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.
I make contact easily when I meet people
I often make a fuss about unimportant things
I often talk to strangers
I often feel unhappy
I am often irritated
I often feel inhibited in social interactions
I take a gloomy view of things
I find it hard to start a conversation
I am often in a bad mood
I am a closed kind of person
I would rather keep other people at a distance
I often find myself worrying about something
I am often down in the dumps
When socializing, I don’t find the right things to talk about
suppressPackageStartupMessages({
library("mokken")
library("tidyverse")
library("mice")
})
data(DS14)
head(DS14)
| Male | Age | Si1* | Na2 | Si3* | Na4 | Na5 | Si6 | Na7 | Si8 | Na9 | Si10 | Si11 | Na12 | Na13 | Si14 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 59 | 2 | 3 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 2 | 4 | 2 | 4 |
| 1 | 54 | 2 | 0 | 3 | 0 | 0 | 2 | 0 | 2 | 0 | 2 | 4 | 3 | 0 | 2 |
| 1 | 50 | 1 | 3 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |
| 1 | 52 | 2 | 3 | 2 | 0 | 0 | 1 | 0 | 2 | 1 | 3 | 1 | 1 | 0 | 1 |
| 1 | 59 | 2 | 2 | 1 | 2 | 2 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 1 | 3 |
| 0 | 58 | 4 | 3 | 4 | 1 | 2 | 0 | 1 | 0 | 2 | 0 | 0 | 4 | 2 | 0 |
# 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)
| Si1 | Na2 | Si3 | Na4 | Na5 | Si6 | Na7 | Si8 | Na9 | Si10 | Si11 | Na12 | Na13 | Si14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 1 | 2 | 3 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 2 | 4 | 2 | 4 |
| 2 | 2 | 0 | 3 | 0 | 0 | 2 | 0 | 2 | 0 | 2 | 4 | 3 | 0 | 2 |
| 3 | 1 | 3 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |
| 4 | 2 | 3 | 2 | 0 | 0 | 1 | 0 | 2 | 1 | 3 | 1 | 1 | 0 | 1 |
| 5 | 2 | 2 | 1 | 2 | 2 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 1 | 3 |
| 6 | 4 | 3 | 4 | 1 | 2 | 0 | 1 | 0 | 2 | 0 | 0 | 4 | 2 | 0 |
67.2. Step 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)
| Si1 | Na2 | Si3 | Na4 | Na5 | Si6 | Na7 | Si8 | Na9 | Si10 | Si11 | Na12 | Na13 | Si14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | <dbl> | |
| 1 | 2 | 3 | 2 | 2 | 2 | 2 | 3 | 3 | 2 | 2 | 2 | 4 | 2 | 4 |
| 2 | 2 | 0 | 1 | 0 | 0 | 2 | 0 | 2 | 0 | 2 | 4 | 3 | 0 | 2 |
| 3 | 3 | 3 | 3 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |
| 4 | 2 | 3 | 2 | 0 | 0 | 1 | 0 | 2 | 1 | 3 | 1 | 1 | 0 | 1 |
| 5 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 1 | 3 |
| 6 | 0 | 3 | 0 | 1 | 2 | 0 | 1 | 0 | 2 | 0 | 0 | 4 | 2 | 0 |
67.3. Step 2#
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#
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)
# Correlation of G+ with X+, X+ ()
xPlus <- rowSums(itemsScores)
xPlusNa <- rowSums(itemsScores[, Na])
xPlusSi <- rowSums(itemsScores[, Si])
cor(cbind(gPlus, xPlus, xPlusNa, xPlusSi))
| gPlus | xPlus | xPlusNa | xPlusSi | |
|---|---|---|---|---|
| gPlus | 1.0000000 | 0.2826675 | 0.3224755 | 0.1416448 |
| xPlus | 0.2826675 | 1.0000000 | 0.8194633 | 0.8211281 |
| xPlusNa | 0.3224755 | 0.8194633 | 1.0000000 | 0.3457729 |
| xPlusSi | 0.1416448 | 0.8211281 | 0.3457729 | 1.0000000 |
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#
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.
