Potrebné R libraries

library(lavaan, quietly = TRUE, warn.conflicts = FALSE)
## This is lavaan 0.5-22
## lavaan is BETA software! Please report any bugs.
library(semPlot, quietly = TRUE, warn.conflicts = FALSE)
library(dplyr, quietly = TRUE, warn.conflicts = FALSE)
library(psych, quietly = TRUE, warn.conflicts = FALSE)
library(ICC, quietly = TRUE, warn.conflicts = FALSE)
library(Amelia, quietly = TRUE, warn.conflicts = FALSE)
## ## 
## ## Amelia II: Multiple Imputation
## ## (Version 1.7.4, built: 2015-12-05)
## ## Copyright (C) 2005-2017 James Honaker, Gary King and Matthew Blackwell
## ## Refer to http://gking.harvard.edu/amelia/ for more information
## ##
library(BaylorEdPsych, quietly = TRUE, warn.conflicts = FALSE)

Príprava dát

Načítanie dátového súboru

#rm(list = ls())
setwd(dir = "/Users/ivanropovik/OneDrive/MANUSCRIPTS/2017 HQL Validizacna studia")
full.data <- read.csv(file = "data_4countries_raw.csv", header = TRUE, sep = ";")
#View(full.data)

Selekcia premenných pre CFA nástroja

HLQ.collumns <- full.data %>% filter(cntr == 1) %>% select(HL1:HL25)
delete.na <- function(HLQ.collumns, n=NULL) {
  HLQ.collumns[rowSums(is.na(HLQ.collumns)) <= n,]
}

Vizualizácia chýbajucich dát po odstránení prázdnych riadkov

data.na.rm <- delete.na(HLQ.collumns, n = 10)
missmap(data.na.rm, rank.order = TRUE)

Percento chýbajúcich dát

paste(round(sum(is.na(data.na.rm))/prod(dim(data.na.rm))*100, 3), "%", sep = "")
## [1] "0.23%"

Imputácia chýbajúcich dát - bootstraped expected maximization

set.seed(123)
data_imput <- amelia(data.na.rm, ords = c("HL1", "HL2", "HL3", "HL4", "HL5",
                                          "HL6", "HL7", "HL8", "HL9", "HL10",
                                          "HL11", "HL12", "HL13", "HL14", "HL15",
                                          "HL16", "HL17", "HL18", "HL19", "HL20",
                                          "HL21", "HL22", "HL23", "HL24", "HL25"), m = 1)
## -- Imputation 1 --
## 
##   1  2  3  4  5  6  7  8  9 10 11
data <- as.data.frame(data_imput$imputations)
names(data) <- c("HL1", "HL2", "HL3", "HL4", "HL5", "HL6", "HL7", "HL8", "HL9",
                 "HL10", "HL11", "HL12", "HL13", "HL14", "HL15", "HL16", "HL17",
                 "HL18", "HL19", "HL20", "HL21", "HL22", "HL23", "HL24", "HL25")

Frekvenčné tabuľky

lapply(data[,c("HL1", "HL2", "HL3", "HL4", "HL5", "HL6", "HL7", "HL8", "HL9",
               "HL10", "HL11", "HL12", "HL13", "HL14", "HL15", "HL16", "HL17",
               "HL18", "HL19", "HL20", "HL21", "HL22", "HL23", "HL24", "HL25")],
       function(x){table(x, useNA = "ifany")})
## $HL1
## x
##  1  2  3  4 
##  1  3 80 90 
## 
## $HL2
## x
##   1   2   3   4 
##   1   9  61 103 
## 
## $HL3
## x
##  1  2  3  4 
##  7 20 83 64 
## 
## $HL4
## x
##  1  2  3  4 
##  2 13 65 94 
## 
## $HL5
## x
##  1  2  3  4 
##  2  8 76 88 
## 
## $HL6
## x
##  1  2  3  4 
##  4 15 57 98 
## 
## $HL7
## x
##  1  2  3  4 
##  2 13 81 78 
## 
## $HL8
## x
##  1  2  3  4 
##  2 27 83 62 
## 
## $HL9
## x
##  1  2  3  4 
##  2 20 82 70 
## 
## $HL10
## x
##  1  2  3  4 
##  1 13 74 86 
## 
## $HL11
## x
##  1  2  3  4 
##  1 11 81 81 
## 
## $HL12
## x
##  1  2  3  4 
##  1 17 91 65 
## 
## $HL13
## x
##  1  2  3  4 
## 11 41 76 46 
## 
## $HL14
## x
##   1   2   3   4 
##   1   7  38 128 
## 
## $HL15
## x
##  1  2  3  4 
##  2 15 63 94 
## 
## $HL16
## x
##  1  2  3  4 
##  2 19 84 69 
## 
## $HL17
## x
##   1   2   3   4 
##   1  10  50 113 
## 
## $HL18
## x
##  1  2  3  4 
##  1 11 63 99 
## 
## $HL19
## x
##  1  2  3  4 
##  4 23 85 62 
## 
## $HL20
## x
##  1  2  3  4 
##  3 15 82 74 
## 
## $HL21
## x
##  1  2  3  4 
##  2 17 84 71 
## 
## $HL22
## x
##  2  3  4 
## 16 69 89 
## 
## $HL23
## x
##  1  2  3  4 
##  1 20 82 71 
## 
## $HL24
## x
##  2  3  4 
## 13 80 81 
## 
## $HL25
## x
##   2   3   4 
##  13  59 102

Finálne dáta

#View(data)

Deskriptívna analýza

Deskriptívne štatistiky

describe(data, na.rm = TRUE, skew = TRUE, ranges = FALSE)
##      vars   n mean   sd  skew kurtosis   se
## HL1     1 174 3.49 0.57 -0.71     0.57 0.04
## HL2     2 174 3.53 0.62 -1.10     0.79 0.05
## HL3     3 174 3.17 0.79 -0.81     0.37 0.06
## HL4     4 174 3.44 0.68 -1.03     0.65 0.05
## HL5     5 174 3.44 0.64 -0.95     0.99 0.05
## HL6     6 174 3.43 0.75 -1.21     0.95 0.06
## HL7     7 174 3.35 0.67 -0.77     0.41 0.05
## HL8     8 174 3.18 0.73 -0.46    -0.42 0.06
## HL9     9 174 3.26 0.70 -0.61    -0.09 0.05
## HL10   10 174 3.41 0.65 -0.77     0.05 0.05
## HL11   11 174 3.39 0.63 -0.67     0.10 0.05
## HL12   12 174 3.26 0.65 -0.45    -0.19 0.05
## HL13   13 174 2.90 0.86 -0.40    -0.55 0.07
## HL14   14 174 3.68 0.58 -1.82     3.10 0.04
## HL15   15 174 3.43 0.70 -1.01     0.47 0.05
## HL16   16 174 3.26 0.70 -0.61    -0.02 0.05
## HL17   17 174 3.58 0.63 -1.34     1.26 0.05
## HL18   18 174 3.49 0.64 -1.02     0.49 0.05
## HL19   19 174 3.18 0.74 -0.63     0.07 0.06
## HL20   20 174 3.30 0.70 -0.79     0.49 0.05
## HL21   21 174 3.29 0.69 -0.65     0.11 0.05
## HL22   22 174 3.42 0.66 -0.68    -0.60 0.05
## HL23   23 174 3.28 0.69 -0.53    -0.38 0.05
## HL24   24 174 3.39 0.62 -0.51    -0.67 0.05
## HL25   25 174 3.51 0.63 -0.92    -0.23 0.05

Veľkosť vzorky

nrow(data)
## [1] 174

Redukcia počtu kategórií v prípade nízkej frekvencie odpoveďovej kategórie

(odhad polychorickej kovariančnej matice predpokladá absenciu buniek HLa x HLb s nulovou frekvenciou)

data$HL1 <- ifelse(data$HL1 == 1, yes = 2, no = data$HL1)
data$HL1 <- ifelse(data$HL1 == 2, yes = 3, no = data$HL1)
data$HL2 <- ifelse(data$HL2 == 1, yes = 2, no = data$HL2)
data$HL2 <- ifelse(data$HL2 == 2, yes = 3, no = data$HL2)
data$HL3 <- ifelse(data$HL3 == 1, yes = 2, no = data$HL3)
data$HL4 <- ifelse(data$HL4 == 1, yes = 2, no = data$HL4)
data$HL5 <- ifelse(data$HL5 == 1, yes = 2, no = data$HL5)
data$HL6 <- ifelse(data$HL6 == 1, yes = 2, no = data$HL6)
data$HL7 <- ifelse(data$HL7 == 1, yes = 2, no = data$HL7)
data$HL8 <- ifelse(data$HL8 == 1, yes = 2, no = data$HL8)
data$HL9 <- ifelse(data$HL9 == 1, yes = 2, no = data$HL9)
data$HL10 <- ifelse(data$HL10 == 1, yes = 2, no = data$HL10)
data$HL11 <- ifelse(data$HL11 == 1, yes = 2, no = data$HL11)
data$HL12 <- ifelse(data$HL12 == 1, yes = 2, no = data$HL12)
data$HL13 <- ifelse(data$HL13 == 1, yes = 2, no = data$HL13)
data$HL14 <- ifelse(data$HL14 == 1, yes = 2, no = data$HL14)
data$HL14 <- ifelse(data$HL14 == 2, yes = 3, no = data$HL14)
data$HL15 <- ifelse(data$HL15 == 1, yes = 2, no = data$HL15)
data$HL16 <- ifelse(data$HL16 == 1, yes = 2, no = data$HL16)
data$HL17 <- ifelse(data$HL17 == 1, yes = 2, no = data$HL17)
data$HL18 <- ifelse(data$HL18 == 1, yes = 2, no = data$HL18)
data$HL19 <- ifelse(data$HL19 == 1, yes = 2, no = data$HL19)
data$HL20 <- ifelse(data$HL20 == 1, yes = 2, no = data$HL20)
data$HL21 <- ifelse(data$HL21 == 1, yes = 2, no = data$HL21)
data$HL22 <- ifelse(data$HL22 == 1, yes = 2, no = data$HL22)
data$HL23 <- ifelse(data$HL23 == 1, yes = 2, no = data$HL23)
data$HL24 <- ifelse(data$HL24 == 1, yes = 2, no = data$HL24)
data$HL25 <- ifelse(data$HL25 == 1, yes = 2, no = data$HL25)

