396  (0.117)
     Na5      0% ci   Si6      0% ci   Na7      0% ci   Si8     0% ci  
Si1    0.174  (0.127)   0.354  (0.122)   0.019  (0.123)  0.512  (0.114)
Na2    0.508  (0.114)   0.210  (0.122)   0.543  (0.092)  0.161  (0.129)
Si3   -0.310  (0.131)  -0.058  (0.149)  -0.143  (0.130)  0.215  (0.142)
Na4    0.371  (0.106)   0.347  (0.132)   0.720  (0.088)  0.400  (0.126)
Na5                     0.293  (0.151)   0.401  (0.123)  0.267  (0.144)
Si6    0.293  (0.151)                    0.427  (0.126)  0.571  (0.117)
Na7    0.401  (0.123)   0.427  (0.126)                   0.372  (0.121)
Si8    0.267  (0.144)   0.571  (0.117)   0.372  (0.121)                
Na9    0.599  (0.087)   0.340  (0.138)   0.512  (0.111)  0.304  (0.136)
Si10   0.170  (0.143)   0.556  (0.115)   0.300  (0.122)  0.671  (0.083)
Si11   0.181  (0.118)   0.400  (0.139)   0.214  (0.124)  0.514  (0.114)
Na12   0.430  (0.109)   0.238  (0.112)   0.603  (0.081)  0.198  (0.112)
Na13   0.404  (0.098)   0.467  (0.117)   0.809  (0.047)  0.413  (0.109)
Si14   0.341  (0.135)   0.471  (0.125)   0.358  (0.134)  0.641  (0.096)
     Na9      0% ci   Si10    0% ci   Si11    0% ci   Na12     0% ci   Na13    
Si1    0.064  (0.117)  0.627  (0.094)  0.563  (0.102)   0.016  (0.095)   0.114 
Na2    0.518  (0.110)  0.062  (0.121)  0.006  (0.132)   0.569  (0.091)   0.588 
Si3   -0.179  (0.128)  0.195  (0.133)  0.173  (0.134)  -0.196  (0.117)  -0.081 
Na4    0.552  (0.116)  0.216  (0.125)  0.235  (0.128)   0.581  (0.106)   0.779 
Na5    0.599  (0.087)  0.170  (0.143)  0.181  (0.118)   0.430  (0.109)   0.404 
Si6    0.340  (0.138)  0.556  (0.115)  0.400  (0.139)   0.238  (0.112)   0.467 
Na7    0.512  (0.111)  0.300  (0.122)  0.214  (0.124)   0.603  (0.081)   0.809 
Si8    0.304  (0.136)  0.671  (0.083)  0.514  (0.114)   0.198  (0.112)   0.413 
Na9                    0.242  (0.121)  0.353  (0.108)   0.345  (0.122)   0.598 
Si10   0.242  (0.121)                  0.696  (0.094)   0.177  (0.105)   0.327 
Si11   0.353  (0.108)  0.696  (0.094)                   0.057  (0.114)   0.272 
Na12   0.345  (0.122)  0.177  (0.105)  0.057  (0.114)                    0.710 
Na13   0.598  (0.111)  0.327  (0.101)  0.272  (0.114)   0.710  (0.075)         
Si14   0.453  (0.101)  0.411  (0.109)  0.413  (0.134)   0.096  (0.104)   0.395 
     0% ci   Si14    0% ci  
Si1  (0.109)  0.347  (0.117)
Na2  (0.079)  0.172  (0.117)
Si3  (0.124)  0.137  (0.146)
Na4  (0.058)  0.396  (0.117)
Na5  (0.098)  0.341  (0.135)
Si6  (0.117)  0.471  (0.125)
Na7  (0.047)  0.358  (0.134)
Si8  (0.109)  0.641  (0.096)
Na9  (0.111)  0.453  (0.101)
Si10 (0.101)  0.411  (0.109)
Si11 (0.114)  0.413  (0.134)
Na12 (0.075)  0.096  (0.104)
Na13          0.395  (0.096)
Si14 (0.096)                

$Groups$`0`$Hi
     Item H  se     
Si1    0.247 (0.074)
Na2    0.250 (0.071)
Si3   -0.011 (0.094)
Na4    0.372 (0.061)
Na5    0.291 (0.067)
Si6    0.358 (0.072)
Na7    0.389 (0.056)
Si8    0.403 (0.054)
Na9    0.356 (0.052)
Si10   0.355 (0.063)
Si11   0.309 (0.074)
Na12   0.270 (0.065)
Na13   0.432 (0.048)
Si14   0.352 (0.055)

$Groups$`0`$H
 Scale H se     
   0.313 (0.042)


$Groups$`1`
$Groups$`1`$Hij
     Si1     0% ci   Na2      0% ci   Si3      0% ci   Na4     0% ci   Na5     
Si1                    0.087  (0.053)   0.681  (0.038)  0.264  (0.053)   0.081 
Na2   0.087  (0.053)                   -0.034  (0.051)  0.373  (0.052)   0.523 
Si3   0.681  (0.038)  -0.034  (0.051)                   0.151  (0.057)  -0.022 
Na4   0.264  (0.053)   0.373  (0.052)   0.151  (0.057)                   0.451 
Na5   0.081  (0.053)   0.523  (0.041)  -0.022  (0.049)  0.451  (0.052)         
Si6   0.547  (0.044)   0.278  (0.052)   0.337  (0.050)  0.470  (0.045)   0.381 
Na7   0.254  (0.052)   0.445  (0.050)   0.165  (0.052)  0.647  (0.043)   0.514 
Si8   0.574  (0.042)   0.180  (0.051)   0.510  (0.045)  0.303  (0.052)   0.150 
Na9   0.127  (0.053)   0.456  (0.048)   0.074  (0.053)  0.490  (0.049)   0.578 
Si10  0.580  (0.043)   0.179  (0.051)   0.511  (0.043)  0.252  (0.052)   0.173 
Si11  0.537  (0.044)   0.156  (0.052)   0.438  (0.046)  0.230  (0.054)   0.189 
Na12  0.220  (0.050)   0.513  (0.039)   0.086  (0.049)  0.612  (0.043)   0.482 
Na13  0.249  (0.054)   0.461  (0.045)   0.136  (0.055)  0.708  (0.038)   0.531 
Si14  0.532  (0.043)   0.092  (0.053)   0.449  (0.044)  0.326  (0.052)   0.124 
     0% ci   Si6     0% ci   Na7     0% ci   Si8     0% ci   Na9     0% ci  
Si1  (0.053)  0.547  (0.044)  0.254  (0.052)  0.574  (0.042)  0.127  (0.053)
Na2  (0.041)  0.278  (0.052)  0.445  (0.050)  0.180  (0.051)  0.456  (0.048)
Si3  (0.049)  0.337  (0.050)  0.165  (0.052)  0.510  (0.045)  0.074  (0.053)
Na4  (0.052)  0.470  (0.045)  0.647  (0.043)  0.303  (0.052)  0.490  (0.049)
Na5           0.381  (0.049)  0.514  (0.042)  0.150  (0.052)  0.578  (0.041)
Si6  (0.049)                  0.474  (0.046)  0.599  (0.041)  0.401  (0.048)
Na7  (0.042)  0.474  (0.046)                  0.353  (0.049)  0.560  (0.046)
Si8  (0.052)  0.599  (0.041)  0.353  (0.049)                  0.273  (0.052)
Na9  (0.041)  0.401  (0.048)  0.560  (0.046)  0.273  (0.052)                
Si10 (0.049)  0.551  (0.042)  0.321  (0.051)  0.601  (0.037)  0.231  (0.052)
Si11 (0.052)  0.512  (0.043)  0.276  (0.052)  0.517  (0.044)  0.151  (0.054)
Na12 (0.042)  0.375  (0.046)  0.646  (0.040)  0.259  (0.048)  0.444  (0.048)
Na13 (0.045)  0.396  (0.047)  0.699  (0.036)  0.295  (0.051)  0.532  (0.043)
Si14 (0.051)  0.534  (0.042)  0.354  (0.049)  0.685  (0.036)  0.244  (0.054)
     Si10    0% ci   Si11    0% ci   Na12    0% ci   Na13    0% ci   Si14   
Si1   0.580  (0.043)  0.537  (0.044)  0.220  (0.050)  0.249  (0.054)  0.532 
Na2   0.179  (0.051)  0.156  (0.052)  0.513  (0.039)  0.461  (0.045)  0.092 
Si3   0.511  (0.043)  0.438  (0.046)  0.086  (0.049)  0.136  (0.055)  0.449 
Na4   0.252  (0.052)  0.230  (0.054)  0.612  (0.043)  0.708  (0.038)  0.326 
Na5   0.173  (0.049)  0.189  (0.052)  0.482  (0.042)  0.531  (0.045)  0.124 
Si6   0.551  (0.042)  0.512  (0.043)  0.375  (0.046)  0.396  (0.047)  0.534 
Na7   0.321  (0.051)  0.276  (0.052)  0.646  (0.040)  0.699  (0.036)  0.354 
Si8   0.601  (0.037)  0.517  (0.044)  0.259  (0.048)  0.295  (0.051)  0.685 
Na9   0.231  (0.052)  0.151  (0.054)  0.444  (0.048)  0.532  (0.043)  0.244 
Si10                  0.529  (0.042)  0.249  (0.049)  0.207  (0.053)  0.542 
Si11  0.529  (0.042)                  0.231  (0.048)  0.239  (0.057)  0.457 
Na12  0.249  (0.049)  0.231  (0.048)                  0.666  (0.035)  0.267 
Na13  0.207  (0.053)  0.239  (0.057)  0.666  (0.035)                  0.291 
Si14  0.542  (0.042)  0.457  (0.047)  0.267  (0.049)  0.291  (0.052)        
     0% ci  
Si1  (0.043)
Na2  (0.053)
Si3  (0.044)
Na4  (0.052)
Na5  (0.051)
Si6  (0.042)
Na7  (0.049)
Si8  (0.036)
Na9  (0.054)
Si10 (0.042)
Si11 (0.047)
Na12 (0.049)
Na13 (0.052)
Si14        

$Groups$`1`$Hi
     Item H  se     
Si1    0.368 (0.026)
Na2    0.281 (0.030)
Si3    0.266 (0.029)
Na4    0.406 (0.029)
Na5    0.313 (0.030)
Si6    0.451 (0.025)
Na7    0.438 (0.026)
Si8    0.410 (0.026)
Na9    0.351 (0.029)
Si10   0.379 (0.025)
Si11   0.346 (0.027)
Na12   0.379 (0.025)
Na13   0.417 (0.027)
Si14   0.379 (0.026)

$Groups$`1`$H
 Scale H se     
   0.369 (0.020)

Per uomini e donne separatamente, si possono calcolare i percentili di rango per NA, SI e DS14. In una figura, Sijtsma and van der Ark [SvdA17] mostrano che per NA e DS14, lo stesso punteggio al test porta a un percentile di rango più elevato per gli uomini rispetto alle donne. Tuttavia, per DS14 gli intervalli di confidenza sovrapposti suggeriscono che la maggior parte delle differenze di punteggio tra uomini e donne non sono marcate. Per quanto riguarda SI, le donne hanno punteggi percentile costantemente più alti, ma le differenze sono piccole. Dato il minor numero di osservazioni, gli intervalli di confidenza delle donne sono più ampi.

67.10. Step 10#

  1. Confronto tra gruppi. Se il campione contiene sottogruppi significativi, si può indagare se la composizione delle scale e le proprietà della scala (passi 4–9) possono essere generalizzate tra i sottogruppi. Se la composizione della scala e le proprietà variano tra i gruppi, la conoscenza di questa variazione può essere utile nell’interpretazione delle prestazioni dei test degli individui e nella ricerca in cui caratteristiche di gruppo come i punteggi medi della scala e le correlazioni dei punteggi della scala con altre variabili sono di interesse.

coefH(itemsScores[, Na], group.var = male)
$Hij
     Na2     se      Na4     se      Na5     se      Na7     se      Na9    
Na2                   0.391  (0.048)  0.522  (0.039)  0.465  (0.045)  0.468 
Na4   0.391  (0.048)                  0.439  (0.047)  0.661  (0.039)  0.503 
Na5   0.522  (0.039)  0.439  (0.047)                  0.499  (0.040)  0.581 
Na7   0.465  (0.045)  0.661  (0.039)  0.499  (0.040)                  0.555 
Na9   0.468  (0.045)  0.503  (0.045)  0.581  (0.038)  0.555  (0.043)        
Na12  0.532  (0.035)  0.616  (0.040)  0.475  (0.040)  0.648  (0.036)  0.440 
Na13  0.493  (0.040)  0.725  (0.033)  0.508  (0.042)  0.722  (0.031)  0.548 
     se      Na12    se      Na13    se     
Na2  (0.045)  0.532  (0.035)  0.493  (0.040)
Na4  (0.045)  0.616  (0.040)  0.725  (0.033)
Na5  (0.038)  0.475  (0.040)  0.508  (0.042)
Na7  (0.043)  0.648  (0.036)  0.722  (0.031)
Na9           0.440  (0.045)  0.548  (0.041)
Na12 (0.045)                  0.685  (0.031)
Na13 (0.041)  0.685  (0.031)                

$Hi
     Item H  se     
Na2    0.483 (0.028)
Na4    0.557 (0.030)
Na5    0.503 (0.028)
Na7    0.591 (0.026)
Na9    0.515 (0.029)
Na12   0.562 (0.025)
Na13   0.616 (0.024)

$H
Scale H      se 
  0.546 (0.022) 