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
-
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- $Index
- $W1
A matrix: 7 × 7 of type dbl Na2 Na4 Na5 Na7 Na9 Na12 Na13 Na2 NA 0.6179697 1.2066679 1.379887 1.0918364 3.5995994 2.164015 Na4 0.4210748 NA 0.8414810 1.753125 1.0550188 2.6399419 3.698480 Na5 0.5506875 0.8513984 NA 1.883061 1.6898703 1.1305348 2.105468 Na7 0.1219797 0.5447578 0.2169763 NA 0.7527397 1.6090471 1.404433 Na9 0.7567135 0.9076606 1.1558442 1.629162 NA 0.2244819 1.904042 Na12 0.8473397 0.6294961 0.2911338 1.861060 0.8821990 NA 2.135409 Na13 0.1200216 0.3472191 0.2334970 1.101058 0.3292302 1.9645768 NA - $W2
A matrix: 1 × 7 of type dbl 46.05904 39.59751 43.65944 36.36045 44.05644 36.08189 39.60723 - $W3
A matrix: 7 × 7 of type dbl Na2 Na4 Na5 Na7 Na9 Na12 Na13 Na2 NA 12.289372 3.243247 10.058823 6.395469 3.918299 10.153830 Na4 12.289372 NA 9.886621 3.011686 7.617531 4.007542 2.784763 Na5 3.243247 9.886621 NA 9.606688 2.424949 6.988068 11.509870 Na7 10.058823 3.011686 9.606688 NA 6.554529 4.415711 2.713013 Na9 6.395469 7.617531 2.424949 6.554529 NA 12.685237 8.378724 Na12 3.918299 4.007542 6.988068 4.415711 12.685237 NA 4.067033 Na13 10.153830 2.784763 11.509870 2.713013 8.378724 4.067033 NA
- $Flagged
- $F1
A matrix: 7 × 7 of type dbl Na2 Na4 Na5 Na7 Na9 Na12 Na13 Na2 0 0 0 0 0 0 0 Na4 0 0 0 0 0 0 0 Na5 0 0 0 0 0 0 0 Na7 0 0 0 0 0 0 0 Na9 0 0 0 0 0 0 0 Na12 0 0 0 0 0 0 0 Na13 0 0 0 0 0 0 0 - $F2
A matrix: 1 × 7 of type dbl 0 0 0 0 0 0 0 - $F3
A matrix: 7 × 7 of type dbl Na2 Na4 Na5 Na7 Na9 Na12 Na13 Na2 0 0 0 0 0 0 0 Na4 0 0 0 0 0 0 0 Na5 0 0 0 0 0 0 0 Na7 0 0 0 0 0 0 0 Na9 0 0 0 0 0 0 0 Na12 0 0 0 0 0 0 0 Na13 0 0 0 0 0 0 0
check.ca(itemsScores[, Si], TRUE)
- $InScale
-
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- TRUE
- FALSE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- TRUE
- FALSE
- TRUE
- TRUE
- TRUE
- TRUE
- FALSE
-
- $Index
- $W1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA 0.61080275 0.13233200 0.3864878 0.3214138 0.39027350 0.2545415 Si3 7.4940537 NA 0.14788369 3.3404313 2.2940595 1.62689279 1.9854466 Si6 3.2383893 0.02665348 NA 3.0148224 3.0785904 1.69901340 2.0204872 Si8 0.8887082 0.14169155 0.07253119 NA 0.3775119 0.09634922 0.4288780 Si10 1.5960351 0.08681354 0.13281054 0.8860611 NA 0.83018918 0.2547350 Si11 1.6889198 0.27593365 0.27492005 0.8375871 1.0178655 NA 0.1092758 Si14 1.5630712 0.16251226 0.53781990 2.5512166 1.3677266 0.16834674 NA - $W2
A matrix: 1 × 7 of type dbl 39.50309 45.65888 45.38552 34.33251 37.19939 42.15621 40.21989 - $W3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA 1.235175 6.876940 8.953452 6.179279 7.308560 8.949681 Si3 1.235175 NA 14.953617 8.153276 6.268706 6.972669 8.075439 Si6 6.876940 14.953617 NA 3.861704 7.052217 6.761927 5.879112 Si8 8.953452 8.153276 3.861704 NA 5.155177 6.799279 1.409627 Si10 6.179279 6.268706 7.052217 5.155177 NA 5.475873 7.068136 Si11 7.308560 6.972669 6.761927 6.799279 5.475873 NA 8.837899 Si14 8.949681 8.075439 5.879112 1.409627 7.068136 8.837899 NA
- $W1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA NA 0.13233200 0.3864849 0.3214011 0.38246417 0.25232684 Si3 NA NA NA NA NA NA NA Si6 0.14118765 NA NA 0.6130808 1.1122510 0.44549143 0.26424484 Si8 0.07884079 NA 0.06649432 NA 0.2590659 0.06108522 0.25906970 Si10 0.33580780 NA 0.12444040 0.7630631 NA 0.61772374 0.21501398 Si11 0.38493217 NA 0.25941331 0.6862065 0.8826178 NA 0.09181554 Si14 0.54030147 NA 0.41984998 1.8869084 1.2937128 0.05051468 NA - $W2
A matrix: 1 × 7 of type dbl 20.21876 NA 24.34267 18.70754 22.2938 25.93124 24.02858 - $W3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA NA 4.917433 4.099943 2.760407 3.594524 4.846455 Si3 NA NA NA NA NA NA NA Si6 4.917433 NA NA 3.022826 5.692270 5.835754 4.874390 Si8 4.099943 NA 3.022826 NA 4.364169 6.050361 1.170238 Si10 2.760407 NA 5.692270 4.364169 NA 3.395029 6.081922 Si11 3.594524 NA 5.835754 6.050361 3.395029 NA 7.055575 Si14 4.846455 NA 4.874390 1.170238 6.081922 7.055575 NA
- $W1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA NA 0.04749283 0.10001891 0.2706452 0.36325565 NA Si3 NA NA NA NA NA NA NA Si6 0.06539702 NA NA 0.25563275 0.3206986 0.43438917 NA Si8 0.07880992 NA 0.06644315 NA 0.2589359 0.06108031 NA Si10 0.06804149 NA 0.01301436 0.04022932 NA 0.59752476 NA Si11 0.18821851 NA 0.03587970 0.16604595 0.4313432 NA NA Si14 NA NA NA NA NA NA NA - $W2