Matica polychorických korelácií

polychoric.cor <- polychoric(data, correct = FALSE, smooth = TRUE,
                             global = FALSE, na.rm = TRUE)
## Warning in cor.smooth(mat): Matrix was not positive definite, smoothing was
## done
round(polychoric.cor$rho, 2)
##       HL1  HL2  HL3  HL4  HL5  HL6  HL7  HL8  HL9 HL10 HL11 HL12 HL13 HL14
## HL1  1.00 0.69 0.37 0.48 0.55 0.37 0.37 0.49 0.52 0.53 0.58 0.54 0.48 0.34
## HL2  0.69 1.00 0.59 0.44 0.66 0.53 0.23 0.36 0.42 0.54 0.51 0.54 0.38 0.35
## HL3  0.37 0.59 1.00 0.58 0.62 0.49 0.31 0.62 0.56 0.57 0.62 0.65 0.51 0.53
## HL4  0.48 0.44 0.58 1.00 0.75 0.56 0.44 0.55 0.64 0.67 0.47 0.62 0.39 0.50
## HL5  0.55 0.66 0.62 0.75 1.00 0.63 0.37 0.58 0.58 0.61 0.57 0.55 0.41 0.41
## HL6  0.37 0.53 0.49 0.56 0.63 1.00 0.20 0.45 0.41 0.46 0.56 0.62 0.38 0.43
## HL7  0.37 0.23 0.31 0.44 0.37 0.20 1.00 0.49 0.50 0.46 0.42 0.59 0.48 0.44
## HL8  0.49 0.36 0.62 0.55 0.58 0.45 0.49 1.00 0.77 0.55 0.62 0.64 0.63 0.43
## HL9  0.52 0.42 0.56 0.64 0.58 0.41 0.50 0.77 1.00 0.64 0.59 0.66 0.63 0.52
## HL10 0.53 0.54 0.57 0.67 0.61 0.46 0.46 0.55 0.64 1.00 0.66 0.67 0.50 0.57
## HL11 0.58 0.51 0.62 0.47 0.57 0.56 0.42 0.62 0.59 0.66 1.00 0.71 0.50 0.56
## HL12 0.54 0.54 0.65 0.62 0.55 0.62 0.59 0.64 0.66 0.67 0.71 1.00 0.67 0.56
## HL13 0.48 0.38 0.51 0.39 0.41 0.38 0.48 0.63 0.63 0.50 0.50 0.67 1.00 0.44
## HL14 0.34 0.35 0.53 0.50 0.41 0.43 0.44 0.43 0.52 0.57 0.56 0.56 0.44 1.00
## HL15 0.42 0.39 0.58 0.48 0.53 0.43 0.52 0.57 0.52 0.53 0.60 0.57 0.67 0.75
## HL16 0.53 0.50 0.50 0.42 0.52 0.37 0.51 0.54 0.53 0.61 0.52 0.66 0.70 0.51
## HL17 0.47 0.57 0.44 0.40 0.50 0.57 0.26 0.49 0.46 0.59 0.55 0.52 0.48 0.59
## HL18 0.48 0.54 0.56 0.43 0.47 0.43 0.48 0.65 0.54 0.64 0.57 0.63 0.44 0.57
## HL19 0.41 0.34 0.57 0.40 0.53 0.35 0.53 0.58 0.67 0.54 0.46 0.65 0.61 0.45
## HL20 0.53 0.54 0.60 0.54 0.66 0.50 0.52 0.68 0.74 0.68 0.62 0.68 0.56 0.61
## HL21 0.53 0.50 0.55 0.52 0.67 0.51 0.55 0.65 0.64 0.57 0.59 0.71 0.69 0.56
## HL22 0.38 0.26 0.48 0.54 0.51 0.42 0.51 0.62 0.56 0.51 0.50 0.57 0.56 0.55
## HL23 0.44 0.46 0.49 0.53 0.56 0.45 0.40 0.58 0.59 0.58 0.56 0.65 0.63 0.52
## HL24 0.60 0.40 0.58 0.62 0.63 0.40 0.53 0.73 0.69 0.62 0.59 0.64 0.58 0.66
## HL25 0.35 0.30 0.53 0.63 0.59 0.42 0.50 0.64 0.65 0.53 0.44 0.60 0.53 0.79
##      HL15 HL16 HL17 HL18 HL19 HL20 HL21 HL22 HL23 HL24 HL25
## HL1  0.42 0.53 0.47 0.48 0.41 0.53 0.53 0.38 0.44 0.60 0.35
## HL2  0.39 0.50 0.57 0.54 0.34 0.54 0.50 0.26 0.46 0.40 0.30
## HL3  0.58 0.50 0.44 0.56 0.57 0.60 0.55 0.48 0.49 0.58 0.53
## HL4  0.48 0.42 0.40 0.43 0.40 0.54 0.52 0.54 0.53 0.62 0.63
## HL5  0.53 0.52 0.50 0.47 0.53 0.66 0.67 0.51 0.56 0.63 0.59
## HL6  0.43 0.37 0.57 0.43 0.35 0.50 0.51 0.42 0.45 0.40 0.42
## HL7  0.52 0.51 0.26 0.48 0.53 0.52 0.55 0.51 0.40 0.53 0.50
## HL8  0.57 0.54 0.49 0.65 0.58 0.68 0.65 0.62 0.58 0.73 0.64
## HL9  0.52 0.53 0.46 0.54 0.67 0.74 0.64 0.56 0.59 0.69 0.65
## HL10 0.53 0.61 0.59 0.64 0.54 0.68 0.57 0.51 0.58 0.62 0.53
## HL11 0.60 0.52 0.55 0.57 0.46 0.62 0.59 0.50 0.56 0.59 0.44
## HL12 0.57 0.66 0.52 0.63 0.65 0.68 0.71 0.57 0.65 0.64 0.60
## HL13 0.67 0.70 0.48 0.44 0.61 0.56 0.69 0.56 0.63 0.58 0.53
## HL14 0.75 0.51 0.59 0.57 0.45 0.61 0.56 0.55 0.52 0.66 0.79
## HL15 1.00 0.67 0.56 0.50 0.49 0.59 0.65 0.52 0.59 0.65 0.66
## HL16 0.67 1.00 0.62 0.63 0.60 0.67 0.68 0.47 0.58 0.60 0.54
## HL17 0.56 0.62 1.00 0.62 0.41 0.63 0.47 0.45 0.52 0.54 0.55
## HL18 0.50 0.63 0.62 1.00 0.55 0.69 0.55 0.53 0.51 0.69 0.55
## HL19 0.49 0.60 0.41 0.55 1.00 0.69 0.70 0.55 0.68 0.70 0.56
## HL20 0.59 0.67 0.63 0.69 0.69 1.00 0.82 0.73 0.73 0.73 0.68
## HL21 0.65 0.68 0.47 0.55 0.70 0.82 1.00 0.70 0.71 0.69 0.60
## HL22 0.52 0.47 0.45 0.53 0.55 0.73 0.70 1.00 0.76 0.60 0.66
## HL23 0.59 0.58 0.52 0.51 0.68 0.73 0.71 0.76 1.00 0.72 0.66
## HL24 0.65 0.60 0.54 0.69 0.70 0.73 0.69 0.60 0.72 1.00 0.81
## HL25 0.66 0.54 0.55 0.55 0.56 0.68 0.60 0.66 0.66 0.81 1.00

Priemerná korelácia

polychoric.cor.low <- polychoric.cor$rho[lower.tri(polychoric.cor$rho)]
mean(abs(polychoric.cor.low))
## [1] 0.5495773

Výpočet polychorickej kovariančnej matice

SDs <- describe(data, na.rm = TRUE)$sd
polychoric.cov <- cor2cov(R = polychoric.cor$rho, sds = SDs)