$covHij
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 0.0022989144 3.556849e-04 0.0010052778 0.0007801401 5.414757e-04
 [2,] 0.0003556849 1.522519e-03 0.0004450386 0.0007497889 3.237255e-04
 [3,] 0.0010052778 4.450386e-04 0.0020145721 0.0008348416 6.037465e-04
 [4,] 0.0007801401 7.497889e-04 0.0008348416 0.0020011917 2.133779e-04
 [5,] 0.0005414757 3.237255e-04 0.0006037465 0.0002133779 1.252743e-03
 [6,] 0.0010327520 4.223827e-04 0.0009859993 0.0007096234 5.688558e-04
 [7,] 0.0009265585 2.924636e-04 0.0005067649 0.0001641998 1.687561e-04
 [8,] 0.0005798666 2.057109e-04 0.0003789838 0.0004366579 2.382688e-05
 [9,] 0.0006313731 2.724419e-05 0.0005297773 0.0003579973 2.259319e-04
[10,] 0.0011515255 1.166517e-04 0.0002853404 0.0004386392 1.252333e-04
[11,] 0.0006354989 1.030805e-04 0.0002116375 0.0002939252 3.066150e-06
[12,] 0.0004848910 4.089064e-04 0.0007576294 0.0003694439 2.548367e-04
[13,] 0.0001304570 3.282199e-04 0.0002764868 0.0006001385 1.110339e-04
[14,] 0.0003022050 6.120800e-04 0.0003822614 0.0004062380 5.161931e-04
[15,] 0.0004406155 4.664556e-04 0.0003028667 0.0003416939 2.205691e-04
[16,] 0.0005615340 2.062509e-04 0.0005319594 0.0004577893 1.855316e-04
[17,] 0.0002657088 1.385843e-04 0.0007070134 0.0003594403 1.705285e-04
[18,] 0.0002539180 2.503942e-05 0.0003831389 0.0001757285 1.111084e-04
[19,] 0.0005975976 3.847111e-04 0.0005597349 0.0009951346 3.942800e-04
[20,] 0.0005391523 2.356209e-04 0.0004123386 0.0006353813 2.340805e-04
[21,] 0.0002714302 1.195848e-04 0.0003704439 0.0002956231 2.230986e-04
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 0.0010327520 0.0009265585 5.798666e-04 6.313731e-04 0.0011515255
 [2,] 0.0004223827 0.0002924636 2.057109e-04 2.724419e-05 0.0001166517
 [3,] 0.0009859993 0.0005067649 3.789838e-04 5.297773e-04 0.0002853404
 [4,] 0.0007096234 0.0001641998 4.366579e-04 3.579973e-04 0.0004386392
 [5,] 0.0005688558 0.0001687561 2.382688e-05 2.259319e-04 0.0001252333
 [6,] 0.0015846387 0.0003935561 1.920062e-04 3.838401e-04 0.0002211614
 [7,] 0.0003935561 0.0021757415 6.996295e-04 1.169290e-03 0.0006095637
 [8,] 0.0001920062 0.0006996295 1.498185e-03 6.613515e-04 0.0007660527
 [9,] 0.0003838401 0.0011692901 6.613515e-04 2.069302e-03 0.0004557181
[10,] 0.0002211614 0.0006095637 7.660527e-04 4.557181e-04 0.0015846511
[11,] 0.0001713933 0.0005058242 7.652694e-04 5.736487e-04 0.0007183495
[12,] 0.0002827819 0.0008792980 3.867651e-04 5.449631e-04 0.0003061978
[13,] 0.0002354823 0.0006316330 2.183373e-04 3.339671e-04 0.0001292073
[14,] 0.0003047019 0.0007142048 2.929320e-04 3.818841e-04 0.0003075222
[15,] 0.0006623985 0.0010685493 3.329102e-04 5.349169e-04 0.0001767506
[16,] 0.0003197038 0.0005806718 5.702923e-04 8.745371e-04 0.0003711308
[17,] 0.0003423557 0.0003033842 4.373767e-04 3.304571e-04 0.0005130346
[18,] 0.0003252324 0.0003000955 5.448684e-04 3.037242e-04 0.0002086832
[19,] 0.0004934985 0.0004892996 4.631575e-04 7.818722e-04 0.0006107260
[20,] 0.0005399889 0.0005728860 4.015112e-04 1.064776e-03 0.0003366808
[21,] 0.0005161993 0.0001559809 2.597643e-04 2.100049e-04 0.0005114014
             [,11]        [,12]        [,13]        [,14]        [,15]
 [1,] 6.354989e-04 4.848910e-04 0.0001304570 3.022050e-04 4.406155e-04
 [2,] 1.030805e-04 4.089064e-04 0.0003282199 6.120800e-04 4.664556e-04
 [3,] 2.116375e-04 7.576294e-04 0.0002764868 3.822614e-04 3.028667e-04
 [4,] 2.939252e-04 3.694439e-04 0.0006001385 4.062380e-04 3.416939e-04
 [5,] 3.066150e-06 2.548367e-04 0.0001110339 5.161931e-04 2.205691e-04
 [6,] 1.713933e-04 2.827819e-04 0.0002354823 3.047019e-04 6.623985e-04
 [7,] 5.058242e-04 8.792980e-04 0.0006316330 7.142048e-04 1.068549e-03
 [8,] 7.652694e-04 3.867651e-04 0.0002183373 2.929320e-04 3.329102e-04
 [9,] 5.736487e-04 5.449631e-04 0.0003339671 3.818841e-04 5.349169e-04
[10,] 7.183495e-04 3.061978e-04 0.0001292073 3.075222e-04 1.767506e-04
[11,] 1.095457e-03 2.360418e-04 0.0001053015 1.287099e-04 2.507401e-04
[12,] 2.360418e-04 1.638270e-03 0.0004761083 8.155179e-04 9.520111e-04
[13,] 1.053015e-04 4.761083e-04 0.0014120850 2.918993e-04 5.221017e-04
[14,] 1.287099e-04 8.155179e-04 0.0002918993 1.601433e-03 7.607755e-04
[15,] 2.507401e-04 9.520111e-04 0.0005221017 7.607755e-04 1.728808e-03
[16,] 3.259419e-04 8.933070e-04 0.0003351606 4.722255e-04 6.352700e-04
[17,] 2.258234e-04 3.189966e-04 0.0001774220 3.426430e-04 8.507645e-05
[18,] 3.412301e-04 3.520174e-04 0.0002307829 3.587954e-05 3.314236e-04
[19,] 3.483552e-04 5.709602e-04 0.0002905545 9.107817e-04 5.868172e-04
[20,] 4.162964e-04 6.569933e-04 0.0003601311 5.128423e-04 8.315401e-04
[21,] 3.203275e-04 8.104277e-05 0.0001796005 2.713080e-04 3.432581e-04
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 5.615340e-04 2.657088e-04 2.539180e-04 0.0005975976 0.0005391523
 [2,] 2.062509e-04 1.385843e-04 2.503942e-05 0.0003847111 0.0002356209
 [3,] 5.319594e-04 7.070134e-04 3.831389e-04 0.0005597349 0.0004123386
 [4,] 4.577893e-04 3.594403e-04 1.757285e-04 0.0009951346 0.0006353813
 [5,] 1.855316e-04 1.705285e-04 1.111084e-04 0.0003942800 0.0002340805
 [6,] 3.197038e-04 3.423557e-04 3.252324e-04 0.0004934985 0.0005399889
 [7,] 5.806718e-04 3.033842e-04 3.000955e-04 0.0004892996 0.0005728860
 [8,] 5.702923e-04 4.373767e-04 5.448684e-04 0.0004631575 0.0004015112
 [9,] 8.745371e-04 3.304571e-04 3.037242e-04 0.0007818722 0.0010647764
[10,] 3.711308e-04 5.130346e-04 2.086832e-04 0.0006107260 0.0003366808
[11,] 3.259419e-04 2.258234e-04 3.412301e-04 0.0003483552 0.0004162964
[12,] 8.933070e-04 3.189966e-04 3.520174e-04 0.0005709602 0.0006569933
[13,] 3.351606e-04 1.774220e-04 2.307829e-04 0.0002905545 0.0003601311
[14,] 4.722255e-04 3.426430e-04 3.587954e-05 0.0009107817 0.0005128423
[15,] 6.352700e-04 8.507645e-05 3.314236e-04 0.0005868172 0.0008315401
[16,] 1.815778e-03 1.593929e-04 4.435823e-04 0.0008161650 0.0010984076
[17,] 1.593929e-04 1.284653e-03 3.534202e-04 0.0006703988 0.0001603725
[18,] 4.435823e-04 3.534202e-04 9.484849e-04 0.0001866630 0.0004338891
[19,] 8.161650e-04 6.703988e-04 1.866630e-04 0.0020466051 0.0010073351
[20,] 1.098408e-03 1.603725e-04 4.338891e-04 0.0010073351 0.0016866111
[21,] 5.837058e-05 5.632637e-04 3.272104e-04 0.0004892206 0.0002115278
             [,21]
 [1,] 2.714302e-04
 [2,] 1.195848e-04
 [3,] 3.704439e-04
 [4,] 2.956231e-04
 [5,] 2.230986e-04
 [6,] 5.161993e-04
 [7,] 1.559809e-04
 [8,] 2.597643e-04
 [9,] 2.100049e-04
[10,] 5.114014e-04
[11,] 3.203275e-04
[12,] 8.104277e-05
[13,] 1.796005e-04
[14,] 2.713080e-04
[15,] 3.432581e-04
[16,] 5.837058e-05
[17,] 5.632637e-04
[18,] 3.272104e-04
[19,] 4.892206e-04
[20,] 2.115278e-04
[21,] 9.677864e-04

$covHi
             [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 0.0007936386 0.0004303348 0.0004343871 0.0004279487 0.0004653750
[2,] 0.0004303348 0.0009277628 0.0004418741 0.0005147918 0.0005365340
[3,] 0.0004343871 0.0004418741 0.0007830148 0.0004287359 0.0005138697
[4,] 0.0004279487 0.0005147918 0.0004287359 0.0006750199 0.0005097711
[5,] 0.0004653750 0.0005365340 0.0005138697 0.0005097711 0.0008657743
[6,] 0.0004398289 0.0004324170 0.0003986552 0.0004105594 0.0004411029
[7,] 0.0003926113 0.0004640153 0.0003907992 0.0004252847 0.0004690683
             [,6]         [,7]
[1,] 0.0004398289 0.0003926113
[2,] 0.0004324170 0.0004640153
[3,] 0.0003986552 0.0003907992
[4,] 0.0004105594 0.0004252847
[5,] 0.0004411029 0.0004690683
[6,] 0.0006177435 0.0003637520
[7,] 0.0003637520 0.0005604125

$covH
             [,1]
[1,] 0.0004901546

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Na2     0% ci   Na4     0% ci   Na5     0% ci   Na7     0% ci   Na9    
Na2                   0.441  (0.117)  0.508  (0.114)  0.543  (0.092)  0.518 
Na4   0.441  (0.117)                  0.371  (0.106)  0.720  (0.088)  0.552 
Na5   0.508  (0.114)  0.371  (0.106)                  0.401  (0.123)  0.599 
Na7   0.543  (0.092)  0.720  (0.088)  0.401  (0.123)                  0.512 
Na9   0.518  (0.110)  0.552  (0.116)  0.599  (0.087)  0.512  (0.111)        
Na12  0.569  (0.091)  0.581  (0.106)  0.430  (0.109)  0.603  (0.081)  0.345 
Na13  0.588  (0.079)  0.779  (0.058)  0.404  (0.098)  0.809  (0.047)  0.598 
     0% ci   Na12    0% ci   Na13    0% ci  
Na2  (0.110)  0.569  (0.091)  0.588  (0.079)
Na4  (0.116)  0.581  (0.106)  0.779  (0.058)
Na5  (0.087)  0.430  (0.109)  0.404  (0.098)
Na7  (0.111)  0.603  (0.081)  0.809  (0.047)
Na9           0.345  (0.122)  0.598  (0.111)
Na12 (0.122)                  0.710  (0.075)
Na13 (0.111)  0.710  (0.075)                

$Groups$`0`$Hi
     Item H  se     
Na2    0.530 (0.065)
Na4    0.583 (0.067)
Na5    0.449 (0.084)
Na7    0.608 (0.058)
Na9    0.527 (0.084)
Na12   0.544 (0.065)
Na13   0.648 (0.049)

$Groups$`0`$H
 Scale H se     
   0.557 (0.057)


$Groups$`1`
$Groups$`1`$Hij
     Na2     0% ci   Na4     0% ci   Na5     0% ci   Na7     0% ci   Na9    
Na2                   0.373  (0.052)  0.523  (0.041)  0.445  (0.050)  0.456 
Na4   0.373  (0.052)                  0.451  (0.052)  0.647  (0.043)  0.490 
Na5   0.523  (0.041)  0.451  (0.052)                  0.514  (0.042)  0.578 
Na7   0.445  (0.050)  0.647  (0.043)  0.514  (0.042)                  0.560 
Na9   0.456  (0.048)  0.490  (0.049)  0.578  (0.041)  0.560  (0.046)        
Na12  0.513  (0.039)  0.612  (0.043)  0.482  (0.042)  0.646  (0.040)  0.444 
Na13  0.461  (0.045)  0.708  (0.038)  0.531  (0.045)  0.699  (0.036)  0.532 
     0% ci   Na12    0% ci   Na13    0% ci  
Na2  (0.048)  0.513  (0.039)  0.461  (0.045)
Na4  (0.049)  0.612  (0.043)  0.708  (0.038)
Na5  (0.041)  0.482  (0.042)  0.531  (0.045)
Na7  (0.046)  0.646  (0.040)  0.699  (0.036)
Na9           0.444  (0.048)  0.532  (0.043)
Na12 (0.048)                  0.666  (0.035)
Na13 (0.043)  0.666  (0.035)                

$Groups$`1`$Hi
     Item H  se     
Na2    0.467 (0.031)
Na4    0.547 (0.034)
Na5    0.512 (0.029)
Na7    0.583 (0.029)
Na9    0.509 (0.031)
Na12   0.555 (0.027)
Na13   0.601 (0.027)