A matrix: 1 × 7 of type dbl 11.14005 NA 13.20044 9.150614 11.47446 12.69603 NA - $W3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 NA NA 3.599736 2.185717 2.639904 2.714694 NA Si3 NA NA NA NA NA NA NA Si6 3.599736 NA NA 1.330815 4.817293 3.452590 NA Si8 2.185717 NA 1.330815 NA 1.561302 4.072780 NA Si10 2.639904 NA 4.817293 1.561302 NA 2.455961 NA Si11 2.714694 NA 3.452590 4.072780 2.455961 NA NA Si14 NA NA NA NA NA NA NA
- $Flagged
- $F1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 0 0 0 0 0 0 Si3 1 0 0 0 0 0 0 Si6 0 0 0 0 0 0 0 Si8 0 0 0 0 0 0 0 Si10 0 0 0 0 0 0 0 Si11 0 0 0 0 0 0 0 Si14 0 0 0 0 0 0 0 - $F2
A matrix: 1 × 7 of type dbl 0 0 0 0 0 0 0 - $F3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 0 0 0 0 0 0 Si3 0 0 1 0 0 0 0 Si6 0 1 0 0 0 0 0 Si8 0 0 0 0 0 0 0 Si10 0 0 0 0 0 0 0 Si11 0 0 0 0 0 0 0 Si14 0 0 0 0 0 0 0
- $F1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 NA 0 0 0 0 0 Si3 NA NA NA NA NA NA NA Si6 0 NA 0 0 0 0 0 Si8 0 NA 0 0 0 0 0 Si10 0 NA 0 0 0 0 0 Si11 0 NA 0 0 0 0 0 Si14 0 NA 0 1 0 0 0 - $F2
A matrix: 1 × 7 of type dbl 0 NA 0 0 0 0 0 - $F3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 NA 0 0 0 0 0 Si3 NA NA NA NA NA NA NA Si6 0 NA 0 0 0 0 0 Si8 0 NA 0 0 0 0 0 Si10 0 NA 0 0 0 0 0 Si11 0 NA 0 0 0 0 0 Si14 0 NA 0 0 0 0 0
- $F1
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 NA 0 0 0 0 NA Si3 NA NA NA NA NA NA NA Si6 0 NA 0 0 0 0 NA Si8 0 NA 0 0 0 0 NA Si10 0 NA 0 0 0 0 NA Si11 0 NA 0 0 0 0 NA Si14 NA NA NA NA NA NA NA - $F2
A matrix: 1 × 7 of type dbl 0 NA 0 0 0 0 NA - $F3
A matrix: 7 × 7 of type dbl Si1 Si3 Si6 Si8 Si10 Si11 Si14 Si1 0 NA 0 0 0 0 NA Si3 NA NA NA NA NA NA NA Si6 0 NA 0 0 0 0 NA Si8 0 NA 0 0 0 0 NA Si10 0 NA 0 0 0 0 NA Si11 0 NA 0 0 0 0 NA Si14 NA NA NA NA NA NA NA
check.ca(itemsScores, TRUE)
- $InScale
-
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- TRUE
- TRUE
- FALSE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- FALSE
- TRUE
- FALSE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
- TRUE
-
- $Index
- $W1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA 3.7656759 5.3950361 12.763969 5.392215 22.27823 13.89110 18.465576 7.967065 16.551151 13.990934 10.170014 13.621740 15.756574 Na2 9.338788 NA 3.1339634 16.357831 13.147263 17.60705 19.81005 14.050577 15.865210 13.169944 12.459782 21.209560 20.672213 12.380653 Si3 31.467695 8.3767345 NA 16.654163 7.654408 23.64544 18.93421 27.580420 14.432880 27.338030 23.133233 14.694454 17.397528 26.568026 Na4 5.849691 2.0894263 1.9303778 NA 3.342817 13.93560 11.92809 9.399139 5.810212 6.290490 6.446997 8.583626 11.018004 8.642545 Na5 10.014376 9.0500166 2.9697158 16.619004 NA 21.90283 20.61846 11.172094 15.296915 11.746344 13.844898 13.650013 17.805039 11.374531 Si6 5.409296 0.8488675 0.2330259 5.003882 2.895776 NA 6.80852 5.595272 6.359225 3.790967 3.408145 2.813723 7.055205 4.341929 Na7 6.806945 1.4946857 1.4407670 8.238079 1.905501 11.80435 NA 8.795147 3.962045 7.965476 5.593104 8.210832 8.798303 8.797831 Si8 6.859512 2.3198355 1.5996206 9.563978 1.520464 14.96694 11.04066 NA 8.590548 5.904984 5.125885 5.524485 9.223541 7.712751 Na9 7.898193 4.6657959 2.0920162 11.162755 7.147696 17.49868 12.94410 12.835822 NA 9.737938 7.423739 8.347900 11.672639 11.733514 Si10 8.465390 2.2860736 2.4677840 8.180382 3.338846 14.92748 13.27133 12.138669 7.431532 NA 9.332409 7.344684 8.272975 10.098650 Si11 9.480336 2.4753882 3.7213631 9.469153 6.390568 15.69793 11.28610 10.091799 6.319459 10.205066 NA 8.830749 12.620963 8.874111 Na12 9.660531 4.4743872 1.3038690 11.187390 3.997470 13.56376 14.16189 10.886371 6.534872 9.563710 8.738885 NA 14.280056 10.183019 Na13 7.556236 2.2730320 1.8801824 10.161251 2.783035 12.08124 12.78433 10.008027 4.055762 6.292040 6.135067 7.821810 NA 8.712854 Si14 10.261308 1.9078247 2.5234735 9.320444 2.522014 12.30929 11.65321 13.136709 8.191802 8.646156 7.115753 7.669230 9.186305 NA - $W2