Definovanie, test a estimácia CFA modelu

Špecifikácia 5-faktorového modelu merania

model <- '
theor_know =~ a*HL1 + b*HL8 + c*HL14 + d*HL18 + e*HL25
prac_know =~ f*HL2 + g*HL4 + h*HL6 + i*HL10 + j*HL17
crit_think =~ k*HL7 + l*HL12 + m*HL16 + n*HL21 + o*HL24
self_aware =~ p*HL5 + q*HL11 + r*HL15 + s*HL19 + t*HL22
citizenship =~ u*HL3 + v*HL9 + x*HL13 + y*HL20 + z*HL23
'

Estimácia a test modelu, podľa Muthén, 1984

fitted.model <- cfa(model = model, data = data, meanstructure = TRUE, std.lv = TRUE, mimic = "Mplus",
                    estimator = "WLSMVS", test = "Satterthwaite", orthogonal = FALSE, bootstrap = 5000,
                    ordered = c("HL1", "HL2", "HL3", "HL4", "HL5", "HL6", "HL7", "HL8", "HL9", "HL10",
                                "HL11", "HL12", "HL13", "HL14", "HL15", "HL16", "HL17", "HL18", "HL19",
                                "HL20", "HL21", "HL22", "HL23", "HL24", "HL25"))
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL7 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL9 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL18
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL17 x
## HL25
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL25
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL25
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL5 x
## HL25
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL25
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL5 x
## HL4
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL10
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL10
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL20 x
## HL17
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL7
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL7
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL16 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL21 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL19 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL3 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL20 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL3 x
## HL24
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL24
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL20 x
## HL24
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL3 x
## HL11
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL15
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL19
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL22
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL20 x
## HL22
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL23 x
## HL22
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL23 x
## HL13
## Warning in lav_object_post_check(lavobject): lavaan WARNING: covariance matrix of latent variables
##                 is not positive definite;
##                 use inspect(fit,"cov.lv") to investigate.

Počet buniek HLa x HLb s nulovou frekvenciou je tak na hrane. Majú malú vzorku a tým pádom nízke frekvencie v rámci odpoveďových kategórií

Analýza štatistickej sily pre test blízkej zhody (na základe RMSEA distribúcie)

Štatistická sila pre detekciu chybného modelu (RMSEA > .08)

df <- fitted.model@test[[1]]$df
alfa <- .05
n <- nrow(data)
rmsea0 <- .05           # RMSEA za predpokladu H0
rmseaa <- .08           # RMSEA za predpokladu H1

ncp0 <- (n-1)*df*rmsea0**2 ;
ncpa <-(n-1)*df*rmseaa**2 ;
if(rmsea0 < rmseaa) {
  cval <- qchisq(1-alfa,df=df,ncp=ncp0)
  sila.rmsea <- 1 - pchisq(cval,df=df,ncp=ncpa)
} else {
  cval <- qchisq(alfa,df=df,ncp=ncp0)
  sila.rmsea <- pchisq(cval,df=df,ncp=ncpa)
}
rm(ncp0, ncpa, cval)
print(round(sila.rmsea,10))
## [1] 0.9994319

Výsledky

Kovariančná matica je non-positive definite z dôvodu, že viaceré z definovaných latentných premenných su kolineárne (de facto identické). Štyri z korelácií v rámci štrukturálneho modelu sú väčšie ako 1.

eigen(inspect(fitted.model, "cov.lv") )$values
## [1]  4.93376296  0.14667059  0.02932833 -0.02102687 -0.08873501

Štvrtá a piata eigenvalue majú negatívnu ale relatívne nízku hodnotu, výsledky testu modelu sú ako-tak interpretovateľné.

Test modelu, odhady voľných parametrov (faktorové náboje)

Stačí si všímať “Robust” test, Latent variable, Covariances a R-square. Intercepts, Thresholds, Intercepts (…) môžte kľudne ignorovať.