$Groups$`1`$H
 Scale H se     
   0.538 (0.024)
coefH(itemsScores[, Si], group.var = male)
$Hij
     Si1     se      Si3     se      Si6     se      Si8     se      Si10   
Si1                   0.671  (0.036)  0.515  (0.043)  0.566  (0.040)  0.588 
Si3   0.671  (0.036)                  0.277  (0.049)  0.469  (0.044)  0.468 
Si6   0.515  (0.043)  0.277  (0.049)                  0.595  (0.039)  0.551 
Si8   0.566  (0.040)  0.469  (0.044)  0.595  (0.039)                  0.611 
Si10  0.588  (0.039)  0.468  (0.042)  0.551  (0.040)  0.611  (0.034)        
Si11  0.543  (0.040)  0.403  (0.044)  0.493  (0.043)  0.516  (0.041)  0.554 
Si14  0.506  (0.041)  0.410  (0.044)  0.526  (0.040)  0.680  (0.033)  0.523 
     se      Si11    se      Si14    se     
Si1  (0.039)  0.543  (0.040)  0.506  (0.041)
Si3  (0.042)  0.403  (0.044)  0.410  (0.044)
Si6  (0.040)  0.493  (0.043)  0.526  (0.040)
Si8  (0.034)  0.516  (0.041)  0.680  (0.033)
Si10          0.554  (0.038)  0.523  (0.039)
Si11 (0.038)                  0.451  (0.045)
Si14 (0.039)  0.451  (0.045)                

$Hi
     Item H  se     
Si1    0.566 (0.026)
Si3    0.451 (0.031)
Si6    0.494 (0.031)
Si8    0.573 (0.025)
Si10   0.549 (0.024)
Si11   0.494 (0.029)
Si14   0.518 (0.028)

$H
Scale H      se 
  0.521 (0.022) 

$covHij
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 1.326234e-03 3.148230e-05 0.0003423128 0.0003894712 0.0004268642
 [2,] 3.148230e-05 1.822688e-03 0.0007018545 0.0005715538 0.0004868289
 [3,] 3.423128e-04 7.018545e-04 0.0015823404 0.0008274935 0.0004407275
 [4,] 3.894712e-04 5.715538e-04 0.0008274935 0.0014996080 0.0005850977
 [5,] 4.268642e-04 4.868289e-04 0.0004407275 0.0005850977 0.0016027152
 [6,] 2.387396e-04 5.128700e-04 0.0008772929 0.0006510906 0.0003378176
 [7,] 7.331617e-04 1.451832e-03 0.0006355201 0.0005320106 0.0004183089
 [8,] 5.533883e-04 4.994686e-04 0.0009478469 0.0005276416 0.0001007506
 [9,] 5.041181e-04 4.236027e-04 0.0005162177 0.0008249585 0.0002356199
[10,] 6.626651e-04 2.863598e-04 0.0001412691 0.0002272101 0.0008740511
[11,] 5.745834e-04 3.584135e-04 0.0005068683 0.0004482119 0.0001233220
[12,] 1.370246e-04 8.228506e-04 0.0004681540 0.0003085023 0.0002401868
[13,] 1.395707e-04 8.293709e-04 0.0003388724 0.0003648660 0.0001140969
[14,] 4.144024e-05 8.137073e-04 0.0003217256 0.0001090130 0.0005304653
[15,] 1.065186e-04 6.932608e-04 0.0003275542 0.0003227576 0.0003272020
[16,] 1.929262e-04 3.007363e-04 0.0004967575 0.0003867450 0.0001979057
[17,] 2.143675e-05 3.543813e-04 0.0007628287 0.0003646496 0.0006124136
[18,] 7.494426e-05 2.210940e-04 0.0003861432 0.0001951433 0.0001821352
[19,] 3.410130e-05 7.432037e-05 0.0002758960 0.0004158360 0.0005040973
[20,] 1.856760e-04 3.876625e-04 0.0003531423 0.0003934886 0.0002614172
[21,] 8.913423e-06 4.811298e-04 0.0004626634 0.0003652616 0.0006662474
              [,6]         [,7]         [,8]          [,9]         [,10]
 [1,] 0.0002387396 0.0007331617 5.533883e-04  5.041181e-04  6.626651e-04
 [2,] 0.0005128700 0.0014518319 4.994686e-04  4.236027e-04  2.863598e-04
 [3,] 0.0008772929 0.0006355201 9.478469e-04  5.162177e-04  1.412691e-04
 [4,] 0.0006510906 0.0005320106 5.276416e-04  8.249585e-04  2.272101e-04
 [5,] 0.0003378176 0.0004183089 1.007506e-04  2.356199e-04  8.740511e-04
 [6,] 0.0016939188 0.0004890351 4.983521e-04  4.158569e-04  1.352208e-04
 [7,] 0.0004890351 0.0024468732 1.108801e-03  8.892630e-04  9.209044e-04
 [8,] 0.0004983521 0.0011088006 1.939729e-03  8.865508e-04  6.959694e-04
 [9,] 0.0004158569 0.0008892630 8.865508e-04  1.769998e-03  7.871405e-04
[10,] 0.0001352208 0.0009209044 6.959694e-04  7.871405e-04  1.962134e-03
[11,] 0.0009287999 0.0009070149 1.138977e-03  7.359981e-04  6.945996e-04
[12,] 0.0002803957 0.0008456847 1.058809e-04  1.867356e-04  1.212024e-04
[13,] 0.0003489007 0.0008222433 2.101908e-04  3.210863e-06 -5.547986e-05
[14,] 0.0003795883 0.0008492032 2.005457e-04 -7.892562e-05  1.296154e-04
[15,] 0.0005283547 0.0006696172 4.552146e-05  1.926017e-04  1.761486e-04
[16,] 0.0003371062 0.0003824320 3.805428e-04  3.653072e-04  2.514581e-04
[17,] 0.0004406999 0.0003950374 5.975313e-04  3.519937e-04  5.951065e-04
[18,] 0.0004454892 0.0002034270 3.908572e-04  1.849098e-04  1.161549e-04
[19,] 0.0002515276 0.0001121089 2.721215e-04  3.210100e-04  5.052162e-04
[20,] 0.0007914413 0.0003963630 3.066623e-04  3.802799e-04  3.333191e-04
[21,] 0.0007611678 0.0004232794 2.941310e-04  3.603859e-04  5.613659e-04
             [,11]        [,12]         [,13]         [,14]        [,15]
 [1,] 5.745834e-04 1.370246e-04  1.395707e-04  4.144024e-05 1.065186e-04
 [2,] 3.584135e-04 8.228506e-04  8.293709e-04  8.137073e-04 6.932608e-04
 [3,] 5.068683e-04 4.681540e-04  3.388724e-04  3.217256e-04 3.275542e-04
 [4,] 4.482119e-04 3.085023e-04  3.648660e-04  1.090130e-04 3.227576e-04
 [5,] 1.233220e-04 2.401868e-04  1.140969e-04  5.304653e-04 3.272020e-04
 [6,] 9.287999e-04 2.803957e-04  3.489007e-04  3.795883e-04 5.283547e-04
 [7,] 9.070149e-04 8.456847e-04  8.222433e-04  8.492032e-04 6.696172e-04
 [8,] 1.138977e-03 1.058809e-04  2.101908e-04  2.005457e-04 4.552146e-05
 [9,] 7.359981e-04 1.867356e-04  3.210863e-06 -7.892562e-05 1.926017e-04
[10,] 6.945996e-04 1.212024e-04 -5.547986e-05  1.296154e-04 1.761486e-04
[11,] 1.918183e-03 4.847524e-05  2.123517e-04  2.278268e-04 1.062812e-04
[12,] 4.847524e-05 1.552705e-03  7.503131e-04  6.928588e-04 8.604778e-04
[13,] 2.123517e-04 7.503131e-04  1.589336e-03  8.930087e-04 4.930575e-04
[14,] 2.278268e-04 6.928588e-04  8.930087e-04  1.867909e-03 3.592243e-04
[15,] 1.062812e-04 8.604778e-04  4.930575e-04  3.592243e-04 1.594745e-03
[16,] 2.805824e-04 4.085177e-04  4.861942e-04  2.032543e-04 2.278487e-04
[17,] 3.219529e-04 3.801083e-04  2.342123e-04  6.915337e-04 1.881575e-04
[18,] 3.939816e-04 3.522066e-04  1.303340e-04  8.959822e-05 5.339055e-04
[19,] 3.241841e-04 9.995056e-05  3.974028e-04  5.274966e-04 5.290067e-05
[20,] 5.817733e-04 2.659919e-04  3.289984e-04  1.601106e-04 6.777408e-04
[21,] 5.490426e-04 2.610918e-04  2.200481e-04  7.613368e-04 6.030693e-04
             [,16]        [,17]        [,18]        [,19]        [,20]
 [1,] 0.0001929262 2.143675e-05 7.494426e-05 3.410130e-05 0.0001856760
 [2,] 0.0003007363 3.543813e-04 2.210940e-04 7.432037e-05 0.0003876625
 [3,] 0.0004967575 7.628287e-04 3.861432e-04 2.758960e-04 0.0003531423
 [4,] 0.0003867450 3.646496e-04 1.951433e-04 4.158360e-04 0.0003934886
 [5,] 0.0001979057 6.124136e-04 1.821352e-04 5.040973e-04 0.0002614172
 [6,] 0.0003371062 4.406999e-04 4.454892e-04 2.515276e-04 0.0007914413
 [7,] 0.0003824320 3.950374e-04 2.034270e-04 1.121089e-04 0.0003963630
 [8,] 0.0003805428 5.975313e-04 3.908572e-04 2.721215e-04 0.0003066623
 [9,] 0.0003653072 3.519937e-04 1.849098e-04 3.210100e-04 0.0003802799
[10,] 0.0002514581 5.951065e-04 1.161549e-04 5.052162e-04 0.0003333191
[11,] 0.0002805824 3.219529e-04 3.939816e-04 3.241841e-04 0.0005817733
[12,] 0.0004085177 3.801083e-04 3.522066e-04 9.995056e-05 0.0002659919
[13,] 0.0004861942 2.342123e-04 1.303340e-04 3.974028e-04 0.0003289984
[14,] 0.0002032543 6.915337e-04 8.959822e-05 5.274966e-04 0.0001601106
[15,] 0.0002278487 1.881575e-04 5.339055e-04 5.290067e-05 0.0006777408
[16,] 0.0011319410 6.597845e-04 3.378432e-04 2.733794e-04 0.0005961831
[17,] 0.0006597845 1.709023e-03 3.148906e-04 7.107327e-04 0.0004110028
[18,] 0.0003378432 3.148906e-04 1.121554e-03 1.553415e-04 0.0005613125
[19,] 0.0002733794 7.107327e-04 1.553415e-04 1.477243e-03 0.0002347616
[20,] 0.0005961831 4.110028e-04 5.613125e-04 2.347616e-04 0.0015446835
[21,] 0.0004232531 1.089428e-03 4.414152e-04 6.733900e-04 0.0008475472
             [,21]
 [1,] 8.913423e-06
 [2,] 4.811298e-04
 [3,] 4.626634e-04
 [4,] 3.652616e-04
 [5,] 6.662474e-04
 [6,] 7.611678e-04
 [7,] 4.232794e-04
 [8,] 2.941310e-04
 [9,] 3.603859e-04
[10,] 5.613659e-04
[11,] 5.490426e-04
[12,] 2.610918e-04
[13,] 2.200481e-04
[14,] 7.613368e-04
[15,] 6.030693e-04
[16,] 4.232531e-04
[17,] 1.089428e-03
[18,] 4.414152e-04
[19,] 6.733900e-04
[20,] 8.475472e-04
[21,] 1.985525e-03

$covHi
             [,1]         [,2]         [,3]         [,4]         [,5]
[1,] 0.0006807785 0.0005123966 0.0004796531 0.0004503299 0.0004347937
[2,] 0.0005123966 0.0009839775 0.0004356884 0.0004590853 0.0004434675
[3,] 0.0004796531 0.0004356884 0.0009666859 0.0004585805 0.0004173673
[4,] 0.0004503299 0.0004590853 0.0004585805 0.0006409695 0.0004226465
[5,] 0.0004347937 0.0004434675 0.0004173673 0.0004226465 0.0005748214
[6,] 0.0004140468 0.0004309778 0.0004171204 0.0004103270 0.0004028547
[7,] 0.0004442039 0.0004375897 0.0004333364 0.0004463414 0.0004259015
             [,6]         [,7]
[1,] 0.0004140468 0.0004442039
[2,] 0.0004309778 0.0004375897
[3,] 0.0004171204 0.0004333364
[4,] 0.0004103270 0.0004463414
[5,] 0.0004028547 0.0004259015
[6,] 0.0008178897 0.0004142683
[7,] 0.0004142683 0.0007626027

$covH
             [,1]
[1,] 0.0004876375

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Si1     0% ci   Si3      0% ci   Si6      0% ci   Si8     0% ci   Si10   
Si1                    0.598  (0.119)   0.354  (0.122)  0.512  (0.114)  0.627 
Si3   0.598  (0.119)                   -0.058  (0.149)  0.215  (0.142)  0.195 
Si6   0.354  (0.122)  -0.058  (0.149)                   0.571  (0.117)  0.556 
Si8   0.512  (0.114)   0.215  (0.142)   0.571  (0.117)                  0.671 
Si10  0.627  (0.094)   0.195  (0.133)   0.556  (0.115)  0.671  (0.083)        
Si11  0.563  (0.102)   0.173  (0.134)   0.400  (0.139)  0.514  (0.114)  0.696 
Si14  0.347  (0.117)   0.137  (0.146)   0.471  (0.125)  0.641  (0.096)  0.411 
     0% ci   Si11    0% ci   Si14    0% ci  
Si1  (0.094)  0.563  (0.102)  0.347  (0.117)
Si3  (0.133)  0.173  (0.134)  0.137  (0.146)
Si6  (0.115)  0.400  (0.139)  0.471  (0.125)
Si8  (0.083)  0.514  (0.114)  0.641  (0.096)
Si10          0.696  (0.094)  0.411  (0.109)
Si11 (0.094)                  0.413  (0.134)
Si14 (0.109)  0.413  (0.134)                