A matrix: 1 × 14 of type dbl 199.7975 209.1171 222.4811 196.5573 208.3068 171.5022 184.1062 183.4612 201.4381 196.0021 208.553 201.7752 187.5183 200.3439 - $W3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA 23.583543 1.439905 21.025183 23.756321 7.990476 23.449608 4.690190 24.787752 4.642923 7.043891 24.943112 22.994205 9.450376 Na2 23.583543 NA 26.436852 13.401040 5.599161 17.729224 10.278958 20.919021 7.929977 21.576151 22.591901 5.733513 8.679145 24.658609 Si3 1.439905 26.436852 NA 23.000517 28.979946 14.350101 24.146972 5.481497 25.389764 8.066076 7.754072 24.237619 23.679720 9.518100 Na4 21.025183 13.401040 23.000517 NA 11.491672 15.805479 5.786337 21.039569 8.789801 23.734776 21.745469 6.876545 5.704178 18.156704 Na5 23.756321 5.599161 28.979946 11.491672 NA 16.944251 8.575985 23.184673 5.977763 21.660071 21.430096 8.312872 8.498457 23.895494 Si6 7.990476 17.729224 14.350101 15.805479 16.944251 NA 15.115749 6.570141 17.411380 7.376653 9.288402 17.497212 15.955490 9.467630 Na7 23.449608 10.278958 24.146972 5.786337 8.575985 15.115749 NA 20.015148 7.338796 21.783799 20.889961 5.418474 3.985706 17.320702 Si8 4.690190 20.919021 5.481497 21.039569 23.184673 6.570141 20.015148 NA 21.120330 4.503019 8.217481 22.857170 20.365858 4.497078 Na9 24.787752 7.929977 25.389764 8.789801 5.977763 17.411380 7.338796 21.120330 NA 19.852483 23.506620 12.247466 7.808877 19.277134 Si10 4.642923 21.576151 8.066076 23.734776 21.660071 7.376653 21.783799 4.503019 19.852483 NA 8.434822 21.681058 23.542237 9.148065 Si11 7.043891 22.591901 7.754072 21.745469 21.430096 9.288402 20.889961 8.217481 23.506620 8.434822 NA 24.074272 21.045965 12.530008 Na12 24.943112 5.733513 24.237619 6.876545 8.312872 17.497212 5.418474 22.857170 12.247466 21.681058 24.074272 NA 5.365182 22.530682 Na13 22.994205 8.679145 23.679720 5.704178 8.498457 15.955490 3.985706 20.365858 7.808877 23.542237 21.045965 5.365182 NA 19.893302 Si14 9.450376 24.658609 9.518100 18.156704 23.895494 9.467630 17.320702 4.497078 19.277134 9.148065 12.530008 22.530682 19.893302 NA
- $W1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA 3.7656759 NA 12.763803 5.392211 22.278227 13.890982 18.465573 7.808112 16.551138 13.983125 10.170014 13.620763 15.754359 Na2 5.168384 NA NA 12.824940 10.346170 13.525239 16.005403 9.639891 12.308310 8.645005 8.419605 17.101838 17.080766 8.085127 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 2.927259 1.2302787 NA NA 2.513425 11.102750 9.784654 6.507296 4.532399 3.582967 4.163946 7.334070 9.050631 5.468034 Na5 6.149700 6.2307747 NA 13.181291 NA 17.414401 16.366912 7.565300 11.569358 7.454093 9.777547 9.710678 14.526032 7.269407 Si6 2.312094 0.5199761 NA 4.835524 2.579262 NA 6.038700 3.193530 4.973205 1.824628 2.154623 2.699062 6.212732 2.585687 Na7 3.868915 0.9290250 NA 6.547796 1.342486 9.087505 NA 5.792234 3.062543 4.845919 3.281795 6.415142 6.926073 5.819706 Si8 6.049644 2.3196208 NA 9.551355 1.519434 14.960905 10.981691 NA 8.423854 5.786538 5.090621 5.522902 9.166333 7.542943 Na9 4.762954 3.2093002 NA 8.249070 5.811365 13.672466 10.287373 8.927097 NA 6.050103 4.225303 6.310433 9.102697 8.056472 Si10 7.205163 2.2859751 NA 8.179009 3.311999 14.919108 13.119987 12.015671 7.276035 NA 9.119943 7.336979 8.238073 10.058929 Si11 8.176349 2.4752589 NA 9.466454 6.367092 15.682419 11.217817 9.940419 6.255304 10.069818 NA 8.829939 12.611387 8.856651 Na12 5.838051 2.9750387 NA 8.379742 2.845856 10.914908 11.385362 7.453634 4.717835 5.808480 5.693636 NA 11.353235 6.892064 Na13 4.435854 1.4388142 NA 8.081367 2.185438 9.178688 10.547555 7.021736 2.926157 3.335403 3.574300 6.383381 NA 5.651557 Si14 9.238538 1.8945364 NA 9.313604 2.514519 12.191325 11.637176 12.472400 8.098654 8.572142 6.997921 7.667735 8.940731 NA - $W2