summary(fitted.model, standardized = TRUE, rsquare = TRUE)
## lavaan (0.5-22) converged normally after  49 iterations
## 
##   Number of observations                           174
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              333.517     123.899
##   Degrees of freedom                               265          51
##   P-value (Chi-square)                           0.003       0.000
##   Scaling correction factor                                  2.692
##     for the mean and variance adjusted correction (WLSMV)
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   theor_know =~                                                         
##     HL1        (a)    0.653    0.061   10.637    0.000    0.653    0.653
##     HL8        (b)    0.815    0.034   23.930    0.000    0.815    0.815
##     HL14       (c)    0.755    0.058   13.012    0.000    0.755    0.755
##     HL18       (d)    0.757    0.041   18.439    0.000    0.757    0.757
##     HL25       (e)    0.812    0.035   23.049    0.000    0.812    0.812
##   prac_know =~                                                          
##     HL2        (f)    0.679    0.063   10.845    0.000    0.679    0.679
##     HL4        (g)    0.771    0.040   19.121    0.000    0.771    0.771
##     HL6        (h)    0.659    0.056   11.744    0.000    0.659    0.659
##     HL10       (i)    0.829    0.033   24.758    0.000    0.829    0.829
##     HL17       (j)    0.729    0.051   14.414    0.000    0.729    0.729
##   crit_think =~                                                         
##     HL7        (k)    0.605    0.053   11.461    0.000    0.605    0.605
##     HL12       (l)    0.835    0.031   26.634    0.000    0.835    0.835
##     HL16       (m)    0.765    0.040   19.230    0.000    0.765    0.765
##     HL21       (n)    0.849    0.025   33.371    0.000    0.849    0.849
##     HL24       (o)    0.853    0.025   33.779    0.000    0.853    0.853
##   self_aware =~                                                         
##     HL5        (p)    0.734    0.046   15.862    0.000    0.734    0.734
##     HL11       (q)    0.723    0.044   16.457    0.000    0.723    0.723
##     HL15       (r)    0.729    0.042   17.266    0.000    0.729    0.729
##     HL19       (s)    0.729    0.038   19.347    0.000    0.729    0.729
##     HL22       (t)    0.728    0.041   17.651    0.000    0.728    0.728
##   citizenship =~                                                        
##     HL3        (u)    0.717    0.042   16.971    0.000    0.717    0.717
##     HL9        (v)    0.806    0.033   24.338    0.000    0.806    0.806
##     HL13       (x)    0.734    0.042   17.341    0.000    0.734    0.734
##     HL20       (y)    0.873    0.025   34.241    0.000    0.873    0.873
##     HL23       (z)    0.796    0.035   22.938    0.000    0.796    0.796
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   theor_know ~~                                                         
##     prac_know         0.916    0.032   28.595    0.000    0.916    0.916
##     crit_think        0.987    0.022   45.602    0.000    0.987    0.987
##     self_aware        1.011    0.021   47.057    0.000    1.011    1.011
##     citizenship       0.989    0.022   44.847    0.000    0.989    0.989
##   prac_know ~~                                                          
##     crit_think        0.887    0.034   26.384    0.000    0.887    0.887
##     self_aware        0.985    0.031   31.378    0.000    0.985    0.985
##     citizenship       0.909    0.030   30.490    0.000    0.909    0.909
##   crit_think ~~                                                         
##     self_aware        1.048    0.018   57.067    0.000    1.048    1.048
##     citizenship       1.022    0.018   57.915    0.000    1.022    1.022
##   self_aware ~~                                                         
##     citizenship       1.072    0.019   56.762    0.000    1.072    1.072
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .HL1               0.000                               0.000    0.000
##    .HL8               0.000                               0.000    0.000
##    .HL14              0.000                               0.000    0.000
##    .HL18              0.000                               0.000    0.000
##    .HL25              0.000                               0.000    0.000
##    .HL2               0.000                               0.000    0.000
##    .HL4               0.000                               0.000    0.000
##    .HL6               0.000                               0.000    0.000
##    .HL10              0.000                               0.000    0.000
##    .HL17              0.000                               0.000    0.000
##    .HL7               0.000                               0.000    0.000
##    .HL12              0.000                               0.000    0.000
##    .HL16              0.000                               0.000    0.000
##    .HL21              0.000                               0.000    0.000
##    .HL24              0.000                               0.000    0.000
##    .HL5               0.000                               0.000    0.000
##    .HL11              0.000                               0.000    0.000
##    .HL15              0.000                               0.000    0.000
##    .HL19              0.000                               0.000    0.000
##    .HL22              0.000                               0.000    0.000
##    .HL3               0.000                               0.000    0.000
##    .HL9               0.000                               0.000    0.000
##    .HL13              0.000                               0.000    0.000
##    .HL20              0.000                               0.000    0.000
##    .HL23              0.000                               0.000    0.000
##     theor_know        0.000                               0.000    0.000
##     prac_know         0.000                               0.000    0.000
##     crit_think        0.000                               0.000    0.000
##     self_aware        0.000                               0.000    0.000
##     citizenship       0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     HL1|t1           -0.043    0.095   -0.454    0.650   -0.043   -0.043
##     HL8|t1           -0.967    0.113   -8.531    0.000   -0.967   -0.967
##     HL8|t2            0.368    0.098    3.771    0.000    0.368    0.368
##     HL14|t1          -0.630    0.102   -6.146    0.000   -0.630   -0.630
##     HL18|t1          -1.484    0.145  -10.222    0.000   -1.484   -1.484
##     HL18|t2          -0.174    0.096   -1.813    0.070   -0.174   -0.174
##     HL25|t1          -1.442    0.142  -10.178    0.000   -1.442   -1.442
##     HL25|t2          -0.218    0.096   -2.266    0.023   -0.218   -0.218
##     HL2|t1           -0.233    0.096   -2.417    0.016   -0.233   -0.233
##     HL4|t1           -1.364    0.136  -10.056    0.000   -1.364   -1.364
##     HL4|t2           -0.101    0.095   -1.058    0.290   -0.101   -0.101
##     HL6|t1           -1.231    0.127   -9.709    0.000   -1.231   -1.231
##     HL6|t2           -0.159    0.096   -1.662    0.096   -0.159   -0.159
##     HL10|t1          -1.402    0.139  -10.122    0.000   -1.402   -1.402
##     HL10|t2           0.014    0.095    0.151    0.880    0.014    0.014
##     HL17|t1          -1.528    0.149  -10.250    0.000   -1.528   -1.528
##     HL17|t2          -0.384    0.098   -3.921    0.000   -0.384   -0.384
##     HL7|t1           -1.364    0.136  -10.056    0.000   -1.364   -1.364
##     HL7|t2            0.130    0.096    1.360    0.174    0.130    0.130
##     HL12|t1          -1.262    0.129   -9.806    0.000   -1.262   -1.262
##     HL12|t2           0.322    0.097    3.320    0.001    0.322    0.322
##     HL16|t1          -1.172    0.123   -9.501    0.000   -1.172   -1.172
##     HL16|t2           0.262    0.096    2.718    0.007    0.262    0.262
##     HL21|t1          -1.231    0.127   -9.709    0.000   -1.231   -1.231
##     HL21|t2           0.233    0.096    2.417    0.016    0.233    0.233
##     HL24|t1          -1.442    0.142  -10.178    0.000   -1.442   -1.442
##     HL24|t2           0.087    0.095    0.907    0.364    0.087    0.087
##     HL5|t1           -1.576    0.154  -10.259    0.000   -1.576   -1.576
##     HL5|t2           -0.014    0.095   -0.151    0.880   -0.014   -0.014
##     HL11|t1          -1.484    0.145  -10.222    0.000   -1.484   -1.484
##     HL11|t2           0.087    0.095    0.907    0.364    0.087    0.087
##     HL15|t1          -1.295    0.131   -9.896    0.000   -1.295   -1.295
##     HL15|t2          -0.101    0.095   -1.058    0.290   -0.101   -0.101
##     HL19|t1          -1.014    0.115   -8.788    0.000   -1.014   -1.014
##     HL19|t2           0.368    0.098    3.771    0.000    0.368    0.368
##     HL22|t1          -1.329    0.133   -9.980    0.000   -1.329   -1.329
##     HL22|t2          -0.029    0.095   -0.302    0.762   -0.029   -0.029
##     HL3|t1           -1.014    0.115   -8.788    0.000   -1.014   -1.014
##     HL3|t2            0.338    0.097    3.471    0.001    0.338    0.338
##     HL9|t1           -1.143    0.122   -9.390    0.000   -1.143   -1.143
##     HL9|t2            0.247    0.096    2.568    0.010    0.247    0.247
##     HL13|t1          -0.528    0.100   -5.263    0.000   -0.528   -0.528
##     HL13|t2           0.630    0.102    6.146    0.000    0.630    0.630
##     HL20|t1          -1.262    0.129   -9.806    0.000   -1.262   -1.262
##     HL20|t2           0.188    0.096    1.964    0.049    0.188    0.188
##     HL23|t1          -1.172    0.123   -9.501    0.000   -1.172   -1.172
##     HL23|t2           0.233    0.096    2.417    0.016    0.233    0.233
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .HL1               0.574                               0.574    0.574
##    .HL8               0.335                               0.335    0.335
##    .HL14              0.431                               0.431    0.431
##    .HL18              0.426                               0.426    0.426
##    .HL25              0.341                               0.341    0.341
##    .HL2               0.538                               0.538    0.538
##    .HL4               0.406                               0.406    0.406
##    .HL6               0.566                               0.566    0.566
##    .HL10              0.313                               0.313    0.313
##    .HL17              0.468                               0.468    0.468
##    .HL7               0.634                               0.634    0.634
##    .HL12              0.304                               0.304    0.304
##    .HL16              0.415                               0.415    0.415
##    .HL21              0.279                               0.279    0.279
##    .HL24              0.273                               0.273    0.273
##    .HL5               0.461                               0.461    0.461
##    .HL11              0.477                               0.477    0.477
##    .HL15              0.468                               0.468    0.468
##    .HL19              0.468                               0.468    0.468
##    .HL22              0.470                               0.470    0.470
##    .HL3               0.485                               0.485    0.485
##    .HL9               0.351                               0.351    0.351
##    .HL13              0.461                               0.461    0.461
##    .HL20              0.238                               0.238    0.238
##    .HL23              0.367                               0.367    0.367
##     theor_know        1.000                               1.000    1.000
##     prac_know         1.000                               1.000    1.000
##     crit_think        1.000                               1.000    1.000
##     self_aware        1.000                               1.000    1.000
##     citizenship       1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     HL1               1.000                               1.000    1.000
##     HL8               1.000                               1.000    1.000
##     HL14              1.000                               1.000    1.000
##     HL18              1.000                               1.000    1.000
##     HL25              1.000                               1.000    1.000
##     HL2               1.000                               1.000    1.000
##     HL4               1.000                               1.000    1.000
##     HL6               1.000                               1.000    1.000
##     HL10              1.000                               1.000    1.000
##     HL17              1.000                               1.000    1.000
##     HL7               1.000                               1.000    1.000
##     HL12              1.000                               1.000    1.000
##     HL16              1.000                               1.000    1.000
##     HL21              1.000                               1.000    1.000
##     HL24              1.000                               1.000    1.000
##     HL5               1.000                               1.000    1.000
##     HL11              1.000                               1.000    1.000
##     HL15              1.000                               1.000    1.000
##     HL19              1.000                               1.000    1.000
##     HL22              1.000                               1.000    1.000
##     HL3               1.000                               1.000    1.000
##     HL9               1.000                               1.000    1.000
##     HL13              1.000                               1.000    1.000
##     HL20              1.000                               1.000    1.000
##     HL23              1.000                               1.000    1.000
## 
## R-Square:
##                    Estimate
##     HL1               0.426
##     HL8               0.665
##     HL14              0.569
##     HL18              0.574
##     HL25              0.659
##     HL2               0.462
##     HL4               0.594
##     HL6               0.434
##     HL10              0.687
##     HL17              0.532
##     HL7               0.366
##     HL12              0.696
##     HL16              0.585
##     HL21              0.721
##     HL24              0.727
##     HL5               0.539
##     HL11              0.523
##     HL15              0.532
##     HL19              0.532
##     HL22              0.530
##     HL3               0.515
##     HL9               0.649
##     HL13              0.539
##     HL20              0.762
##     HL23              0.633

Test modelu, indexy blízkej zhody modelu a dát

Treba si všímať .scaled indexy

fitMeasures(fitted.model)
##                          npar                          fmin 
##                        82.000                         0.958 
##                         chisq                            df 
##                       333.517                       265.000 
##                        pvalue                  chisq.scaled 
##                         0.003                       123.899 
##                     df.scaled                 pvalue.scaled 
##                        51.000                         0.000 
##          chisq.scaling.factor                baseline.chisq 
##                         2.692                     24290.950 
##                   baseline.df               baseline.pvalue 
##                       300.000                         0.000 
##         baseline.chisq.scaled            baseline.df.scaled 
##                      1140.130                        14.000 
##        baseline.pvalue.scaled baseline.chisq.scaling.factor 
##                         0.000                        21.305 
##                           cfi                           tli 
##                         0.997                         0.997 
##                          nnfi                           rfi 
##                         0.997                         0.984 
##                           nfi                          pnfi 
##                         0.986                         0.871 
##                           ifi                           rni 
##                         0.997                         0.997 
##                    cfi.scaled                    tli.scaled 
##                         0.935                         0.982 
##                    cfi.robust                    tli.robust 
##                            NA                            NA 
##                   nnfi.scaled                   nnfi.robust 
##                         0.982                            NA 
##                    rfi.scaled                    nfi.scaled 
##                         0.970                         0.891 
##                    ifi.scaled                    rni.scaled 
##                         0.891                         0.997 
##                    rni.robust                         rmsea 
##                            NA                         0.039 
##                rmsea.ci.lower                rmsea.ci.upper 
##                         0.024                         0.051 
##                  rmsea.pvalue                  rmsea.scaled 
##                         0.933                         0.091 
##         rmsea.ci.lower.scaled         rmsea.ci.upper.scaled 
##                         0.079                         0.103 
##           rmsea.pvalue.scaled                  rmsea.robust 
##                         0.000                            NA 
##         rmsea.ci.lower.robust         rmsea.ci.upper.robust 
##                            NA                            NA 
##           rmsea.pvalue.robust                           rmr 
##                            NA                         0.069 
##                    rmr_nomean                          srmr 
##                         0.072                         0.069 
##                  srmr_bentler           srmr_bentler_nomean 
##                         0.069                         0.072 
##                   srmr_bollen            srmr_bollen_nomean 
##                         0.069                         0.072 
##                    srmr_mplus             srmr_mplus_nomean 
##                         0.069                         0.072 
##                         cn_05                         cn_01 
##                       158.674                       167.755 
##                           gfi                          agfi 
##                         0.987                         0.984 
##                          pgfi                           mfi 
##                         0.754                         0.820