$Groups$`0`$Hi
     Item H  se     
Si1    0.498 (0.076)
Si3    0.205 (0.113)
Si6    0.388 (0.096)
Si8    0.523 (0.065)
Si10   0.526 (0.063)
Si11   0.462 (0.087)
Si14   0.404 (0.084)

$Groups$`0`$H
 Scale H se     
   0.431 (0.070)


$Groups$`1`
$Groups$`1`$Hij
     Si1     0% ci   Si3     0% ci   Si6     0% ci   Si8     0% ci   Si10   
Si1                   0.681  (0.038)  0.547  (0.044)  0.574  (0.042)  0.580 
Si3   0.681  (0.038)                  0.337  (0.050)  0.510  (0.045)  0.511 
Si6   0.547  (0.044)  0.337  (0.050)                  0.599  (0.041)  0.551 
Si8   0.574  (0.042)  0.510  (0.045)  0.599  (0.041)                  0.601 
Si10  0.580  (0.043)  0.511  (0.043)  0.551  (0.042)  0.601  (0.037)        
Si11  0.537  (0.044)  0.438  (0.046)  0.512  (0.043)  0.517  (0.044)  0.529 
Si14  0.532  (0.043)  0.449  (0.044)  0.534  (0.042)  0.685  (0.036)  0.542 
     0% ci   Si11    0% ci   Si14    0% ci  
Si1  (0.043)  0.537  (0.044)  0.532  (0.043)
Si3  (0.043)  0.438  (0.046)  0.449  (0.044)
Si6  (0.042)  0.512  (0.043)  0.534  (0.042)
Si8  (0.037)  0.517  (0.044)  0.685  (0.036)
Si10          0.529  (0.042)  0.542  (0.042)
Si11 (0.042)                  0.457  (0.047)
Si14 (0.042)  0.457  (0.047)                

$Groups$`1`$Hi
     Item H  se     
Si1    0.576 (0.028)
Si3    0.489 (0.031)
Si6    0.514 (0.032)
Si8    0.581 (0.027)
Si10   0.552 (0.026)
Si11   0.498 (0.030)
Si14   0.535 (0.029)

$Groups$`1`$H
 Scale H se     
   0.536 (0.023)
coefH(itemsScores[, ], group.var = male)
$Hij
     Si1     se      Na2      se      Si3      se      Na4     se      Na5     
Si1                    0.050  (0.049)   0.671  (0.036)  0.219  (0.051)   0.092 
Na2   0.050  (0.049)                   -0.062  (0.047)  0.391  (0.048)   0.522 
Si3   0.671  (0.036)  -0.062  (0.047)                   0.097  (0.053)  -0.059 
Na4   0.219  (0.051)   0.391  (0.048)   0.097  (0.053)                   0.439 
Na5   0.092  (0.049)   0.522  (0.039)  -0.059  (0.046)  0.439  (0.047)         
Si6   0.515  (0.043)   0.270  (0.048)   0.277  (0.049)  0.450  (0.044)   0.368 
Na7   0.211  (0.050)   0.465  (0.045)   0.114  (0.049)  0.661  (0.039)   0.499 
Si8   0.566  (0.040)   0.176  (0.048)   0.469  (0.044)  0.318  (0.048)   0.165 
Na9   0.112  (0.050)   0.468  (0.045)   0.033  (0.050)  0.503  (0.045)   0.581 
Si10  0.588  (0.039)   0.156  (0.048)   0.468  (0.042)  0.242  (0.048)   0.172 
Si11  0.543  (0.040)   0.129  (0.050)   0.403  (0.044)  0.225  (0.051)   0.188 
Na12  0.172  (0.048)   0.532  (0.035)   0.042  (0.047)  0.616  (0.040)   0.475 
Na13  0.212  (0.052)   0.493  (0.040)   0.091  (0.052)  0.725  (0.033)   0.508 
Si14  0.506  (0.041)   0.104  (0.049)   0.410  (0.044)  0.337  (0.047)   0.148 
     se      Si6     se      Na7     se      Si8     se      Na9     se     
Si1  (0.049)  0.515  (0.043)  0.211  (0.050)  0.566  (0.040)  0.112  (0.050)
Na2  (0.039)  0.270  (0.048)  0.465  (0.045)  0.176  (0.048)  0.468  (0.045)
Si3  (0.046)  0.277  (0.049)  0.114  (0.049)  0.469  (0.044)  0.033  (0.050)
Na4  (0.047)  0.450  (0.044)  0.661  (0.039)  0.318  (0.048)  0.503  (0.045)
Na5           0.368  (0.047)  0.499  (0.040)  0.165  (0.049)  0.581  (0.038)
Si6  (0.047)                  0.468  (0.044)  0.595  (0.039)  0.392  (0.046)
Na7  (0.040)  0.468  (0.044)                  0.355  (0.046)  0.555  (0.043)
Si8  (0.049)  0.595  (0.039)  0.355  (0.046)                  0.277  (0.049)
Na9  (0.038)  0.392  (0.046)  0.555  (0.043)  0.277  (0.049)                
Si10 (0.046)  0.551  (0.040)  0.314  (0.047)  0.611  (0.034)  0.230  (0.048)
Si11 (0.047)  0.493  (0.043)  0.260  (0.049)  0.516  (0.041)  0.181  (0.049)
Na12 (0.040)  0.357  (0.043)  0.648  (0.036)  0.249  (0.045)  0.440  (0.045)
Na13 (0.042)  0.413  (0.045)  0.722  (0.031)  0.315  (0.047)  0.548  (0.041)
Si14 (0.048)  0.526  (0.040)  0.356  (0.046)  0.680  (0.033)  0.273  (0.049)
     Si10    se      Si11    se      Na12    se      Na13    se      Si14   
Si1   0.588  (0.039)  0.543  (0.040)  0.172  (0.048)  0.212  (0.052)  0.506 
Na2   0.156  (0.048)  0.129  (0.050)  0.532  (0.035)  0.493  (0.040)  0.104 
Si3   0.468  (0.042)  0.403  (0.044)  0.042  (0.047)  0.091  (0.052)  0.410 
Na4   0.242  (0.048)  0.225  (0.051)  0.616  (0.040)  0.725  (0.033)  0.337 
Na5   0.172  (0.046)  0.188  (0.047)  0.475  (0.040)  0.508  (0.042)  0.148 
Si6   0.551  (0.040)  0.493  (0.043)  0.357  (0.043)  0.413  (0.045)  0.526 
Na7   0.314  (0.047)  0.260  (0.049)  0.648  (0.036)  0.722  (0.031)  0.356 
Si8   0.611  (0.034)  0.516  (0.041)  0.249  (0.045)  0.315  (0.047)  0.680 
Na9   0.230  (0.048)  0.181  (0.049)  0.440  (0.045)  0.548  (0.041)  0.273 
Si10                  0.554  (0.038)  0.230  (0.046)  0.224  (0.048)  0.523 
Si11  0.554  (0.038)                  0.197  (0.046)  0.236  (0.053)  0.451 
Na12  0.230  (0.046)  0.197  (0.046)                  0.685  (0.031)  0.245 
Na13  0.224  (0.048)  0.236  (0.053)  0.685  (0.031)                  0.310 
Si14  0.523  (0.039)  0.451  (0.045)  0.245  (0.045)  0.310  (0.046)        
     se     
Si1  (0.041)
Na2  (0.049)
Si3  (0.044)
Na4  (0.047)
Na5  (0.048)
Si6  (0.040)
Na7  (0.046)
Si8  (0.033)
Na9  (0.049)
Si10 (0.039)
Si11 (0.045)
Na12 (0.045)
Na13 (0.046)
Si14        

$Hi
     Item H  se     
Si1    0.347 (0.026)
Na2    0.280 (0.028)
Si3    0.225 (0.029)
Na4    0.403 (0.026)
Na5    0.310 (0.027)
Si6    0.437 (0.024)
Na7    0.433 (0.024)
Si8    0.409 (0.024)
Na9    0.354 (0.026)
Si10   0.374 (0.024)
Si11   0.338 (0.026)
Na12   0.367 (0.024)
Na13   0.423 (0.024)
Si14   0.376 (0.024)

$H
Scale H      se 
  0.361 (0.018) 