A matrix: 1 × 14 of type dbl 183.4906 181.9844 NA 165.8003 180.8347 150.7912 164.063 174.6936 178.8568 180.665 190.4845 171.4054 154.802 181.3141 - $W3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA 23.780790 NA 19.535316 22.963098 5.731670 22.406986 5.536139 23.920166 4.078907 6.204828 22.230852 20.088205 7.013683 Na2 23.780790 NA NA 13.770937 6.825600 16.444537 10.386683 22.431811 7.770439 21.910459 21.797842 5.995459 8.190031 22.679833 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 19.535316 13.770937 NA NA 11.374518 15.656150 4.508709 19.855592 10.628301 21.069658 21.264498 8.063787 3.249037 16.823782 Na5 22.963098 6.825600 NA 11.374518 NA 16.912847 8.922352 24.230329 6.125241 22.208279 20.842778 6.581999 8.189950 25.657758 Si6 5.731670 16.444537 NA 15.656150 16.912847 NA 17.411490 6.472869 16.403934 6.207183 8.173074 16.623782 15.934809 8.818826 Na7 22.406986 10.386683 NA 4.508709 8.922352 17.411490 NA 19.508576 8.685418 20.636972 22.486362 6.005155 4.358228 18.746045 Si8 5.536139 22.431811 NA 19.855592 24.230329 6.472869 19.508576 NA 19.775288 4.532032 6.864838 22.769496 18.754285 3.962326 Na9 23.920166 7.770439 NA 10.628301 6.125241 16.403934 8.685418 19.775288 NA 20.567545 22.102593 13.031775 9.474248 20.371856 Si10 4.078907 21.910459 NA 21.069658 22.208279 6.207183 20.636972 4.532032 20.567545 NA 6.794242 22.415608 22.100840 8.143277 Si11 6.204828 21.797842 NA 21.264498 20.842778 8.173074 22.486362 6.864838 22.102593 6.794242 NA 21.908414 21.966164 10.078817 Na12 22.230852 5.995459 NA 8.063787 6.581999 16.623782 6.005155 22.769496 13.031775 22.415608 21.908414 NA 4.628721 21.150367 Na13 20.088205 8.190031 NA 3.249037 8.189950 15.934809 4.358228 18.754285 9.474248 22.100840 21.966164 4.628721 NA 17.867491 Si14 7.013683 22.679833 NA 16.823782 25.657758 8.818826 18.746045 3.962326 20.371856 8.143277 10.078817 21.150367 17.867491 NA
- $W1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na2 NA NA NA 9.911902 8.045225 9.852553 12.864620 6.329706 9.953431 5.293336 5.695918 13.811017 13.726837 5.303845 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 NA 1.0436371 NA NA 2.019564 8.209863 8.334766 4.567775 4.112617 2.089980 2.688691 6.609983 7.594499 3.901180 Na5 NA 4.8930832 NA 10.445484 NA 13.717248 13.370997 4.844171 9.683839 4.652835 6.974582 7.442898 12.071869 4.792993 Si6 NA 0.5155162 NA 4.827466 2.541566 NA 5.834359 3.112316 4.730148 1.648497 2.073000 2.697738 6.089226 2.472399 Na7 NA 0.6202472 NA 4.935163 1.035004 6.047585 NA 3.621332 2.568974 2.800166 1.637648 4.890220 5.374256 3.911354 Si8 NA 2.3195831 NA 9.429798 1.518974 14.927251 10.942139 NA 7.777493 5.759874 5.057029 5.522007 9.055772 7.425219 Na9 NA 2.0479517 NA 5.965457 4.564073 9.582883 7.899129 5.621354 NA 3.165950 1.952049 4.601055 6.809659 5.044614 Si10 NA 2.2859736 NA 8.178933 3.295717 14.911891 13.116214 12.007243 7.141527 NA 8.871903 7.335115 8.193650 10.058164 Si11 NA 2.4752299 NA 9.459187 6.272177 15.675798 11.195626 9.930042 6.022304 10.001968 NA 8.829922 12.605660 8.836101 Na12 NA 2.5223799 NA 6.708784 2.279759 8.563978 9.518220 4.988942 4.177720 3.765587 4.035683 NA 9.321894 5.050960 Na13 NA 1.1490103 NA 6.706954 1.862815 6.775952 8.788081 4.854821 2.503683 1.724380 2.550900 5.746211 NA 3.735390 Si14 NA 1.8703108 NA 9.277222 2.509960 12.106485 11.617496 12.185934 7.663806 8.521386 6.978712 7.655978 8.744605 NA - $W2
A matrix: 1 × 14 of type dbl NA 153.0343 NA 140.2051 149.8509 137.0658 139.9683 159.1131 152.8541 162.9803 164.3808 144.6456 138.9441 162.3001 - $W3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na2 NA NA NA 13.368235 7.628871 15.829520 9.990274 20.042775 8.947831 20.813679 19.083393 4.915126 9.369114 23.045519 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 NA 13.368235 NA NA 11.811750 16.171848 5.020097 18.969383 10.447759 19.627398 19.650382 6.201317 2.843713 16.093198 Na5 NA 7.628871 NA 11.811750 NA 13.796792 10.654213 21.916268 5.765976 19.509011 18.555753 7.742425 10.253061 22.216814 Si6 NA 15.829520 NA 16.171848 13.796792 NA 14.896317 5.825505 15.893522 5.468681 7.034744 16.457941 18.247187 7.443786 Na7 NA 9.990274 NA 5.020097 10.654213 14.896317 NA 20.044285 9.923651 20.218434 20.350933 6.509602 6.127556 16.232976 Si8 NA 20.042775 NA 18.969383 21.916268 5.825505 20.044285 NA 18.308179 3.873418 5.968182 21.513202 20.190087 2.461829 Na9 NA 8.947831 NA 10.447759 5.765976 15.893522 9.923651 18.308179 NA 19.685657 20.741003 15.384444 8.604593 19.151466 Si10 NA 20.813679 NA 19.627398 19.509011 5.468681 20.218434 3.873418 19.685657 NA 4.713258 20.628075 20.186516 8.256204 Si11 NA 19.083393 NA 19.650382 18.555753 7.034744 20.350933 5.968182 20.741003 4.713258 NA 19.611732 20.571127 8.100257 Na12 NA 4.915126 NA 6.201317 7.742425 16.457941 6.509602 21.513202 15.384444 20.628075 19.611732 NA 4.467404 21.214324 Na13 NA 9.369114 NA 2.843713 10.253061 18.247187 6.127556 20.190087 8.604593 20.186516 20.571127 4.467404 NA 18.083776 Si14 NA 23.045519 NA 16.093198 22.216814 7.443786 16.232976 2.461829 19.151466 8.256204 8.100257 21.214324 18.083776 NA