Diagram

semPaths(fitted.model, style = "mx", layout = "circle",
         edge.label.cex = 0.5, sizeLat = 5, nCharNodes = 0,
         nDigits = 2, "Standardized", intercepts = FALSE,
         residuals = TRUE, exoVar = FALSE, fade = TRUE,
         groups = "latents", pastel = TRUE)

Test modelu indikuje prítomnosť chybnej špecifikácie modelu. Popri indexoch blízkej zhody je preto potrebné analyzovať lokálne zdroje chybnej špecifikácie na základe matice reziduálnych korelácií

Matica reziduálnych korelácií

residuals <- residuals(fitted.model, type = "cor")$cor
residuals
##      HL1    HL8    HL14   HL18   HL25   HL2    HL4    HL6    HL10   HL17  
## HL1   0.000                                                               
## HL8  -0.040  0.000                                                        
## HL14 -0.155 -0.183  0.000                                                 
## HL18 -0.016  0.035 -0.003  0.000                                          
## HL25 -0.183 -0.020  0.175 -0.063  0.000                                   
## HL2   0.291 -0.143 -0.112  0.072 -0.204  0.000                            
## HL4   0.023 -0.024 -0.033 -0.102  0.060 -0.081  0.000                     
## HL6  -0.021 -0.044 -0.028 -0.032 -0.074  0.087  0.050  0.000              
## HL10  0.031 -0.072 -0.004  0.069 -0.091 -0.017  0.029 -0.088  0.000       
## HL17  0.030 -0.058  0.086  0.113  0.004  0.083 -0.163  0.088 -0.019  0.000
## HL7  -0.022  0.005 -0.012  0.030  0.013 -0.132  0.027 -0.155  0.012 -0.129
## HL12  0.003 -0.027 -0.058  0.006 -0.071  0.039  0.048  0.135  0.060 -0.024
## HL16  0.037 -0.077 -0.058  0.061 -0.073  0.042 -0.100 -0.073  0.051  0.126
## HL21 -0.018 -0.037 -0.078 -0.081 -0.076 -0.009 -0.059  0.012 -0.056 -0.083
## HL24  0.058  0.047  0.024  0.051  0.129 -0.120  0.035 -0.093 -0.004 -0.012
## HL5   0.069 -0.027 -0.152 -0.095 -0.013  0.176  0.193  0.159  0.008 -0.032
## HL11  0.103  0.022  0.015  0.020 -0.150  0.025 -0.079  0.093  0.075  0.031
## HL15 -0.055 -0.033  0.197 -0.052  0.063 -0.095 -0.077 -0.041 -0.063  0.036
## HL19 -0.066 -0.021 -0.100 -0.005 -0.043 -0.147 -0.150 -0.121 -0.051 -0.108
## HL22 -0.095  0.023  0.000 -0.028  0.065 -0.231 -0.012 -0.056 -0.082 -0.073
## HL3  -0.096  0.044 -0.010  0.022 -0.040  0.158  0.084  0.064  0.029 -0.033
## HL9  -0.001  0.123 -0.081 -0.063  0.000 -0.070  0.078 -0.076  0.034 -0.078
## HL13  0.008  0.040 -0.109 -0.112 -0.063 -0.073 -0.123 -0.059 -0.050 -0.009
## HL20 -0.031 -0.024 -0.044  0.035 -0.023  0.003 -0.074 -0.027  0.025  0.056
## HL23 -0.080 -0.055 -0.072 -0.087  0.027 -0.019 -0.023 -0.026 -0.014 -0.012
##      HL7    HL12   HL16   HL21   HL24   HL5    HL11   HL15   HL19   HL22  
## HL1                                                                       
## HL8                                                                       
## HL14                                                                      
## HL18                                                                      
## HL25                                                                      
## HL2                                                                       
## HL4                                                                       
## HL6                                                                       
## HL10                                                                      
## HL17                                                                      
## HL7   0.000                                                               
## HL12  0.088  0.000                                                        
## HL16  0.048  0.022  0.000                                                 
## HL21  0.033  0.003  0.035  0.000                                          
## HL24  0.012 -0.067 -0.056 -0.031  0.000                                   
## HL5  -0.097 -0.086 -0.066  0.018 -0.025  0.000                            
## HL11 -0.037  0.081 -0.062 -0.048 -0.055  0.046  0.000                     
## HL15  0.061 -0.072  0.081  0.002 -0.007 -0.003  0.074  0.000              
## HL19  0.074  0.011  0.012  0.050  0.048  0.000 -0.071 -0.040  0.000       
## HL22  0.046 -0.063 -0.113  0.057 -0.051 -0.020 -0.026 -0.012  0.014  0.000
## HL3  -0.131  0.036 -0.063 -0.068 -0.042  0.053  0.065  0.019  0.013 -0.079
## HL9   0.006 -0.024 -0.103 -0.061 -0.009 -0.052 -0.034 -0.113  0.039 -0.067
## HL13  0.027  0.046  0.125  0.054 -0.063 -0.172 -0.072  0.093  0.033 -0.010
## HL20 -0.018 -0.064 -0.009  0.061 -0.028 -0.024 -0.058 -0.092  0.010  0.045
## HL23 -0.092 -0.023 -0.039  0.019  0.030 -0.071 -0.052 -0.023  0.063  0.147
##      HL3    HL9    HL13   HL20   HL23  
## HL1                                    
## HL8                                    
## HL14                                   
## HL18                                   
## HL25                                   
## HL2                                    
## HL4                                    
## HL6                                    
## HL10                                   
## HL17                                   
## HL7                                    
## HL12                                   
## HL16                                   
## HL21                                   
## HL24                                   
## HL5                                    
## HL11                                   
## HL15                                   
## HL19                                   
## HL22                                   
## HL3   0.000                            
## HL9  -0.015  0.000                     
## HL13 -0.015  0.035  0.000              
## HL20 -0.024  0.042 -0.082  0.000       
## HL23 -0.081 -0.053  0.051  0.035  0.000

Pre prehladnejšiu vizualizáciu, matica reziduí s vyznačenými reziduálnymi hodnotami > .1 (štandardizované z-reziduá je možné odhadnúť iba v prípade použitia estimátora z rodiny maximum likelihood. Arbitrárna hodnota .1 preto, lebo neumožní produkt dvoch nábojov > .3)

Počet premenných

p = 25

Ak máme v matici (p(p+1)/2 - p) = 300 elementov, tak

(p*(p+1)/2 - p)*.05
## [1] 15

z nich môže byť signifikantných na hladine alfa = .05

HRUBÁ APROXIMÁCIA - približne tolko elementov môže byť > .1 Diag = diagonála, >.1 = reziduálna hodnota vyššia ako .1