$covHij
               [,1]          [,2]          [,3]          [,4]          [,5]
 [1,]  2.434238e-03 -1.495269e-04  8.594139e-04  1.257516e-03  4.151211e-04
 [2,] -1.495269e-04  1.326234e-03 -6.211550e-06 -3.789549e-04  3.148230e-05
 [3,]  8.594139e-04 -6.211550e-06  2.622031e-03  7.594278e-04  7.551575e-04
 [4,]  1.257516e-03 -3.789549e-04  7.594278e-04  2.433117e-03  4.008195e-04
 [5,]  4.151211e-04  3.148230e-05  7.551575e-04  4.008195e-04  1.822688e-03
 [6,]  8.610112e-04 -1.630711e-05  1.566734e-03  8.526865e-04  7.492925e-04
 [7,]  2.709405e-04  3.423128e-04  5.212472e-04  9.950627e-05  7.018545e-04
 [8,]  1.103668e-03 -1.706341e-04  1.228477e-03  1.402898e-03  6.821965e-04
 [9,]  2.110546e-04  3.894712e-04  3.677207e-04  3.772704e-05  5.715538e-04
[10,]  3.702751e-05  4.268642e-04  2.485208e-04 -1.191778e-05  4.868289e-04
[11,]  1.151212e-03 -9.101252e-05  1.181871e-03  9.432152e-04  3.951396e-04
[12,]  1.040878e-03 -3.500551e-05  1.877626e-03  1.022770e-03  6.377324e-04
[13,]  1.772294e-04  2.387396e-04  5.810354e-04  1.084298e-04  5.128700e-04
[14,]  1.505274e-03  2.103932e-04  4.141674e-04  6.282812e-04  2.144128e-04
[15,]  5.245784e-04 -1.249220e-04 -1.451571e-04  3.953097e-04  2.473014e-05
[16,]  1.356779e-04 -1.063259e-04  1.104419e-04  8.579419e-05 -7.437012e-06
[17,]  1.050261e-03 -1.487516e-04  3.614334e-04  5.303926e-04 -2.722630e-05
[18,]  3.542381e-04 -1.054809e-04  7.103924e-06  2.698007e-04 -5.128920e-05
[19,]  1.307711e-03  5.072716e-05  2.642618e-04  5.563795e-04  1.209411e-04
[20,]  2.656278e-04 -6.468823e-05  1.936449e-04  1.125675e-04 -3.852466e-05
[21,]  1.337394e-03  7.973286e-06  5.521338e-04  5.820986e-04  1.927765e-04
[22,]  1.353143e-03 -3.549755e-05  3.516577e-04  6.938719e-04  2.531976e-05
[23,]  3.145673e-04 -1.649429e-04  5.109162e-05  3.531082e-04 -5.732922e-05
[24,]  4.183864e-04 -1.253598e-04 -8.004636e-06  3.629808e-04 -5.859445e-05
[25,]  1.055036e-03 -3.216684e-05  2.348789e-04  4.484452e-04  1.243449e-04
[26,]  4.028604e-04  4.239013e-04  1.741616e-03  3.539726e-04  4.566631e-04
[27,]  6.384266e-04  3.417927e-04  3.878872e-04  1.353818e-03  1.786841e-04
[28,]  1.478353e-04  7.331617e-04  4.631666e-04  1.152104e-05  1.451832e-03
[29,]  4.424294e-04  4.109802e-04  8.953324e-04  4.008604e-04  4.969152e-04
[30,]  1.777531e-04  5.533883e-04  2.843017e-04 -9.110099e-05  4.994686e-04
[31,]  5.617561e-04  1.688257e-04  5.601073e-04  7.549291e-04  4.328453e-04
[32,]  8.691149e-05  5.041181e-04  2.096599e-04 -7.374291e-05  4.236027e-04
[33,]  5.693732e-05  6.626651e-04  2.950461e-05 -5.335879e-05  2.863598e-04
[34,]  5.785526e-04  3.079035e-04  7.451123e-04  5.072114e-04  2.968744e-04
[35,]  5.504606e-04  3.785055e-04  1.172784e-03  4.600633e-04  4.481258e-04
[36,]  5.825737e-06  5.745834e-04  3.454125e-04 -1.464405e-04  3.584135e-04
[37,]  3.648446e-04 -1.474616e-04 -2.473914e-04  6.153476e-04  4.206993e-05
[38,]  4.423817e-04 -8.222259e-05  1.075266e-03  4.703075e-04  3.387502e-04
[39,]  2.160853e-04 -5.427949e-05  3.127918e-05  3.459440e-04  1.558594e-04
[40,]  2.938853e-04  3.974018e-05  1.082763e-03  2.722079e-04  2.399818e-04
[41,]  3.590014e-04 -1.211744e-04 -7.827564e-05  3.729310e-04  8.423477e-06
[42,]  5.881346e-04  1.068661e-04  1.535035e-03  4.164136e-04  5.262943e-04
[43,]  3.819032e-04 -3.591748e-05  1.484208e-03  4.278047e-04  4.092308e-04
[44,]  2.610635e-04 -3.475434e-06  1.397773e-04  2.243270e-04  1.645992e-04
[45,]  1.540091e-04 -1.788314e-05  4.454794e-05  1.066920e-04  8.508835e-05
[46,]  2.496438e-04  6.629115e-05  1.133468e-03  1.877287e-04  9.014975e-05
[47,]  5.162332e-04 -3.077021e-04  3.339470e-04  1.143457e-03 -1.196333e-04
[48,]  2.686081e-04 -1.773492e-04  1.087970e-04  3.553610e-04  8.517616e-05
[49,]  5.627835e-04 -1.539524e-04  2.285180e-04  1.348592e-03  3.714875e-04
[50,]  1.017129e-04 -4.104462e-05  9.834629e-05  1.807792e-04  2.407260e-05
[51,]  5.826099e-04 -1.216401e-04  3.796085e-04  1.171845e-03  3.023066e-04
[52,]  6.603283e-04 -1.604907e-04  3.766725e-04  1.138396e-03  1.936556e-04
[53,]  3.834807e-04 -5.440377e-05  5.268493e-05  4.424806e-04  3.230096e-05
[54,]  3.763377e-04 -1.991902e-04 -7.556787e-05  5.514414e-04  5.227489e-05
[55,]  4.500508e-04 -1.925890e-04  1.529525e-04  1.127649e-03  1.785393e-04
[56,]  3.282473e-04 -9.166534e-05  5.897628e-04  3.641356e-04  1.232471e-04
[57,]  2.096189e-04  1.370246e-04  3.034857e-04  3.954278e-04  8.228506e-04
[58,]  4.225693e-04 -1.174585e-04  3.133533e-04  6.270530e-04 -1.915143e-04
[59,]  2.973053e-04  1.395707e-04  5.007641e-04  3.355178e-04  8.293709e-04
[60,]  5.614288e-05  4.144024e-05  3.508089e-04  2.384237e-04  8.137073e-04
[61,]  4.578122e-04 -3.688540e-05  7.242965e-04  4.236678e-04  2.216164e-04
[62,]  3.703761e-04 -8.945349e-05  7.075276e-04  4.110976e-04  2.115934e-04
[63,]  2.159809e-04  1.065186e-04  2.532768e-04  2.393660e-04  6.932608e-04
[64,]  3.927272e-04  3.091324e-05  6.009505e-04  3.275164e-04  2.235335e-04
[65,]  2.736992e-04 -1.559309e-04  6.225207e-05  2.659073e-04 -5.897097e-06
[66,]  4.145575e-04  9.274789e-05  8.202686e-04  3.890856e-04  1.050143e-04
[67,]  4.243077e-04 -3.879917e-05  9.414010e-04  3.886163e-04  1.351608e-04
[68,]  5.739569e-05 -2.081439e-06  1.430015e-04  1.221103e-04  8.960287e-06
[69,]  1.087919e-04 -8.363185e-05  1.756905e-04  1.515136e-04  4.598911e-05
[70,]  2.990100e-04 -1.070358e-05  3.148289e-04  2.271875e-04  8.816004e-05
[71,]  4.070164e-04 -2.024539e-05  2.856767e-04  6.264584e-04  2.508110e-04
[72,]  1.523195e-04  1.929262e-04  2.781751e-04  1.143907e-04  3.007363e-04
[73,]  1.827666e-04  2.143675e-05  4.222991e-04  2.373517e-04  3.543813e-04
[74,]  5.159228e-04  1.378940e-04  6.509199e-04  4.603671e-04  2.420143e-04
[75,]  4.534827e-04  5.356350e-05  8.304524e-04  3.619599e-04  1.871328e-04
[76,]  8.345225e-05  7.494426e-05  2.500463e-04  5.666443e-05  2.210940e-04
[77,]  4.988681e-04 -9.575360e-05  4.960393e-04  6.129141e-04  2.821682e-04
[78,]  4.310888e-04 -7.338444e-05  4.468038e-04  6.915526e-04  2.078427e-04
[79,]  3.076940e-04 -1.235019e-04  1.875076e-04  3.398605e-04  1.420498e-04
[80,]  1.936897e-04 -1.103800e-04  8.744742e-05  1.824383e-04  1.118073e-04
[81,]  3.304466e-04 -5.949212e-05  1.794516e-04  5.328099e-04  1.034532e-04
[82,]  2.228441e-04  3.410130e-05  2.570520e-04  2.291484e-04  7.432037e-05
[83,]  5.641693e-04  6.756096e-05  8.067309e-04  4.625405e-04  2.200324e-04
[84,]  6.503953e-04  2.776909e-05  1.201146e-03  4.802323e-04  4.351540e-04
[85,]  2.798848e-04  1.856760e-04  3.236686e-04  7.468312e-05  3.876625e-04
[86,]  5.639359e-04  9.609410e-05  7.017259e-04  2.606768e-04  9.445223e-05
[87,]  4.390979e-04 -4.869332e-05  1.143457e-03  4.871396e-04  3.901570e-04
[88,]  2.107497e-04  8.913423e-06  4.882554e-04  3.134183e-04  4.811298e-04
[89,]  2.560965e-04 -1.696488e-05  1.537692e-04  2.283208e-04  3.141594e-05
[90,]  4.023267e-04  2.280926e-05  5.232473e-04  3.191116e-04  1.418941e-04
[91,]  3.649586e-04 -2.568160e-05  6.674159e-04  2.341908e-04  1.614424e-04
               [,6]          [,7]          [,8]          [,9]         [,10]
 [1,]  8.610112e-04  2.709405e-04  1.103668e-03  2.110546e-04  3.702751e-05
 [2,] -1.630711e-05  3.423128e-04 -1.706341e-04  3.894712e-04  4.268642e-04
 [3,]  1.566734e-03  5.212472e-04  1.228477e-03  3.677207e-04  2.485208e-04
 [4,]  8.526865e-04  9.950627e-05  1.402898e-03  3.772704e-05 -1.191778e-05
 [5,]  7.492925e-04  7.018545e-04  6.821965e-04  5.715538e-04  4.868289e-04
 [6,]  2.495428e-03  5.304598e-04  1.227389e-03  4.594352e-04  2.742019e-04
 [7,]  5.304598e-04  1.582340e-03  3.640450e-04  8.274935e-04  4.407275e-04
 [8,]  1.227389e-03  3.640450e-04  2.476326e-03  1.951859e-04  8.803063e-05
 [9,]  4.594352e-04  8.274935e-04  1.951859e-04  1.499608e-03  5.850977e-04
[10,]  2.742019e-04  4.407275e-04  8.803063e-05  5.850977e-04  1.602715e-03
[11,]  1.244302e-03  1.679508e-04  7.715104e-04  6.603075e-05  1.316761e-05
[12,]  1.653860e-03  4.049841e-04  1.455224e-03  1.158197e-04  1.147257e-04
[13,]  5.726972e-04  8.772929e-04  2.736575e-04  6.510906e-04  3.378176e-04
[14,]  4.422446e-04  2.596868e-04  5.379961e-04  1.838939e-04  1.266358e-04
[15,]  7.259195e-05 -1.076720e-04  3.673829e-04  1.070006e-04 -3.972183e-05
[16,]  9.792398e-05 -7.089612e-05  4.378708e-05 -3.921125e-05  5.471853e-05
[17,]  2.813407e-04  2.764372e-05  4.512041e-04  1.013147e-04 -1.087456e-04
[18,] -3.220654e-05 -2.556625e-05  2.633130e-04 -4.125693e-05 -3.625286e-05
[19,]  3.770148e-04  4.779977e-06  4.429790e-04  8.950706e-05  6.757008e-05
[20,]  1.385205e-04  4.589113e-05  1.192035e-04  1.202262e-05 -4.224384e-05
[21,]  4.017834e-04  1.031206e-04  5.232444e-04  5.943174e-05  1.288776e-04
[22,]  3.847078e-04  1.535463e-04  4.337809e-04  1.894539e-04  6.474339e-05
[23,] -2.611508e-05 -6.889827e-05  2.219140e-04 -1.740593e-05 -2.353009e-05
[24,]  3.100937e-05 -1.916054e-05  1.788917e-04  1.442088e-04 -1.061887e-04
[25,]  2.779199e-04  4.139062e-05  3.559571e-04  2.518992e-04  1.754678e-04
[26,]  9.025829e-04  3.567334e-04  5.294416e-04  3.170068e-04  1.376873e-04
[27,]  4.298573e-04  8.524933e-05  7.432633e-04  9.819519e-05  9.736127e-05
[28,]  4.879909e-04  6.355201e-04  3.343953e-04  5.320106e-04  4.183089e-04
[29,]  1.576017e-03  3.736013e-04  5.326265e-04  4.067034e-04  1.762397e-04
[30,]  3.279896e-04  9.478469e-04  2.396375e-04  5.276416e-04  1.007506e-04
[31,]  5.602045e-04  2.909830e-04  1.353583e-03  1.237943e-04  6.279909e-05
[32,]  3.200737e-04  5.162177e-04  1.635959e-05  8.249585e-04  2.356199e-04
[33,]  1.289309e-04  1.412691e-04 -2.394365e-05  2.272101e-04  8.740511e-04
[34,]  7.895158e-04  2.584998e-04  3.293757e-04  2.006959e-04  2.393043e-04
[35,]  9.898819e-04  3.582856e-04  6.838458e-04  1.741513e-04  8.621703e-05
[36,]  3.067381e-04  5.068683e-04  1.454051e-04  4.482119e-04  1.233220e-04
[37,]  2.008105e-04 -1.470502e-04  3.583948e-04 -3.382729e-05  1.258577e-06
[38,]  6.936510e-04  1.783529e-04  4.773327e-04  2.346092e-04  9.563899e-05
[39,]  4.115926e-04  5.105237e-05  2.586723e-04  7.124854e-05  1.256434e-04
[40,]  6.536034e-04  9.340387e-05  3.728271e-04  1.780312e-04  1.872403e-04
[41,]  9.829584e-05 -5.916905e-05  4.398194e-04 -2.133379e-05 -9.946754e-05
[42,]  8.918051e-04  2.873137e-04  5.631096e-04  3.278734e-04  2.338325e-04
[43,]  9.744126e-04  4.044501e-04  4.820406e-04  2.707952e-04  2.116042e-04
[44,]  2.470625e-04  9.523070e-05  2.855332e-04  1.313836e-04  9.896634e-05
[45,]  2.868396e-04  9.007996e-05  2.423307e-04  2.142104e-04  1.051367e-04
[46,]  3.506026e-04  1.578406e-04  2.343840e-04  1.521825e-04  2.309473e-04
[47,]  3.208695e-04  1.719368e-04  6.723434e-04  1.368972e-04  3.264438e-05
[48,]  5.298733e-05 -7.488060e-05  2.951431e-04 -2.772116e-05  7.727217e-07
[49,]  3.387152e-04  5.413386e-05  6.742701e-04  1.355583e-04  1.735262e-04
[50,]  1.311898e-04  4.145494e-05  1.688549e-04 -5.547263e-06  1.053597e-04
[51,]  3.895218e-04  1.184954e-04  6.250941e-04  8.114014e-05  1.888825e-04
[52,]  3.573339e-04  1.726939e-04  6.588833e-04  2.052258e-04 -1.861462e-05
[53,]  8.495001e-05 -3.953305e-05  3.104284e-04 -1.636742e-06 -1.697123e-04
[54,]  1.340375e-04 -9.695942e-05  2.082157e-04  2.884206e-05 -7.135432e-06
[55,]  2.170470e-04  3.275639e-05  5.674202e-04  9.049763e-05  2.841912e-04
[56,]  7.873099e-04  9.615214e-05  3.384266e-04 -6.625455e-05 -5.461738e-05
[57,]  3.283319e-04  4.681540e-04  3.829058e-04  3.085023e-04  2.401868e-04
[58,]  2.179648e-04  1.514600e-04  9.198969e-04  5.425926e-05 -8.855674e-05
[59,]  2.181407e-04  3.388724e-04  3.535483e-04  3.648660e-04  1.140969e-04
[60,]  1.981478e-04  3.217256e-04  2.426756e-04  1.090130e-04  5.304653e-04
[61,]  5.207248e-04  1.903031e-04  4.648308e-04  1.532005e-04  2.982326e-05
[62,]  5.548686e-04  1.258785e-04  6.074667e-04  1.932428e-04  1.283901e-04
[63,]  1.990748e-04  3.275542e-04  2.338496e-04  3.227576e-04  3.272020e-04
[64,]  1.044349e-03  1.322764e-04  2.652025e-04  2.269856e-04  1.758308e-04
[65,]  1.264120e-06 -1.132724e-04  4.041462e-04 -1.161885e-04 -8.940085e-05
[66,]  1.249145e-03  2.748883e-04  3.930427e-04  1.509566e-04  1.875768e-05
[67,]  1.199657e-03  3.236846e-04  3.686262e-04  3.475023e-05 -3.503024e-06
[68,]  2.935687e-04  3.605831e-05  1.460396e-04  1.888430e-04 -4.274896e-05
[69,]  1.517784e-04 -5.908439e-05  2.021830e-04  1.265708e-04  5.755952e-05
[70,]  1.004981e-03  8.425732e-05  1.023468e-04  3.206675e-04  2.725050e-04
[71,]  1.923564e-04 -1.693882e-04  8.083714e-04  1.933054e-04  1.201104e-04
[72,]  3.209676e-04  4.967575e-04  3.219887e-04  3.867450e-04  1.979057e-04
[73,]  3.874605e-04  7.628287e-04  3.556311e-04  3.646496e-04  6.124136e-04
[74,]  6.248343e-04  1.607363e-04  2.708119e-04  3.221256e-04  1.446027e-04
[75,]  5.226246e-04  1.320957e-04  4.532569e-04  2.378641e-04  8.209289e-05
[76,]  2.367913e-04  3.861432e-04  2.349581e-04  1.951433e-04  1.821352e-04
[77,]  3.634520e-04  2.639326e-04  1.090717e-03  6.145277e-05  1.076141e-04
[78,]  3.500399e-04  3.365269e-04  1.035806e-03  1.604210e-04  2.202664e-05
[79,]  1.293833e-04 -5.428948e-05  4.908508e-04  1.498595e-04 -4.017423e-05
[80,]  7.356076e-05 -2.867182e-05  4.071606e-04  1.059201e-04  3.249284e-05
[81,]  1.998421e-05  9.317990e-05  8.374106e-04  1.785230e-04  1.724038e-04
[82,]  1.265919e-04  2.758960e-04  1.950711e-04  4.158360e-04  5.040973e-04
[83,]  8.053222e-04  3.274834e-04  5.233561e-04  1.417132e-04  1.124932e-04
[84,]  9.361472e-04  3.420286e-04  7.259378e-04  3.283635e-04  2.613518e-04
[85,]  4.629423e-04  3.531423e-04  2.693401e-04  3.934886e-04  2.614172e-04
[86,]  5.509018e-04  1.944809e-04  3.373056e-04  1.213739e-04  1.462931e-04
[87,]  9.202240e-04  2.754473e-04  6.266739e-04  2.561741e-04  3.419183e-04
[88,]  5.118179e-04  4.626634e-04  3.342391e-04  3.652616e-04  6.662474e-04
[89,]  7.414652e-05  1.103730e-04  1.973514e-04  1.571687e-04 -2.784296e-05
[90,]  6.477588e-04  1.879430e-04  3.256455e-04  2.755797e-04  1.765123e-04
[91,]  4.531404e-04  2.363351e-04  4.256723e-04  2.889718e-04  2.680587e-04
              [,11]         [,12]         [,13]         [,14]         [,15]
 [1,]  1.151212e-03  1.040878e-03  1.772294e-04  1.505274e-03  5.245784e-04
 [2,] -9.101252e-05 -3.500551e-05  2.387396e-04  2.103932e-04 -1.249220e-04
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 [7,]  1.679508e-04  4.049841e-04  8.772929e-04  2.596868e-04 -1.076720e-04
 [8,]  7.715104e-04  1.455224e-03  2.736575e-04  5.379961e-04  3.673829e-04
 [9,]  6.603075e-05  1.158197e-04  6.510906e-04  1.838939e-04  1.070006e-04
[10,]  1.316761e-05  1.147257e-04  3.378176e-04  1.266358e-04 -3.972183e-05
[11,]  2.270707e-03  1.295938e-03  1.758578e-04  6.034928e-04  1.788702e-04
[12,]  1.295938e-03  2.705336e-03  3.905715e-04  5.320279e-04  5.455172e-05
[13,]  1.758578e-04  3.905715e-04  1.693919e-03  1.174797e-04 -1.470308e-04
[14,]  6.034928e-04  5.320279e-04  1.174797e-04  2.239498e-03  1.952462e-04
[15,]  1.788702e-04  5.455172e-05 -1.470308e-04  1.952462e-04  2.298914e-03
[16,]  2.226474e-04  1.322255e-04 -5.619034e-05 -1.140737e-04  3.556849e-04
[17,]  3.943512e-04  3.126967e-04  2.399795e-05  4.223194e-04  8.826219e-04
[18,] -1.762666e-05  7.797265e-06 -7.580121e-05  2.465320e-04  1.005278e-03
[19,]  4.846435e-04  4.030765e-04 -5.794975e-06  1.065540e-03  5.899302e-04
[20,]  1.729384e-04  2.812538e-05 -2.162077e-05  1.380929e-04  7.801401e-04
[21,]  5.544624e-04  6.313520e-04  2.014899e-04  9.725282e-04  3.780238e-04
[22,]  5.710367e-04  3.883534e-04  1.605339e-04  9.571380e-04  3.885684e-04
[23,] -8.204424e-06  1.280915e-04 -5.787234e-05  1.443124e-04  5.414757e-04
[24,]  1.933416e-04 -1.165096e-04 -4.836977e-05  2.912656e-04  1.032752e-03
[25,]  3.863016e-04  3.308994e-04 -6.014859e-05  8.363689e-04  6.534789e-04
[26,]  8.201857e-04  1.177930e-03  4.099503e-04  7.101253e-04 -3.761715e-04
[27,]  5.675788e-04  5.025063e-04  4.341735e-05  1.073767e-03  5.845911e-05
[28,]  2.991537e-04  4.232581e-04  4.890351e-04  4.962612e-04 -1.391124e-04
[29,]  8.607955e-04  9.827212e-04  3.225253e-04  7.728478e-04 -1.016301e-04
[30,]  2.362833e-04  2.972800e-04  4.983521e-04  3.034783e-04 -2.522457e-04
[31,]  3.821567e-04  7.135594e-04  1.584021e-04  9.453625e-04  3.586482e-05
[32,]  1.694330e-04  7.796945e-05  4.158569e-04  2.146558e-04 -7.913896e-05
[33,]  1.960490e-04  2.981468e-05  1.352208e-04  3.343720e-04 -1.239938e-04
[34,]  1.464822e-03  8.272920e-04  1.400569e-04  1.119494e-03 -8.296229e-05
[35,]  8.998225e-04  1.761202e-03  2.364439e-04  9.527153e-04 -1.998842e-04
[36,]  1.089253e-04  1.669941e-04  9.287999e-04  1.368016e-04 -1.504229e-04
[37,]  7.968852e-05  3.922345e-06 -2.043723e-04  9.152742e-05  9.265585e-04
[38,]  6.829233e-04  7.257352e-04  2.453567e-05  1.644243e-04  2.663926e-04
[39,]  1.764563e-04  2.794382e-04 -2.058999e-04  1.396809e-04  5.798666e-04
[40,]  6.274729e-04  8.365378e-04  1.480852e-04  1.943176e-04  7.336616e-05
[41,]  1.423004e-04  1.141367e-04 -2.057205e-04  1.335412e-04  6.313731e-04
[42,]  8.231956e-04  1.176962e-03  3.173046e-04  3.248728e-04  8.781090e-05
[43,]  7.721936e-04  1.107022e-03  4.322391e-04  2.453541e-04  4.097487e-05
[44,]  1.457938e-04  1.964991e-04 -2.583065e-05  5.504730e-05  1.151525e-03
[45,]  1.480426e-04  1.626770e-04 -3.336231e-05 -2.172860e-05  6.354989e-04
[46,]  4.723493e-04  6.416952e-04  6.282235e-05  2.526807e-04 -3.399836e-05
[47,]  3.204598e-04  3.363434e-04  2.870356e-05  8.363679e-05  5.715944e-04
[48,]  1.482037e-05  9.509445e-05 -1.273937e-04  7.654873e-05  4.848910e-04
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[50,]  1.190691e-04 -7.397069e-06  2.647493e-05  4.707860e-05  1.304570e-04
[51,]  4.395244e-04  4.722943e-04  9.752983e-05  3.898085e-04  3.417459e-04
[52,]  2.449497e-04  4.176278e-04  2.449861e-04  4.387653e-04  3.483783e-04
[53,]  2.645050e-05  1.224855e-04 -8.397161e-05  1.130279e-04  3.022050e-04
[54,]  1.620661e-04 -6.139460e-05 -1.494147e-04  1.581046e-04  4.406155e-04
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[56,]  4.240055e-04  5.265243e-04 -1.973462e-05  8.129064e-05  1.718636e-04
[57,]  2.419264e-04  2.748425e-04  2.803957e-04  2.267123e-04  1.044837e-04
[58,]  2.867212e-04  4.582116e-04 -3.696440e-05  7.012806e-05  5.265334e-04
[59,]  2.577843e-04  3.970990e-04  3.489007e-04  1.363490e-04  2.338867e-05
[60,]  1.068804e-04  3.185129e-04  3.795883e-04 -5.973542e-07 -1.113856e-04
[61,]  9.448108e-04  5.387831e-04  7.372631e-05  3.745784e-05  4.211735e-04
[62,]  4.984559e-04  8.903271e-04  8.291508e-05  1.530548e-05  3.913382e-04
[63,]  1.663279e-04  2.523277e-04  5.283547e-04  1.833964e-04  8.145841e-05
[64,]  5.667517e-04  5.098512e-04  8.740936e-05  3.370508e-04  1.779514e-04
[65,]  2.314783e-05  6.793039e-05 -3.070003e-04  2.210559e-04  5.615340e-04
[66,]  7.844726e-04  9.073095e-04  3.795170e-04  2.884158e-04 -1.142100e-05
[67,]  5.679466e-04  8.628537e-04  4.388622e-04  4.073142e-04 -1.236788e-04
[68,]  1.837596e-05  1.019651e-05  9.269825e-05 -7.602563e-05  2.657088e-04
[69,] -1.334938e-06  4.496160e-05 -6.395378e-05  1.127173e-04  2.539180e-04
[70,]  5.769796e-04  4.180774e-04  2.091009e-05  2.592556e-04  2.183488e-04
[71,]  1.949516e-04  3.657622e-04 -1.299677e-05  3.245772e-04  4.657350e-04
[72,]  2.957613e-04  2.750270e-04  3.371062e-04  1.485347e-04 -4.162078e-05
[73,]  1.939835e-04  2.240768e-04  4.406999e-04  2.006041e-04 -1.054884e-04
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[18,]  1.152408e-04  4.329994e-05 -9.117521e-05  3.704439e-04 2.108579e-04
[19,]  5.228230e-04  5.466024e-04  4.004093e-05  1.895252e-04 6.119792e-04
[20,]  2.262251e-04  1.663052e-05 -4.993361e-05  2.956231e-04 2.790703e-04
[21,]  6.651633e-04  5.675823e-04  7.733711e-06  6.084476e-05 3.666044e-04
[22,]  1.094774e-03  9.389819e-04  4.021428e-05  1.749182e-04 3.813936e-04
[23,]  7.983960e-05  1.213915e-04  1.138626e-05  2.230986e-04 4.439672e-05
[24,]  1.567533e-04 -1.100356e-05 -4.718423e-05  5.161993e-04 2.081107e-04
[25,]  3.855760e-04  3.074936e-04  1.686678e-04  2.415462e-04 1.055838e-03
[26,]  6.036796e-04  9.098015e-04  3.942148e-04  1.190678e-05 5.062303e-04
[27,]  2.676166e-04  4.174651e-04  1.607756e-04  1.027392e-04 2.273655e-04
[28,]  3.413324e-05  2.209339e-04  4.232794e-04 -1.817373e-05 1.420552e-04
[29,]  4.535284e-04  7.914253e-04  2.395313e-04 -3.913319e-05 5.985656e-04
[30,]  4.833133e-05  1.061460e-04  2.941310e-04  5.562046e-05 9.093284e-05
[31,]  2.456143e-04  6.050836e-04  1.319280e-04  2.719833e-05 3.635345e-04
[32,] -2.349140e-05 -5.616074e-05  3.603859e-04  1.326604e-04 1.170242e-04
[33,] -5.932680e-05  1.172726e-04  5.613659e-04  7.887696e-06 6.612668e-05
[34,]  8.850351e-04  6.023898e-04  1.181571e-04  1.508571e-05 7.234630e-04
[35,]  5.755967e-04  1.200529e-03  2.521868e-04 -7.102333e-05 5.262495e-04
[36,]  6.438163e-05  1.727030e-04  5.490426e-04  7.486292e-05 4.353834e-05
[37,]  8.649458e-05  1.258978e-04 -6.013667e-05  1.559809e-04 2.274448e-04
[38,]  2.833515e-04  5.003429e-04  5.364458e-05  2.334561e-04 5.854422e-04
[39,] -4.197727e-05  5.827891e-05  7.744525e-05  2.597643e-04 2.620457e-04
[40,]  5.705345e-04  8.438294e-04  1.757668e-04  1.753646e-04 8.118905e-04
[41,]  1.807359e-04  2.724360e-04 -6.210108e-05  2.100049e-04 2.239610e-04
[42,]  5.907224e-04  1.047586e-03  3.713421e-04  1.039656e-04 5.719711e-04
[43,]  1.066626e-03  1.891917e-03  6.745963e-04  1.142515e-04 4.556389e-04
[44,] -2.011577e-05  8.485508e-05 -4.472159e-05  5.114014e-04 3.046093e-04
[45,]  7.753816e-05  7.795931e-05  3.515667e-05  3.203275e-04 2.338855e-04
[46,]  3.633299e-04  5.726758e-04  1.490990e-04  1.266368e-04 1.036658e-03
[47,]  1.899166e-04  2.450604e-04  8.600386e-05  1.325293e-04 5.188465e-04
[48,]  8.741217e-05  7.919810e-05 -1.392898e-05  8.104277e-05 5.567749e-05
[49,]  3.303885e-04  5.687386e-04  2.112492e-04  3.123350e-05 5.502579e-04
[50,]  2.149729e-04  1.081273e-04  1.960649e-04  1.796005e-04 1.773217e-04
[51,]  4.320528e-04  5.472786e-04  4.580620e-05 -4.367419e-05 5.161892e-04
[52,]  7.868502e-04  8.283976e-04  1.084406e-05  6.372826e-05 2.427065e-04
[53,]  1.123444e-04  2.109042e-05 -3.990401e-05  2.713080e-04 1.222138e-04
[54,]  8.782200e-06  4.598597e-05  9.536745e-05  3.432581e-04 3.394664e-05
[55,]  2.468239e-04  4.249628e-04  1.948961e-04  1.044414e-04 8.299097e-04
[56,]  3.032113e-04  2.900979e-04  4.851721e-05  1.616455e-04 3.877097e-04
[57,]  1.134662e-04  3.092622e-04  2.610918e-04  7.571557e-05 1.873570e-04
[58,]  1.099404e-04  1.980149e-04  2.904029e-05  1.589443e-04 2.346815e-04
[59,]  1.666562e-04  4.309239e-04  2.200481e-04 -7.481281e-06 1.656669e-05
[60,]  3.198210e-04  6.340783e-04  7.613368e-04 -5.473477e-05 3.098868e-05
[61,]  8.393937e-04  4.954971e-04  7.225446e-05  3.112669e-04 8.899494e-04
[62,]  3.751557e-04  8.512182e-04  8.223529e-05  2.737952e-04 5.841263e-04
[63,]  8.820622e-05  1.495440e-04  6.030693e-04  1.077436e-04 3.463130e-04
[64,]  4.500416e-04  8.046375e-04  1.367438e-05  2.408385e-06 7.533731e-04
[65,] -3.985342e-05  8.409580e-05 -1.935671e-04  5.837058e-05 8.358989e-05
[66,]  6.728122e-04  8.790662e-04  2.644023e-04 -9.751587e-05 4.732810e-04
[67,]  1.142858e-03  1.597422e-03  5.390912e-04  6.094583e-06 2.974902e-04
[68,]  5.644790e-05  5.024463e-05 -8.136774e-05  5.632637e-04 2.927440e-04
[69,]  3.721265e-05  1.835508e-04  5.014032e-05  3.272104e-04 6.420229e-05
[70,]  2.582237e-04  4.195337e-04  9.678348e-05  2.176245e-05 1.189836e-03
[71,]  2.128118e-04  6.794391e-04  1.198567e-05 -1.583224e-05 5.213375e-04
[72,]  1.278136e-04  2.532863e-04  4.232531e-04  1.588404e-05 7.385284e-05
[73,]  2.370242e-04  5.614170e-04  1.089428e-03  1.747216e-04 1.362191e-04
[74,]  9.142537e-04  8.158659e-04  1.198249e-04  1.976989e-04 1.216450e-03
[75,]  7.217318e-04  1.213255e-03  1.907056e-04  2.265633e-04 7.029389e-04
[76,]  1.359326e-04  2.041961e-04  4.414152e-04 -6.687589e-06 2.102799e-04
[77,]  4.741888e-04  6.954948e-04  2.441315e-04 -2.637973e-05 3.193672e-04
[78,]  7.517876e-04  1.096577e-03  4.981847e-04  9.324617e-05 2.123481e-04
[79,]  7.974595e-05  1.170806e-04 -1.260288e-04  4.892206e-04 2.918031e-04
[80,]  1.497727e-04  1.752032e-04  9.691943e-05  2.115278e-04 1.774041e-04
[81,]  1.711231e-04  4.365098e-04 -3.232509e-05  7.145716e-05 8.581590e-04
[82,]  1.320532e-04  2.310744e-04  6.733900e-04  1.581439e-04 8.449649e-05
[83,]  1.101112e-03  8.753876e-04  1.284047e-04  5.860524e-05 9.303258e-04
[84,]  8.026137e-04  1.447706e-03  4.591989e-04  1.344561e-04 6.016369e-04
[85,]  1.321520e-04  4.134501e-04  8.475472e-04  1.648952e-05 1.555095e-04
[86,]  2.152119e-03  1.263604e-03  2.558272e-04  6.998596e-05 6.956986e-04
[87,]  1.263604e-03  2.803276e-03  5.482425e-04  1.608652e-05 5.531150e-04
[88,]  2.558272e-04  5.482425e-04  1.985525e-03  1.135516e-04 4.366036e-05
[89,]  6.998596e-05  1.608652e-05  1.135516e-04  9.677864e-04 2.532856e-04
[90,]  6.956986e-04  5.531150e-04  4.366036e-05  2.532856e-04 1.994875e-03
[91,]  4.982358e-04  7.074153e-04  1.710000e-04  2.127409e-04 1.225077e-03
              [,91]
 [1,]  3.649586e-04
 [2,] -2.568160e-05
 [3,]  6.674159e-04
 [4,]  2.341908e-04
 [5,]  1.614424e-04
 [6,]  4.531404e-04
 [7,]  2.363351e-04
 [8,]  4.256723e-04
 [9,]  2.889718e-04
[10,]  2.680587e-04
[11,]  5.603101e-04
[12,]  8.264530e-04
[13,]  1.112237e-04
[14,]  3.365833e-04
[15,]  1.726714e-04
[16,]  1.991470e-05
[17,]  4.902528e-04
[18,]  2.436524e-04
[19,]  5.217462e-04
[20,]  1.570608e-04
[21,]  3.496910e-04
[22,]  2.698810e-04
[23,]  1.315343e-04
[24,]  1.087335e-04
[25,]  1.002831e-03
[26,]  5.929217e-04
[27,]  1.366522e-04
[28,]  1.469423e-04
[29,]  3.425734e-04
[30,]  9.608099e-06
[31,]  3.929317e-04
[32,]  5.163223e-05
[33,]  8.477411e-05
[34,]  4.794893e-04
[35,]  7.770183e-04
[36,] -7.922301e-06
[37,]  7.105016e-05
[38,]  6.137423e-04
[39,]  3.992040e-04
[40,]  1.026450e-03
[41,]  3.111628e-04
[42,]  7.318943e-04
[43,]  6.099982e-04
[44,]  2.270404e-04
[45,]  4.519132e-04
[46,]  1.482591e-03
[47,]  4.187717e-04
[48,]  1.565582e-04
[49,]  4.468531e-04
[50,]  9.067997e-05
[51,]  5.069319e-04
[52,]  3.520901e-04
[53,]  1.027538e-05
[54,] -4.648232e-05
[55,]  8.964609e-04
[56,]  5.780837e-04
[57,]  3.348009e-04
[58,]  4.385803e-04
[59,]  1.257423e-04
[60,]  4.176451e-05
[61,]  5.992598e-04
[62,]  9.419532e-04
[63,]  5.087419e-04
[64,]  6.810668e-04
[65,]  2.807021e-04
[66,]  5.543583e-04
[67,]  4.066769e-04
[68,]  1.139091e-05
[69,]  3.464130e-04
[70,]  1.242895e-03
[71,]  7.446733e-04
[72,]  9.744722e-05
[73,]  1.450635e-04
[74,]  6.730617e-04
[75,]  1.238819e-03
[76,]  2.484554e-04
[77,]  6.001807e-04
[78,]  4.628824e-04
[79,]  1.426331e-04
[80,]  3.981958e-04
[81,]  1.121718e-03
[82,]  2.673968e-04
[83,]  5.909345e-04
[84,]  1.108497e-03
[85,]  1.251671e-04
[86,]  4.982358e-04
[87,]  7.074153e-04
[88,]  1.710000e-04
[89,]  2.127409e-04
[90,]  1.225077e-03
[91,]  2.161564e-03