- $Flagged
- $F1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si3 1 0 0 0 0 0 0 1 0 1 0 0 0 1 Na4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - $F2
A matrix: 1 × 14 of type dbl 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - $F3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Na13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Si14 0 0 0 0 0 0 0 0 0 0 0 0 0 0
- $F1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 0 0 NA 0 0 1 0 1 0 0 0 0 0 0 Na2 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na5 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si6 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na7 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si8 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na9 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si10 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si11 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na12 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na13 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si14 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 - $F2
A matrix: 1 × 14 of type dbl 0 0 NA 0 0 0 0 0 0 0 1 0 0 0 - $F3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na2 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na5 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si6 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na7 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si8 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na9 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si10 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si11 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na12 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na13 0 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si14 0 0 NA 0 0 0 0 0 0 0 0 0 0 0
- $F1
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na2 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na5 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si6 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na7 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si8 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na9 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si10 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si11 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na12 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na13 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si14 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 - $F2
A matrix: 1 × 14 of type dbl NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 - $F3
A matrix: 14 × 14 of type dbl Si1 Na2 Si3 Na4 Na5 Si6 Na7 Si8 Na9 Si10 Si11 Na12 Na13 Si14 Si1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na2 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA Na4 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na5 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si6 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na7 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si8 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na9 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si10 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si11 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na12 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Na13 NA 0 NA 0 0 0 0 0 0 0 0 0 0 0 Si14 NA 0 NA 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#
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)
| ItemH | #ac | #vi | #vi/#ac | maxvi | sum | sum/#ac | zmax | #zsig | crit | |
|---|---|---|---|---|---|---|---|---|---|---|
| Na2 | 0.48 | 84 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
| Na4 | 0.56 | 107 | 1 | 0.01 | 0.04 | 0.04 | 0.0004 | 0.77 | 0 | -1 |
| Na5 | 0.50 | 79 | 1 | 0.01 | 0.05 | 0.05 | 0.0007 | 0.95 | 0 | 4 |
| Na7 | 0.59 | 78 | 2 | 0.03 | 0.07 | 0.10 | 0.0013 | 1.02 | 0 | 5 |