ifelse(residuals == 0, "Diag", ifelse(residuals > .1, ">.1", "."))
##      HL1    HL8    HL14   HL18   HL25   HL2    HL4    HL6    HL10   HL17  
## HL1  "Diag" "."    "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL8  "."    "Diag" "."    "."    "."    "."    "."    "."    "."    "."   
## HL14 "."    "."    "Diag" "."    ">.1"  "."    "."    "."    "."    "."   
## HL18 "."    "."    "."    "Diag" "."    "."    "."    "."    "."    ">.1" 
## HL25 "."    "."    ">.1"  "."    "Diag" "."    "."    "."    "."    "."   
## HL2  ">.1"  "."    "."    "."    "."    "Diag" "."    "."    "."    "."   
## HL4  "."    "."    "."    "."    "."    "."    "Diag" "."    "."    "."   
## HL6  "."    "."    "."    "."    "."    "."    "."    "Diag" "."    "."   
## HL10 "."    "."    "."    "."    "."    "."    "."    "."    "Diag" "."   
## HL17 "."    "."    "."    ">.1"  "."    "."    "."    "."    "."    "Diag"
## HL7  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL12 "."    "."    "."    "."    "."    "."    "."    ">.1"  "."    "."   
## HL16 "."    "."    "."    "."    "."    "."    "."    "."    "."    ">.1" 
## HL21 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL24 "."    "."    "."    "."    ">.1"  "."    "."    "."    "."    "."   
## HL5  "."    "."    "."    "."    "."    ">.1"  ">.1"  ">.1"  "."    "."   
## HL11 ">.1"  "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL15 "."    "."    ">.1"  "."    "."    "."    "."    "."    "."    "."   
## HL19 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL22 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL3  "."    "."    "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL9  "."    ">.1"  "."    "."    "."    "."    "."    "."    "."    "."   
## HL13 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL20 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL23 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
##      HL7    HL12   HL16   HL21   HL24   HL5    HL11   HL15   HL19   HL22  
## HL1  "."    "."    "."    "."    "."    "."    ">.1"  "."    "."    "."   
## HL8  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL14 "."    "."    "."    "."    "."    "."    "."    ">.1"  "."    "."   
## HL18 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL25 "."    "."    "."    "."    ">.1"  "."    "."    "."    "."    "."   
## HL2  "."    "."    "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL4  "."    "."    "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL6  "."    ">.1"  "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL10 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL17 "."    "."    ">.1"  "."    "."    "."    "."    "."    "."    "."   
## HL7  "Diag" "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL12 "."    "Diag" "."    "."    "."    "."    "."    "."    "."    "."   
## HL16 "."    "."    "Diag" "."    "."    "."    "."    "."    "."    "."   
## HL21 "."    "."    "."    "Diag" "."    "."    "."    "."    "."    "."   
## HL24 "."    "."    "."    "."    "Diag" "."    "."    "."    "."    "."   
## HL5  "."    "."    "."    "."    "."    "Diag" "."    "."    "."    "."   
## HL11 "."    "."    "."    "."    "."    "."    "Diag" "."    "."    "."   
## HL15 "."    "."    "."    "."    "."    "."    "."    "Diag" "."    "."   
## HL19 "."    "."    "."    "."    "."    "."    "."    "."    "Diag" "."   
## HL22 "."    "."    "."    "."    "."    "."    "."    "."    "."    "Diag"
## HL3  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL9  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL13 "."    "."    ">.1"  "."    "."    "."    "."    "."    "."    "."   
## HL20 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL23 "."    "."    "."    "."    "."    "."    "."    "."    "."    ">.1" 
##      HL3    HL9    HL13   HL20   HL23  
## HL1  "."    "."    "."    "."    "."   
## HL8  "."    ">.1"  "."    "."    "."   
## HL14 "."    "."    "."    "."    "."   
## HL18 "."    "."    "."    "."    "."   
## HL25 "."    "."    "."    "."    "."   
## HL2  ">.1"  "."    "."    "."    "."   
## HL4  "."    "."    "."    "."    "."   
## HL6  "."    "."    "."    "."    "."   
## HL10 "."    "."    "."    "."    "."   
## HL17 "."    "."    "."    "."    "."   
## HL7  "."    "."    "."    "."    "."   
## HL12 "."    "."    "."    "."    "."   
## HL16 "."    "."    ">.1"  "."    "."   
## HL21 "."    "."    "."    "."    "."   
## HL24 "."    "."    "."    "."    "."   
## HL5  "."    "."    "."    "."    "."   
## HL11 "."    "."    "."    "."    "."   
## HL15 "."    "."    "."    "."    "."   
## HL19 "."    "."    "."    "."    "."   
## HL22 "."    "."    "."    "."    ">.1" 
## HL3  "Diag" "."    "."    "."    "."   
## HL9  "."    "Diag" "."    "."    "."   
## HL13 "."    "."    "Diag" "."    "."   
## HL20 "."    "."    "."    "Diag" "."   
## HL23 "."    "."    "."    "."    "Diag"

Odhad reliability

rel.HLQ.collumns <- full.data %>% select(HL1:HL25, ID3)
delete.na <- function(rel.HLQ.collumns, n=NULL) {
  rel.HLQ.collumns[rowSums(is.na(rel.HLQ.collumns)) <= n,]
}
rel.HLQ.na.rm <- delete.na(rel.HLQ.collumns, n = 10)

Odhad internej konzistencie - Cronbachova alfa

alpha(rel.HLQ.na.rm[,c("HL1", "HL8", "HL14", "HL18", "HL25")], na.rm = TRUE)$total$std.alpha # pre theor_know
## [1] 0.7119647
alpha(rel.HLQ.na.rm[,c("HL2", "HL4", "HL6", "HL10", "HL17")], na.rm = TRUE)$total$std.alpha # pre prac_know
## [1] 0.7288641
alpha(rel.HLQ.na.rm[,c("HL7", "HL12", "HL16", "HL21", "HL24")], na.rm = TRUE)$total$std.alpha # pre crit_think
## [1] 0.7867088
alpha(rel.HLQ.na.rm[,c("HL5", "HL11", "HL15", "HL19", "HL22")], na.rm = TRUE)$total$std.alpha # pre self_aware
## [1] 0.7189408
alpha(rel.HLQ.na.rm[,c("HL3", "HL9", "HL13", "HL20", "HL23")], na.rm = TRUE)$total$std.alpha # pre citizenship
## [1] 0.7546782

Odhad stability v čase

Výpočet sumárneho skóre každej z 5 dimenzií HL

rel.HLQ.na.rm$theor_know <- rowMeans(rel.HLQ.na.rm[,c("HL1", "HL8", "HL14", "HL18", "HL25")], na.rm = TRUE)
rel.HLQ.na.rm$prac_know <- rowMeans(rel.HLQ.na.rm[,c("HL2", "HL4", "HL6", "HL10", "HL17")], na.rm = TRUE)
rel.HLQ.na.rm$crit_think <- rowMeans(rel.HLQ.na.rm[,c("HL7", "HL12", "HL16", "HL21", "HL24")], na.rm = TRUE)
rel.HLQ.na.rm$self_aware <- rowMeans(rel.HLQ.na.rm[,c("HL5", "HL11", "HL15", "HL19", "HL22")], na.rm = TRUE)
rel.HLQ.na.rm$citizenship <- rowMeans(rel.HLQ.na.rm[,c("HL3", "HL9", "HL13", "HL20", "HL23")], na.rm = TRUE)

Výpočet sumárneho skóre každej z 5 dimenzií HL - RETEST

#rel.HLQ.na.rm$Rtheor_know <- rowMeans(rel.HLQ.na.rm[,c("RHL1", "RHL8", "RHL14", "RHL18", "RHL25")], na.rm = TRUE)
#rel.HLQ.na.rm$Rprac_know <- rowMeans(rel.HLQ.na.rm[,c("RHL2", "RHL4", "RHL6", "RHL10", "RHL17")], na.rm = TRUE)
#rel.HLQ.na.rm$Rcrit_think <- rowMeans(rel.HLQ.na.rm[,c("RHL7", "RHL12", "RHL16", "RHL21", "RHL24")], na.rm = TRUE)
#rel.HLQ.na.rm$Rself_aware <- rowMeans(rel.HLQ.na.rm[,c("RHL5", "RHL11", "RHL15", "RHL19", "RHL22")], na.rm = TRUE)
#rel.HLQ.na.rm$Rcitizenship <- rowMeans(rel.HLQ.na.rm[,c("RHL3", "RHL9", "RHL13", "RHL20", "RHL23")], na.rm = TRUE)

Test-retest korelácia

#with(rel.HLQ.na.rm, cor.test(theor_know, Rtheor_know))$estimate # pre theor_know
#with(rel.HLQ.na.rm, cor.test(crit_think, Rcrit_think))$estimate # pre crit_think
##with(rel.HLQ.na.rm, cor.test(prac_know, Rprac_know))$estimate # pre prac_know
#with(rel.HLQ.na.rm, cor.test(self_aware, Rself_aware))$estimate # pre self_aware
#with(rel.HLQ.na.rm, cor.test(citizenship, Rcitizenship))$estimate # pre citizenship

Intra-class korelácie pre 5 dimenzií HL

Overenie prítomnosti hierarchickej štruktúry v dátach, ktorá mohla vznikúť použitým spôsobom vzorkovania populácie (cluster sampling) Cluster = školská trieda (premenná ID3)

ICCs <- (lapply(rel.HLQ.na.rm[,c("theor_know", "prac_know", "crit_think", "self_aware", "citizenship")],
                function(x){ICCest(ID3, x, rel.HLQ.na.rm)}))
## NAs removed from rows:
##  1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297
## Warning in ICCest(ID3, x, rel.HLQ.na.rm):
## Warning in ICCest(ID3, x, rel.HLQ.na.rm): 'x' has been coerced to a factor
## NAs removed from rows:
##  1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297
## Warning in ICCest(ID3, x, rel.HLQ.na.rm):

## Warning in ICCest(ID3, x, rel.HLQ.na.rm): 'x' has been coerced to a factor
## NAs removed from rows:
##  1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297
## Warning in ICCest(ID3, x, rel.HLQ.na.rm):

## Warning in ICCest(ID3, x, rel.HLQ.na.rm): 'x' has been coerced to a factor
## NAs removed from rows:
##  1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297
## Warning in ICCest(ID3, x, rel.HLQ.na.rm):

## Warning in ICCest(ID3, x, rel.HLQ.na.rm): 'x' has been coerced to a factor
## NAs removed from rows:
##  1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297
## Warning in ICCest(ID3, x, rel.HLQ.na.rm):

## Warning in ICCest(ID3, x, rel.HLQ.na.rm): 'x' has been coerced to a factor
ICCs$theor_know$ICC # ICC pre theor_know
## [1] 0.1306571
ICCs$prac_know$ICC # ICC pre prac_know
## [1] 0.06576667
ICCs$crit_think$ICC # ICC pre crit_think
## [1] 0.1114863
ICCs$self_aware$ICC # ICC pre self_aware
## [1] 0.07610024
ICCs$citizenship$ICC # ICC pre citizenship
## [1] 0.05677021

Intra-class korelácie už nie sú zanedbateľnéá (viď ICC pre theor_know a crit_think). Dáta majú už mierne hierarchickú štruktúru, čo bez použitia multi-level techník skresľuje odhady.