$covHi
              [,1]         [,2]         [,3]         [,4]         [,5]
 [1,] 0.0006645838 0.0002304549 4.470618e-04 0.0003266593 2.195585e-04
 [2,] 0.0002304549 0.0007646835 1.152516e-04 0.0003051144 4.120705e-04
 [3,] 0.0004470618 0.0001152516 8.541852e-04 0.0002339629 8.045099e-05
 [4,] 0.0003266593 0.0003051144 2.339629e-04 0.0006913407 3.239688e-04
 [5,] 0.0002195585 0.0004120705 8.045099e-05 0.0003239688 7.396551e-04
 [6,] 0.0003525765 0.0002813870 2.171933e-04 0.0003497003 2.961426e-04
 [7,] 0.0002750415 0.0003006784 2.029810e-04 0.0004041106 2.971901e-04
 [8,] 0.0003661938 0.0002606764 3.237293e-04 0.0003430305 2.411293e-04
 [9,] 0.0002223256 0.0003588539 1.394439e-04 0.0004024452 4.514541e-04
[10,] 0.0004139202 0.0002458037 3.272823e-04 0.0003129578 2.417322e-04
[11,] 0.0003804442 0.0002180598 3.237151e-04 0.0002840287 2.404339e-04
[12,] 0.0002857903 0.0003815629 2.050990e-04 0.0003826860 3.282982e-04
[13,] 0.0003142032 0.0003242748 2.136426e-04 0.0004431976 2.956983e-04
[14,] 0.0003294196 0.0002214053 2.719708e-04 0.0003202643 2.109477e-04
              [,6]         [,7]         [,8]         [,9]        [,10]
 [1,] 0.0003525765 0.0002750415 0.0003661938 0.0002223256 0.0004139202
 [2,] 0.0002813870 0.0003006784 0.0002606764 0.0003588539 0.0002458037
 [3,] 0.0002171933 0.0002029810 0.0003237293 0.0001394439 0.0003272823
 [4,] 0.0003497003 0.0004041106 0.0003430305 0.0004024452 0.0003129578
 [5,] 0.0002961426 0.0002971901 0.0002411293 0.0004514541 0.0002417322
 [6,] 0.0005801617 0.0002818677 0.0003466236 0.0002974021 0.0003349083
 [7,] 0.0002818677 0.0005713878 0.0002915138 0.0003124611 0.0002782050
 [8,] 0.0003466236 0.0002915138 0.0005581007 0.0002982279 0.0003805091
 [9,] 0.0002974021 0.0003124611 0.0002982279 0.0006909820 0.0002750708
[10,] 0.0003349083 0.0002782050 0.0003805091 0.0002750708 0.0005628807
[11,] 0.0002809188 0.0002449153 0.0003475380 0.0002423574 0.0003705075
[12,] 0.0002926391 0.0003291309 0.0002861552 0.0003095475 0.0002922727
[13,] 0.0003074648 0.0003631671 0.0003230056 0.0003660364 0.0003098117
[14,] 0.0003135730 0.0002700939 0.0003807911 0.0002652745 0.0003238305
             [,11]        [,12]        [,13]        [,14]
 [1,] 0.0003804442 0.0002857903 0.0003142032 0.0003294196
 [2,] 0.0002180598 0.0003815629 0.0003242748 0.0002214053
 [3,] 0.0003237151 0.0002050990 0.0002136426 0.0002719708
 [4,] 0.0002840287 0.0003826860 0.0004431976 0.0003202643
 [5,] 0.0002404339 0.0003282982 0.0002956983 0.0002109477
 [6,] 0.0002809188 0.0002926391 0.0003074648 0.0003135730
 [7,] 0.0002449153 0.0003291309 0.0003631671 0.0002700939
 [8,] 0.0003475380 0.0002861552 0.0003230056 0.0003807911
 [9,] 0.0002423574 0.0003095475 0.0003660364 0.0002652745
[10,] 0.0003705075 0.0002922727 0.0003098117 0.0003238305
[11,] 0.0006640774 0.0002533448 0.0002960417 0.0002941563
[12,] 0.0002533448 0.0005523158 0.0003481367 0.0002692463
[13,] 0.0002960417 0.0003481367 0.0005599367 0.0003031403
[14,] 0.0002941563 0.0002692463 0.0003031403 0.0005791888