| Na9 | 0.51 | 86 | 4 | 0.05 | 0.08 | 0.23 | 0.0027 | 1.26 | 0 | 17 |
| Na12 | 0.56 | 78 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
| Na13 | 0.62 | 59 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
summary(resMonSi)
| ItemH | #ac | #vi | #vi/#ac | maxvi | sum | sum/#ac | zmax | #zsig | crit | |
|---|---|---|---|---|---|---|---|---|---|---|
| Si1 | 0.57 | 108 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
| Si3 | 0.45 | 112 | 5 | 0.04 | 0.08 | 0.24 | 0.0021 | 0.91 | 0 | 18 |
| Si6 | 0.49 | 103 | 8 | 0.08 | 0.07 | 0.45 | 0.0044 | 1.76 | 1 | 39 |
| Si8 | 0.57 | 89 | 1 | 0.01 | 0.04 | 0.04 | 0.0005 | 0.92 | 0 | -1 |
| Si10 | 0.55 | 96 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
| Si11 | 0.49 | 97 | 6 | 0.06 | 0.09 | 0.38 | 0.0040 | 1.53 | 0 | 26 |
| Si14 | 0.52 | 89 | 3 | 0.03 | 0.04 | 0.10 | 0.0012 | 1.13 | 0 | 8 |
summary(resMonDs)
| ItemH | #ac | #vi | #vi/#ac | maxvi | sum | sum/#ac | zmax | #zsig | crit | |
|---|---|---|---|---|---|---|---|---|---|---|
| Si1 | 0.35 | 95 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
| Na2 | 0.28 | 144 | 6 | 0.04 | 0.14 | 0.48 | 0.0034 | 1.97 | 1 | 52 |
| Si3 | 0.22 | 112 | 6 | 0.05 | 0.07 | 0.29 | 0.0026 | 1.16 | 0 | 32 |
| Na4 | 0.40 | 96 | 1 | 0.01 | 0.09 | 0.09 | 0.0009 | 0.91 | 0 | 13 |
| Na5 | 0.31 | 112 | 3 | 0.03 | 0.05 | 0.13 | 0.0012 | 0.92 | 0 | 18 |
| Si6 | 0.44 | 118 | 6 | 0.05 | 0.04 | 0.25 | 0.0021 | 1.00 | 0 | 17 |
| Na7 | 0.43 | 95 | 11 | 0.12 | 0.07 | 0.41 | 0.0043 | 1.51 | 0 | 33 |
| Si8 | 0.41 | 91 | 5 | 0.05 | 0.08 | 0.22 | 0.0024 | 1.06 | 0 | 22 |
| Na9 | 0.35 | 83 | 5 | 0.06 | 0.05 | 0.25 | 0.0031 | 1.40 | 0 | 26 |
| Si10 | 0.37 | 129 | 3 | 0.02 | 0.10 | 0.19 | 0.0014 | 0.96 | 0 | 21 |
| Si11 | 0.34 | 131 | 3 | 0.02 | 0.08 | 0.19 | 0.0015 | 1.73 | 1 | 35 |
| Na12 | 0.37 | 105 | 2 | 0.02 | 0.06 | 0.09 | 0.0009 | 0.62 | 0 | 12 |
| Na13 | 0.42 | 97 | 1 | 0.01 | 0.03 | 0.03 | 0.0003 | 0.33 | 0 | 2 |
| Si14 | 0.38 | 90 | 0 | 0.00 | 0.00 | 0.00 | 0.0000 | 0.00 | 0 | 0 |
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#
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/#ac maxvi sum sum/#ac tmax #tsig crit Na2 0.48 36 2 0.06 0.24 0.46 0.0128 1.95 2 70 Na12 0.56 35 3 0.09 0.24 0.59 0.0168 1.95 2 74 Na5 0.50 36 1 0.03 0.13 0.13 0.0036 0.75 0 17 Na7 0.59 36 4 0.11 0.16 0.60 0.0167 2.53 2 71 Na9 0.52 36 5 0.14 0.36 1.11 0.0309 3.13 3 124 Na4 0.56 36 3 0.08 0.28 0.58 0.0162 2.36 3 86 Na13 0.62 35 2 0.06 0.36 0.54 0.0154 3.13 2 85 - $backward.selection
A matrix: 7 × 4 of type dbl step 1 step 2 step 3 step 4 Na2 1 1 1 NA Na12 1 1 1 0 Na5 0 0 0 0 Na7 2 1 0 0 Na9 3 NA NA NA Na4 3 2 NA NA Na13 2 1 0 0 - $HT
- 0.438472566753628
summary(resIioSi)
- $method
- 'MIIO'
- $item.summary
A matrix: 7 × 10 of type dbl ItemH #ac #vi #vi/#ac maxvi sum sum/#ac tmax #tsig crit Si3 0.45 37 0 0.00 0.00 0.00 0.0000 0.00 0 0 Si11 0.49 36 2 0.06 0.32 0.49 0.0136 2.95 2 84 Si10 0.55 37 2 0.05 0.32 0.46 0.0124 2.95 1 72 Si1 0.57 38 2 0.05 0.24 0.40 0.0106 1.61 0 42 Si8 0.57 37 4 0.11 0.26 0.73 0.0196 1.76 1 74 Si6 0.49 36 3 0.08 0.26 0.64 0.0178 1.61 0 60 Si14 0.52 37 1 0.03 0.13 0.13 0.0036 1.12 0 18 - $backward.selection
A matrix: 7 × 2 of type dbl step 1 step 2 Si3 0 0 Si11 2 NA Si10 1 0 Si1 0 0 Si8 1 0 Si6 0 0 Si14 0 0 - $HT
- 0.121036422377558
summary(resIioDs)
- $method
- 'MIIO'
- $item.summary
A matrix: 14 × 10 of type dbl ItemH #ac #vi #vi/#ac maxvi sum sum/#ac tmax #tsig crit Na2 0.28 93 4 0.04 0.35 1.06 0.0114 2.25 1 86 Na12 0.37 94 7 0.07 0.58 2.05 0.0218 2.89 3 135 Si3 0.22 96 7 0.07 0.58 2.05 0.0214 2.89 2 137 Na5 0.31 93 5 0.05 0.25 1.08 0.0116 1.14 0 60 Si11 0.34 96 4 0.04 0.24 0.79 0.0082 1.61 0 53 Si10 0.37 91 2 0.02 0.23 0.36 0.0040 1.61 0 40 Si1 0.35 95 5 0.05 0.39 1.27 0.0133 2.93 2 99 Si8 0.41 94 4 0.04 0.29 0.87 0.0093 2.23 2 75 Si6 0.44 96 8 0.08 0.39 1.71 0.0178 2.93 2 105 Si14 0.38 93 6 0.06 0.30 1.19 0.0128 2.25 2 85 Na7 0.43 96 8 0.08 0.40 1.87 0.0195 2.92 4 116 Na9 0.35 97 10 0.10 0.40 1.92 0.0198 2.49 3 116 Na4 0.40 96 6 0.06 0.28 1.24 0.0130 2.92 4 94 Na13 0.42 94 4 0.04 0.28 0.74 0.0079 1.94 1 64 - $backward.selection