Alternatívny model

Špecifikácia jednofaktorového modelu

model2 <- '
HLQ =~ a*HL1 + b*HL2 + c*HL3 + d*HL4 + e*HL5 + f*HL6 + g*HL7 + h*HL8 + i*HL9 +
j*HL10 + k*HL11 + l*HL12 + m*HL13 + n*HL14 + o*HL15 + p*HL16 + q*HL17 + r*HL18 +
s*HL19 + t*HL20 + u*HL21 + v*HL22 + x*HL23 + y*HL24 + z*HL25
'

Estimácia a test jednofaktorového modelu, podľa Muthén, 1984

fitted.model2 <- cfa(model = model2, data = data, meanstructure = TRUE, std.lv = TRUE, mimic = "Mplus",
                     estimator = "WLSMVS", test = "Satterthwaite", bootstrap = 5000,
                     ordered = c("HL1", "HL2", "HL3", "HL4", "HL5", "HL6", "HL7", "HL8", "HL9", "HL10",
                                 "HL11", "HL12", "HL13", "HL14", "HL15", "HL16", "HL17", "HL18", "HL19",
                                 "HL20", "HL21", "HL22", "HL23", "HL24", "HL25"))
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL11 x
## HL3
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL3
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL3
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL5 x
## HL4
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL5
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL8 x
## HL7
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL7
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL7
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL9 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL13 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL8
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL12 x
## HL10
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL10
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL16 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL18 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL19 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL21 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL12
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL15 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL19 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL21 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL23 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL13
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL20 x
## HL17
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL17
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL21 x
## HL20
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL20
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL20
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL22 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL24 x
## HL21
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL23 x
## HL22
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of HL25 x
## HL24

Počet buniek HLa x HLb s nulovou frekvenciou je tak na hrane. Majú malú vzorku a tým pádom nízke frekvencie v rámci odpoveďových kategórií

Test modelu, odhady voľných parametrov (faktorové náboje)

Stačí si všímať “Robust” test, Latent variable, Covariances a R-square. Intercepts, Thresholds, Intercepts (…) môžte kľudne ignorovať.

summary(fitted.model2, standardized = TRUE, rsquare = TRUE)
## lavaan (0.5-22) converged normally after  17 iterations
## 
##   Number of observations                           174
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              355.106     130.313
##   Degrees of freedom                               275          52
##   P-value (Chi-square)                           0.001       0.000
##   Scaling correction factor                                  2.725
##     for the mean and variance adjusted correction (WLSMV)
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   HLQ =~                                                                
##     HL1        (a)    0.644    0.059   10.839    0.000    0.644    0.644
##     HL2        (b)    0.637    0.060   10.536    0.000    0.637    0.637
##     HL3        (c)    0.722    0.041   17.432    0.000    0.722    0.722
##     HL4        (d)    0.721    0.044   16.507    0.000    0.721    0.721
##     HL5        (e)    0.762    0.045   17.008    0.000    0.762    0.762
##     HL6        (f)    0.618    0.057   10.818    0.000    0.618    0.618
##     HL7        (g)    0.604    0.053   11.345    0.000    0.604    0.604
##     HL8        (h)    0.803    0.032   25.024    0.000    0.803    0.803
##     HL9        (i)    0.812    0.032   24.987    0.000    0.812    0.812
##     HL10       (j)    0.773    0.035   21.822    0.000    0.773    0.773
##     HL11       (k)    0.750    0.042   17.649    0.000    0.750    0.750
##     HL12       (l)    0.834    0.030   27.479    0.000    0.834    0.834
##     HL13       (m)    0.740    0.042   17.514    0.000    0.740    0.740
##     HL14       (n)    0.745    0.058   12.806    0.000    0.745    0.745
##     HL15       (o)    0.755    0.041   18.351    0.000    0.755    0.755
##     HL16       (p)    0.764    0.039   19.464    0.000    0.764    0.764
##     HL17       (q)    0.683    0.050   13.591    0.000    0.683    0.683
##     HL18       (r)    0.747    0.040   18.476    0.000    0.747    0.747
##     HL19       (s)    0.757    0.036   20.926    0.000    0.757    0.757
##     HL20       (t)    0.881    0.025   35.916    0.000    0.881    0.881
##     HL21       (u)    0.850    0.024   35.343    0.000    0.850    0.850
##     HL22       (v)    0.755    0.039   19.174    0.000    0.755    0.755
##     HL23       (x)    0.802    0.035   23.094    0.000    0.802    0.802
##     HL24       (y)    0.853    0.025   34.249    0.000    0.853    0.853
##     HL25       (z)    0.800    0.036   22.527    0.000    0.800    0.800
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .HL1               0.000                               0.000    0.000
##    .HL2               0.000                               0.000    0.000
##    .HL3               0.000                               0.000    0.000
##    .HL4               0.000                               0.000    0.000
##    .HL5               0.000                               0.000    0.000
##    .HL6               0.000                               0.000    0.000
##    .HL7               0.000                               0.000    0.000
##    .HL8               0.000                               0.000    0.000
##    .HL9               0.000                               0.000    0.000
##    .HL10              0.000                               0.000    0.000
##    .HL11              0.000                               0.000    0.000
##    .HL12              0.000                               0.000    0.000
##    .HL13              0.000                               0.000    0.000
##    .HL14              0.000                               0.000    0.000
##    .HL15              0.000                               0.000    0.000
##    .HL16              0.000                               0.000    0.000
##    .HL17              0.000                               0.000    0.000
##    .HL18              0.000                               0.000    0.000
##    .HL19              0.000                               0.000    0.000
##    .HL20              0.000                               0.000    0.000
##    .HL21              0.000                               0.000    0.000
##    .HL22              0.000                               0.000    0.000
##    .HL23              0.000                               0.000    0.000
##    .HL24              0.000                               0.000    0.000
##    .HL25              0.000                               0.000    0.000
##     HLQ               0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     HL1|t1           -0.043    0.095   -0.454    0.650   -0.043   -0.043
##     HL2|t1           -0.233    0.096   -2.417    0.016   -0.233   -0.233
##     HL3|t1           -1.014    0.115   -8.788    0.000   -1.014   -1.014
##     HL3|t2            0.338    0.097    3.471    0.001    0.338    0.338
##     HL4|t1           -1.364    0.136  -10.056    0.000   -1.364   -1.364
##     HL4|t2           -0.101    0.095   -1.058    0.290   -0.101   -0.101
##     HL5|t1           -1.576    0.154  -10.259    0.000   -1.576   -1.576
##     HL5|t2           -0.014    0.095   -0.151    0.880   -0.014   -0.014
##     HL6|t1           -1.231    0.127   -9.709    0.000   -1.231   -1.231
##     HL6|t2           -0.159    0.096   -1.662    0.096   -0.159   -0.159
##     HL7|t1           -1.364    0.136  -10.056    0.000   -1.364   -1.364
##     HL7|t2            0.130    0.096    1.360    0.174    0.130    0.130
##     HL8|t1           -0.967    0.113   -8.531    0.000   -0.967   -0.967
##     HL8|t2            0.368    0.098    3.771    0.000    0.368    0.368
##     HL9|t1           -1.143    0.122   -9.390    0.000   -1.143   -1.143
##     HL9|t2            0.247    0.096    2.568    0.010    0.247    0.247
##     HL10|t1          -1.402    0.139  -10.122    0.000   -1.402   -1.402
##     HL10|t2           0.014    0.095    0.151    0.880    0.014    0.014
##     HL11|t1          -1.484    0.145  -10.222    0.000   -1.484   -1.484
##     HL11|t2           0.087    0.095    0.907    0.364    0.087    0.087
##     HL12|t1          -1.262    0.129   -9.806    0.000   -1.262   -1.262
##     HL12|t2           0.322    0.097    3.320    0.001    0.322    0.322
##     HL13|t1          -0.528    0.100   -5.263    0.000   -0.528   -0.528
##     HL13|t2           0.630    0.102    6.146    0.000    0.630    0.630
##     HL14|t1          -0.630    0.102   -6.146    0.000   -0.630   -0.630
##     HL15|t1          -1.295    0.131   -9.896    0.000   -1.295   -1.295
##     HL15|t2          -0.101    0.095   -1.058    0.290   -0.101   -0.101
##     HL16|t1          -1.172    0.123   -9.501    0.000   -1.172   -1.172
##     HL16|t2           0.262    0.096    2.718    0.007    0.262    0.262
##     HL17|t1          -1.528    0.149  -10.250    0.000   -1.528   -1.528
##     HL17|t2          -0.384    0.098   -3.921    0.000   -0.384   -0.384
##     HL18|t1          -1.484    0.145  -10.222    0.000   -1.484   -1.484
##     HL18|t2          -0.174    0.096   -1.813    0.070   -0.174   -0.174
##     HL19|t1          -1.014    0.115   -8.788    0.000   -1.014   -1.014
##     HL19|t2           0.368    0.098    3.771    0.000    0.368    0.368
##     HL20|t1          -1.262    0.129   -9.806    0.000   -1.262   -1.262
##     HL20|t2           0.188    0.096    1.964    0.049    0.188    0.188
##     HL21|t1          -1.231    0.127   -9.709    0.000   -1.231   -1.231
##     HL21|t2           0.233    0.096    2.417    0.016    0.233    0.233
##     HL22|t1          -1.329    0.133   -9.980    0.000   -1.329   -1.329
##     HL22|t2          -0.029    0.095   -0.302    0.762   -0.029   -0.029
##     HL23|t1          -1.172    0.123   -9.501    0.000   -1.172   -1.172
##     HL23|t2           0.233    0.096    2.417    0.016    0.233    0.233
##     HL24|t1          -1.442    0.142  -10.178    0.000   -1.442   -1.442
##     HL24|t2           0.087    0.095    0.907    0.364    0.087    0.087
##     HL25|t1          -1.442    0.142  -10.178    0.000   -1.442   -1.442
##     HL25|t2          -0.218    0.096   -2.266    0.023   -0.218   -0.218
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .HL1               0.585                               0.585    0.585
##    .HL2               0.595                               0.595    0.595
##    .HL3               0.478                               0.478    0.478
##    .HL4               0.480                               0.480    0.480
##    .HL5               0.420                               0.420    0.420
##    .HL6               0.618                               0.618    0.618
##    .HL7               0.635                               0.635    0.635
##    .HL8               0.355                               0.355    0.355
##    .HL9               0.341                               0.341    0.341
##    .HL10              0.402                               0.402    0.402
##    .HL11              0.438                               0.438    0.438
##    .HL12              0.304                               0.304    0.304
##    .HL13              0.452                               0.452    0.452
##    .HL14              0.445                               0.445    0.445
##    .HL15              0.430                               0.430    0.430
##    .HL16              0.416                               0.416    0.416
##    .HL17              0.534                               0.534    0.534
##    .HL18              0.442                               0.442    0.442
##    .HL19              0.427                               0.427    0.427
##    .HL20              0.224                               0.224    0.224
##    .HL21              0.278                               0.278    0.278
##    .HL22              0.430                               0.430    0.430
##    .HL23              0.356                               0.356    0.356
##    .HL24              0.273                               0.273    0.273
##    .HL25              0.360                               0.360    0.360
##     HLQ               1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     HL1               1.000                               1.000    1.000
##     HL2               1.000                               1.000    1.000
##     HL3               1.000                               1.000    1.000
##     HL4               1.000                               1.000    1.000
##     HL5               1.000                               1.000    1.000
##     HL6               1.000                               1.000    1.000
##     HL7               1.000                               1.000    1.000
##     HL8               1.000                               1.000    1.000
##     HL9               1.000                               1.000    1.000
##     HL10              1.000                               1.000    1.000
##     HL11              1.000                               1.000    1.000
##     HL12              1.000                               1.000    1.000
##     HL13              1.000                               1.000    1.000
##     HL14              1.000                               1.000    1.000
##     HL15              1.000                               1.000    1.000
##     HL16              1.000                               1.000    1.000
##     HL17              1.000                               1.000    1.000
##     HL18              1.000                               1.000    1.000
##     HL19              1.000                               1.000    1.000
##     HL20              1.000                               1.000    1.000
##     HL21              1.000                               1.000    1.000
##     HL22              1.000                               1.000    1.000
##     HL23              1.000                               1.000    1.000
##     HL24              1.000                               1.000    1.000
##     HL25              1.000                               1.000    1.000
## 
## R-Square:
##                    Estimate
##     HL1               0.415
##     HL2               0.405
##     HL3               0.522
##     HL4               0.520
##     HL5               0.580
##     HL6               0.382
##     HL7               0.365
##     HL8               0.645
##     HL9               0.659
##     HL10              0.598
##     HL11              0.562
##     HL12              0.696
##     HL13              0.548
##     HL14              0.555
##     HL15              0.570
##     HL16              0.584
##     HL17              0.466
##     HL18              0.558
##     HL19              0.573
##     HL20              0.776
##     HL21              0.722
##     HL22              0.570
##     HL23              0.644
##     HL24              0.727
##     HL25              0.640