$covH
             [,1]
[1,] 0.0003288151

$Groups
$Groups$`0`
$Groups$`0`$Hij
     Si1      0% ci   Na2      0% ci   Si3      0% ci   Na4      0% ci  
Si1                    -0.088  (0.110)   0.598  (0.119)   0.038  (0.125)
Na2   -0.088  (0.110)                   -0.221  (0.123)   0.441  (0.117)
Si3    0.598  (0.119)  -0.221  (0.123)                   -0.152  (0.122)
Na4    0.038  (0.125)   0.441  (0.117)  -0.152  (0.122)                 
Na5    0.174  (0.127)   0.508  (0.114)  -0.310  (0.131)   0.371  (0.106)
Si6    0.354  (0.122)   0.210  (0.122)  -0.058  (0.149)   0.347  (0.132)
Na7    0.019  (0.123)   0.543  (0.092)  -0.143  (0.130)   0.720  (0.088)
Si8    0.512  (0.114)   0.161  (0.129)   0.215  (0.142)   0.400  (0.126)
Na9    0.064  (0.117)   0.518  (0.110)  -0.179  (0.128)   0.552  (0.116)
Si10   0.627  (0.094)   0.062  (0.121)   0.195  (0.133)   0.216  (0.125)
Si11   0.563  (0.102)   0.006  (0.132)   0.173  (0.134)   0.235  (0.128)
Na12   0.016  (0.095)   0.569  (0.091)  -0.196  (0.117)   0.581  (0.106)
Na13   0.114  (0.109)   0.588  (0.079)  -0.081  (0.124)   0.779  (0.058)
Si14   0.347  (0.117)   0.172  (0.117)   0.137  (0.146)   0.396  (0.117)
     Na5      0% ci   Si6      0% ci   Na7      0% ci   Si8     0% ci  
Si1    0.174  (0.127)   0.354  (0.122)   0.019  (0.123)  0.512  (0.114)
Na2    0.508  (0.114)   0.210  (0.122)   0.543  (0.092)  0.161  (0.129)
Si3   -0.310  (0.131)  -0.058  (0.149)  -0.143  (0.130)  0.215  (0.142)
Na4    0.371  (0.106)   0.347  (0.132)   0.720  (0.088)  0.400  (0.126)
Na5                     0.293  (0.151)   0.401  (0.123)  0.267  (0.144)
Si6    0.293  (0.151)                    0.427  (0.126)  0.571  (0.117)
Na7    0.401  (0.123)   0.427  (0.126)                   0.372  (0.121)
Si8    0.267  (0.144)   0.571  (0.117)   0.372  (0.121)                
Na9    0.599  (0.087)   0.340  (0.138)   0.512  (0.111)  0.304  (0.136)
Si10   0.170  (0.143)   0.556  (0.115)   0.300  (0.122)  0.671  (0.083)
Si11   0.181  (0.118)   0.400  (0.139)   0.214  (0.124)  0.514  (0.114)
Na12   0.430  (0.109)   0.238  (0.112)   0.603  (0.081)  0.198  (0.112)
Na13   0.404  (0.098)   0.467  (0.117)   0.809  (0.047)  0.413  (0.109)
Si14   0.341  (0.135)   0.471  (0.125)   0.358  (0.134)  0.641  (0.096)
     Na9      0% ci   Si10    0% ci   Si11    0% ci   Na12     0% ci   Na13    
Si1    0.064  (0.117)  0.627  (0.094)  0.563  (0.102)   0.016  (0.095)   0.114 
Na2    0.518  (0.110)  0.062  (0.121)  0.006  (0.132)   0.569  (0.091)   0.588 
Si3   -0.179  (0.128)  0.195  (0.133)  0.173  (0.134)  -0.196  (0.117)  -0.081 
Na4    0.552  (0.116)  0.216  (0.125)  0.235  (0.128)   0.581  (0.106)   0.779 
Na5    0.599  (0.087)  0.170  (0.143)  0.181  (0.118)   0.430  (0.109)   0.404 
Si6    0.340  (0.138)  0.556  (0.115)  0.400  (0.139)   0.238  (0.112)   0.467 
Na7    0.512  (0.111)  0.300  (0.122)  0.214  (0.124)   0.603  (0.081)   0.809 
Si8    0.304  (0.136)  0.671  (0.083)  0.514  (0.114)   0.198  (0.112)   0.413 
Na9                    0.242  (0.121)  0.353  (0.108)   0.345  (0.122)   0.598 
Si10   0.242  (0.121)                  0.696  (0.094)   0.177  (0.105)   0.327 
Si11   0.353  (0.108)  0.696  (0.094)                   0.057  (0.114)   0.272 
Na12   0.345  (0.122)  0.177  (0.105)  0.057  (0.114)                    0.710 
Na13   0.598  (0.111)  0.327  (0.101)  0.272  (0.114)   0.710  (0.075)         
Si14   0.453  (0.101)  0.411  (0.109)  0.413  (0.134)   0.096  (0.104)   0.395 
     0% ci   Si14    0% ci  
Si1  (0.109)  0.347  (0.117)
Na2  (0.079)  0.172  (0.117)
Si3  (0.124)  0.137  (0.146)
Na4  (0.058)  0.396  (0.117)
Na5  (0.098)  0.341  (0.135)
Si6  (0.117)  0.471  (0.125)
Na7  (0.047)  0.358  (0.134)
Si8  (0.109)  0.641  (0.096)
Na9  (0.111)  0.453  (0.101)
Si10 (0.101)  0.411  (0.109)
Si11 (0.114)  0.413  (0.134)
Na12 (0.075)  0.096  (0.104)
Na13          0.395  (0.096)
Si14 (0.096)                