A matrix: 14 × 6 of type dbl step 1 step 2 step 3 step 4 step 5 step 6 Na2 1 1 0 0 0 0 Na12 2 2 NA NA NA NA Si3 1 1 0 0 0 0 Na5 0 0 0 0 0 0 Si11 0 0 0 0 0 0 Si10 0 0 0 0 0 0 Si1 2 2 2 NA NA NA Si8 2 2 2 1 0 0 Si6 2 2 2 1 0 0 Si14 2 2 2 2 NA NA Na7 2 1 1 1 1 0 Na9 2 1 1 1 1 NA Na4 3 NA NA NA NA NA Na13 1 0 0 0 0 0 - $HT
- 0.155631246942616
# 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/#ac maxvi sum sum/#ac xmax #xsig crit Na2 0.28 930 67 0.07 0.10 3.28 0.0035 5.00 5 95 Na12 0.37 940 68 0.07 0.14 3.92 0.0042 7.00 10 117 Si3 0.22 960 65 0.07 0.14 3.44 0.0036 7.12 9 120 Na5 0.31 930 72 0.08 0.12 3.87 0.0042 6.00 6 106 Si11 0.34 960 69 0.07 0.14 3.78 0.0039 7.00 9 116 Si10 0.37 910 84 0.09 0.11 4.12 0.0045 7.12 12 122 Si1 0.35 950 65 0.07 0.10 3.37 0.0035 6.00 8 103 Si8 0.41 940 60 0.06 0.16 3.24 0.0034 6.00 6 101 Si6 0.44 960 69 0.07 0.14 3.63 0.0038 7.14 11 115 Si14 0.38 930 56 0.06 0.13 2.87 0.0031 6.40 6 99 Na7 0.43 960 62 0.06 0.17 3.12 0.0032 7.14 5 104 Na9 0.35 970 52 0.05 0.17 3.11 0.0032 9.00 9 123 Na4 0.40 960 38 0.04 0.14 1.78 0.0018 9.00 2 93 Na13 0.42 940 37 0.04 0.09 1.50 0.0016 4.00 2 61 - $backward.selection
A matrix: 14 × 10 of type dbl step 1 step 2 step 3 step 4 step 5 step 6 step 7 step 8 step 9 step 10 Na2 4 4 4 4 3 NA NA NA NA NA Na12 7 6 5 5 NA NA NA NA NA NA Si3 4 4 4 3 2 1 1 1 NA NA Na5 6 6 5 NA NA NA NA NA NA NA Si11 5 5 5 4 3 2 2 NA NA NA Si10 7 6 5 4 3 3 2 1 0 0 Si1 5 4 3 2 2 2 1 1 1 NA Si8 4 3 2 2 2 2 2 1 1 0 Si6 9 8 NA NA NA NA NA NA NA NA Si14 5 4 3 2 1 1 0 0 0 0 Na7 5 4 3 3 3 3 NA NA NA NA Na9 9 NA NA NA NA NA NA NA NA NA Na4 2 1 0 0 0 0 0 0 0 0 Na13 2 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#
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
-
- 0.561109330803049
- 0.672666349202855
- 0.59796006308463
- 0.720428543936926
- 0.62034425728731
- 0.673226022236864
- 0.745593733797823
- $MS
- 0.870585822377467
- $alpha
- 0.870525714715513
- $lambda.2
- 0.873002304002601
- $irc
-
- 0.719531318297224
- 0.53754980794435
- 0.616373529957479
- 0.732414321605589
- 0.689086278309901
- 0.595592592863512
- 0.645843416546044
- $MS
- 0.881483548710253
- $alpha
- 0.874670545530637
- $lambda.2
- 0.883217093565466
- $irc
-
- 0.521684456004778
- 0.408601876069594
- 0.327122024723764
- 0.5960367816755
- 0.45848610474584
- 0.669154194901804
- 0.646226455219469
- 0.623158664363801
- 0.524777674924687
- 0.566485040801581
- 0.496087120703027
- 0.549426117441985
- 0.622125970215216
- 0.568115691718221
- $MS
- 0.892032690253982
- $alpha
- 0.877185217828487
- $lambda.2
- 0.884159430531047
Tutte le stime sono molto alte e quindi soddisfacenti.
67.9. Step 9.#
Norme.
Nell’ambito della verifica delle scale Mokken, i ricercatori possono necessitare di tabelle normative per effettuare misurazioni accurate sugli individui. Una soluzione proposta da Oosterhuis, Van der Ark, e Sijtsma (2016) prevede l’utilizzo di una procedura di regressione per stimare le norme e gli intervalli di confidenza relativi a queste norme. Questo metodo consente di avere riferimenti quantitativi chiari e basati sulla statistica per valutare i risultati dei test in un contesto normativo.
Nel contesto della ricerca scientifica, tuttavia, l’uso di norme per interpretare le prestazioni ai test può non essere necessario. In questi casi, la fase di stima delle norme può essere omessa. Questo approccio è particolarmente utile quando l’obiettivo della ricerca è esplorare relazioni teoriche o costrutti piuttosto che valutare le performance individuali rispetto a un gruppo normativo. La decisione di includere o escludere la stima delle norme dipenderà quindi dagli obiettivi specifici dello studio e dal contesto in cui il test viene applicato.
# STEP 9: NORMS
check.norms(xPlusNa[male == 1])$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
[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
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[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#
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
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[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)
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.
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).
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













