$Groups$`0`$Hi
     Item H  se     
Si1    0.247 (0.074)
Na2    0.250 (0.071)
Si3   -0.011 (0.094)
Na4    0.372 (0.061)
Na5    0.291 (0.067)
Si6    0.358 (0.072)
Na7    0.389 (0.056)
Si8    0.403 (0.054)
Na9    0.356 (0.052)
Si10   0.355 (0.063)
Si11   0.309 (0.074)
Na12   0.270 (0.065)
Na13   0.432 (0.048)
Si14   0.352 (0.055)

$Groups$`0`$H
 Scale H se     
   0.313 (0.042)


$Groups$`1`
$Groups$`1`$Hij
     Si1     0% ci   Na2      0% ci   Si3      0% ci   Na4     0% ci   Na5     
Si1                    0.087  (0.053)   0.681  (0.038)  0.264  (0.053)   0.081 
Na2   0.087  (0.053)                   -0.034  (0.051)  0.373  (0.052)   0.523 
Si3   0.681  (0.038)  -0.034  (0.051)                   0.151  (0.057)  -0.022 
Na4   0.264  (0.053)   0.373  (0.052)   0.151  (0.057)                   0.451 
Na5   0.081  (0.053)   0.523  (0.041)  -0.022  (0.049)  0.451  (0.052)         
Si6   0.547  (0.044)   0.278  (0.052)   0.337  (0.050)  0.470  (0.045)   0.381 
Na7   0.254  (0.052)   0.445  (0.050)   0.165  (0.052)  0.647  (0.043)   0.514 
Si8   0.574  (0.042)   0.180  (0.051)   0.510  (0.045)  0.303  (0.052)   0.150 
Na9   0.127  (0.053)   0.456  (0.048)   0.074  (0.053)  0.490  (0.049)   0.578 
Si10  0.580  (0.043)   0.179  (0.051)   0.511  (0.043)  0.252  (0.052)   0.173 
Si11  0.537  (0.044)   0.156  (0.052)   0.438  (0.046)  0.230  (0.054)   0.189 
Na12  0.220  (0.050)   0.513  (0.039)   0.086  (0.049)  0.612  (0.043)   0.482 
Na13  0.249  (0.054)   0.461  (0.045)   0.136  (0.055)  0.708  (0.038)   0.531 
Si14  0.532  (0.043)   0.092  (0.053)   0.449  (0.044)  0.326  (0.052)   0.124 
     0% ci   Si6     0% ci   Na7     0% ci   Si8     0% ci   Na9     0% ci  
Si1  (0.053)  0.547  (0.044)  0.254  (0.052)  0.574  (0.042)  0.127  (0.053)
Na2  (0.041)  0.278  (0.052)  0.445  (0.050)  0.180  (0.051)  0.456  (0.048)
Si3  (0.049)  0.337  (0.050)  0.165  (0.052)  0.510  (0.045)  0.074  (0.053)
Na4  (0.052)  0.470  (0.045)  0.647  (0.043)  0.303  (0.052)  0.490  (0.049)
Na5           0.381  (0.049)  0.514  (0.042)  0.150  (0.052)  0.578  (0.041)
Si6  (0.049)                  0.474  (0.046)  0.599  (0.041)  0.401  (0.048)
Na7  (0.042)  0.474  (0.046)                  0.353  (0.049)  0.560  (0.046)
Si8  (0.052)  0.599  (0.041)  0.353  (0.049)                  0.273  (0.052)
Na9  (0.041)  0.401  (0.048)  0.560  (0.046)  0.273  (0.052)                
Si10 (0.049)  0.551  (0.042)  0.321  (0.051)  0.601  (0.037)  0.231  (0.052)
Si11 (0.052)  0.512  (0.043)  0.276  (0.052)  0.517  (0.044)  0.151  (0.054)
Na12 (0.042)  0.375  (0.046)  0.646  (0.040)  0.259  (0.048)  0.444  (0.048)
Na13 (0.045)  0.396  (0.047)  0.699  (0.036)  0.295  (0.051)  0.532  (0.043)
Si14 (0.051)  0.534  (0.042)  0.354  (0.049)  0.685  (0.036)  0.244  (0.054)
     Si10    0% ci   Si11    0% ci   Na12    0% ci   Na13    0% ci   Si14   
Si1   0.580  (0.043)  0.537  (0.044)  0.220  (0.050)  0.249  (0.054)  0.532 
Na2   0.179  (0.051)  0.156  (0.052)  0.513  (0.039)  0.461  (0.045)  0.092 
Si3   0.511  (0.043)  0.438  (0.046)  0.086  (0.049)  0.136  (0.055)  0.449 
Na4   0.252  (0.052)  0.230  (0.054)  0.612  (0.043)  0.708  (0.038)  0.326 
Na5   0.173  (0.049)  0.189  (0.052)  0.482  (0.042)  0.531  (0.045)  0.124 
Si6   0.551  (0.042)  0.512  (0.043)  0.375  (0.046)  0.396  (0.047)  0.534 
Na7   0.321  (0.051)  0.276  (0.052)  0.646  (0.040)  0.699  (0.036)  0.354 
Si8   0.601  (0.037)  0.517  (0.044)  0.259  (0.048)  0.295  (0.051)  0.685 
Na9   0.231  (0.052)  0.151  (0.054)  0.444  (0.048)  0.532  (0.043)  0.244 
Si10                  0.529  (0.042)  0.249  (0.049)  0.207  (0.053)  0.542 
Si11  0.529  (0.042)                  0.231  (0.048)  0.239  (0.057)  0.457 
Na12  0.249  (0.049)  0.231  (0.048)                  0.666  (0.035)  0.267 
Na13  0.207  (0.053)  0.239  (0.057)  0.666  (0.035)                  0.291 
Si14  0.542  (0.042)  0.457  (0.047)  0.267  (0.049)  0.291  (0.052)        
     0% ci  
Si1  (0.043)
Na2  (0.053)
Si3  (0.044)
Na4  (0.052)
Na5  (0.051)
Si6  (0.042)
Na7  (0.049)
Si8  (0.036)
Na9  (0.054)
Si10 (0.042)
Si11 (0.047)
Na12 (0.049)
Na13 (0.052)
Si14        

$Groups$`1`$Hi
     Item H  se     
Si1    0.368 (0.026)
Na2    0.281 (0.030)
Si3    0.266 (0.029)
Na4    0.406 (0.029)
Na5    0.313 (0.030)
Si6    0.451 (0.025)
Na7    0.438 (0.026)
Si8    0.410 (0.026)
Na9    0.351 (0.029)
Si10   0.379 (0.025)
Si11   0.346 (0.027)
Na12   0.379 (0.025)
Na13   0.417 (0.027)
Si14   0.379 (0.026)

$Groups$`1`$H
 Scale H se     
   0.369 (0.020)
  1. Analisi di Scalabilità su “NA”:

    • Per l’item 5, è stata osservata la maggiore differenza di scalabilità tra uomini e donne. Gli uomini hanno mostrato un valore di scalabilità superiore (H5 = 0.50) rispetto alle donne (H5 = 0.44).

    • La scalabilità totale, tuttavia, è risultata uguale per entrambi i gruppi.

  2. Analisi di Scalabilità su “SI”:

    • Per l’item 3, la differenza più grande si è verificata tra uomini e donne, con gli uomini che hanno mostrato un valore di scalabilità di H3 = 0.45 (con un errore standard, SE = 0.03) mentre per le donne H3 = 0.19 (SE = 0.11).

    • La scalabilità totale era maggiore per gli uomini (H = 0.52, SE = 0.02) rispetto alle donne (H = 0.42, SE = 0.07).

  3. Analisi di Scalabilità su “DS14”:

    • Tranne che per gli item 9 e 13, la scalabilità degli item è risultata generalmente più alta per gli uomini.

    • Per le donne, l’item 3 ha mostrato una scalabilità di H3 = -0.01 (SE = 0.10) mentre per gli uomini H3 = 0.22 (SE = 0.03).

    • L’item 3, che afferma “Parlo spesso con sconosciuti”, sembra evocare un modello di risposta diverso tra i gruppi di genere.

Gli “H” rappresentano gli indici di scalabilità di Mokken, che misurano quanto bene un item si adatta a una scala monotona. Un valore di H più alto indica che l’item è più discriminante e consistente nel gruppo considerato. L’errore standard (SE) fornisce una stima della variabilità dell’indice di scalabilità, con valori più bassi che indicano stime più precise.

In questo studio, gli item specificati mostrano come uomini e donne possano rispondere diversamente a certi stimoli o domande, il che può riflettere differenze nei tratti o nelle esperienze di vita che il questionario cerca di misurare.

67.11. Considerazioni conclusive#

Sijtsma and van der Ark [SvdA17], concludono proponendo le seguenti considerazioni:

  • Qualsiasi analisi di scala è complessa, e lo è anche l’analisi MSA. In diverse fasi di analisi, per vari insiemi di elementi e singoli elementi, il ricercatore deve valutare le ipotesi dei modelli di misurazione e fornire indici di qualità come scalabilità e affidabilità. Considerare solo i coefficienti di scalabilità fornisce un quadro incompleto e deve essere scoraggiato.

  • La procedura a tre fasi, in dieci passaggi, aiuta il ricercatore nel suo percorso ma deve essere applicata con giudizio; cioè, le decisioni di includere o escludere item e assemblare item in scale non devono essere basate solo su considerazioni statistiche, ma devono anche essere evidenti dal contenuto dell’item, preferibilmente derivato da basi teoriche.

67.12. Session Info#

sessionInfo()
R version 4.3.3 (2024-02-29)
Platform: x86_64-apple-darwin20 (64-bit)
Running under: macOS Sonoma 14.4.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.11.0

locale:
[1] en_US.UTF-8/UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: Europe/Rome
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] mice_3.16.0          lubridate_1.9.3      forcats_1.0.0       
 [4] stringr_1.5.1        dplyr_1.1.4          purrr_1.0.2         
 [7] readr_2.1.5          tidyr_1.3.1          tibble_3.2.1        
[10] ggplot2_3.5.1        tidyverse_2.0.0      mokken_3.1.0        
[13] poLCA_1.6.0.1        MASS_7.3-60.0.1      scatterplot3d_0.3-44

loaded via a namespace (and not attached):
 [1] utf8_1.2.4        generics_0.1.3    shape_1.4.6.1     stringi_1.8.3    
 [5] lattice_0.22-6    lme4_1.1-35.3     mitml_0.4-5       hms_1.1.3        
 [9] digest_0.6.35     magrittr_2.0.3    evaluate_0.23     grid_4.3.3       
[13] timechange_0.3.0  iterators_1.0.14  pbdZMQ_0.3-11     fastmap_1.1.1    
[17] jomo_2.7-6        foreach_1.5.2     jsonlite_1.8.8    glmnet_4.1-8     
[21] Matrix_1.6-5      nnet_7.3-19       backports_1.4.1   survival_3.5-8   
[25] fansi_1.0.6       scales_1.3.0      codetools_0.2-19  cli_3.6.2        
[29] rlang_1.1.3       crayon_1.5.2      splines_4.3.3     munsell_0.5.1    
[33] base64enc_0.1-3   withr_3.0.0       repr_1.1.6        pan_1.9          
[37] tools_4.3.3       tzdb_0.4.0        uuid_1.2-0        nloptr_2.0.3     
[41] minqa_1.2.6       colorspace_2.1-0  boot_1.3-30       broom_1.0.5      
[45] IRdisplay_1.1     rpart_4.1.23      vctrs_0.6.5       R6_2.5.1         
[49] lifecycle_1.0.4   pkgconfig_2.0.3   pillar_1.9.0      gtable_0.3.5     
[53] glue_1.7.0        Rcpp_1.0.12       tidyselect_1.2.1  IRkernel_1.3.2   
[57] nlme_3.1-164      htmltools_0.5.8.1 compiler_4.3.3