Priemerny faktorovy naboj

mean(inspect(fitted.model2,what="std")$lambda)
## [1] 0.752462

Test modelu, indexy blízkej zhody modelu a dát

Treba si všímať .scaled indexy

fitMeasures(fitted.model2)
##                          npar                          fmin 
##                        72.000                         1.020 
##                         chisq                            df 
##                       355.106                       275.000 
##                        pvalue                  chisq.scaled 
##                         0.001                       130.313 
##                     df.scaled                 pvalue.scaled 
##                        52.000                         0.000 
##          chisq.scaling.factor                baseline.chisq 
##                         2.725                     24290.950 
##                   baseline.df               baseline.pvalue 
##                       300.000                         0.000 
##         baseline.chisq.scaled            baseline.df.scaled 
##                      1140.130                        14.000 
##        baseline.pvalue.scaled baseline.chisq.scaling.factor 
##                         0.000                        21.305 
##                           cfi                           tli 
##                         0.997                         0.996 
##                          nnfi                           rfi 
##                         0.996                         0.984 
##                           nfi                          pnfi 
##                         0.985                         0.903 
##                           ifi                           rni 
##                         0.997                         0.997 
##                    cfi.scaled                    tli.scaled 
##                         0.930                         0.981 
##                    cfi.robust                    tli.robust 
##                            NA                            NA 
##                   nnfi.scaled                   nnfi.robust 
##                         0.981                            NA 
##                    rfi.scaled                    nfi.scaled 
##                         0.969                         0.886 
##                    ifi.scaled                    rni.scaled 
##                         0.886                         0.997 
##                    rni.robust                         rmsea 
##                            NA                         0.041 
##                rmsea.ci.lower                rmsea.ci.upper 
##                         0.027                         0.053 
##                  rmsea.pvalue                  rmsea.scaled 
##                         0.890                         0.093 
##         rmsea.ci.lower.scaled         rmsea.ci.upper.scaled 
##                         0.081                         0.105 
##           rmsea.pvalue.scaled                  rmsea.robust 
##                         0.000                            NA 
##         rmsea.ci.lower.robust         rmsea.ci.upper.robust 
##                            NA                            NA 
##           rmsea.pvalue.robust                           rmr 
##                            NA                         0.071 
##                    rmr_nomean                          srmr 
##                         0.074                         0.071 
##                  srmr_bentler           srmr_bentler_nomean 
##                         0.071                         0.074 
##                   srmr_bollen            srmr_bollen_nomean 
##                         0.071                         0.074 
##                    srmr_mplus             srmr_mplus_nomean 
##                         0.071                         0.074 
##                         cn_05                         cn_01 
##                       154.305                       162.977 
##                           gfi                          agfi 
##                         0.987                         0.983 
##                          pgfi                           mfi 
##                         0.782                         0.793

Chi^2 test rozdielov medzi modelmi - p-hodnota

pchisq((fitted.model2@test[[2]]$stat - fitted.model@test[[2]]$stat),
       (fitted.model2@test[[1]]$df - fitted.model@test[[1]]$df),
       lower.tail = FALSE)
## [1] 0.779334

Diagram

semPaths(fitted.model2, style = "mx", layout = "circle",
         edge.label.cex = 0.5, sizeLat = 5, nCharNodes = 0,
         nDigits = 2, "Standardized",
         intercepts = FALSE, residuals = TRUE, exoVar = FALSE,
         fade = TRUE, groups = "latents", pastel = TRUE)

Test modelu indikuje prítomnosť chybnej špecifikácie modelu. Popri indexoch blízkej zhody je preto potrebné analyzovať lokálne zdroje chybnej špecifikácie na základe matice reziduálnych korelácií

Matica reziduálnych korelácií

residuals.m2 <- residuals(fitted.model2, type = "cor" )$cor
residuals.m2
##      HL1    HL2    HL3    HL4    HL5    HL6    HL7    HL8    HL9    HL10  
## HL1   0.000                                                               
## HL2   0.287  0.000                                                        
## HL3  -0.098  0.140  0.000                                                 
## HL4   0.020 -0.017  0.066  0.000                                          
## HL5   0.063  0.182  0.068  0.201  0.000                                   
## HL6  -0.026  0.141  0.047  0.113  0.165  0.000                            
## HL7  -0.021 -0.152 -0.124  0.006 -0.091 -0.174  0.000                     
## HL8  -0.025 -0.147  0.042 -0.028 -0.034 -0.049  0.007  0.000              
## HL9  -0.004 -0.090 -0.024  0.058 -0.035 -0.095  0.014  0.121  0.000       
## HL10  0.028  0.054  0.011  0.110  0.018 -0.020 -0.010 -0.075  0.014  0.000
## HL11  0.097  0.032  0.079 -0.071  0.006  0.099 -0.031  0.016 -0.018  0.086
## HL12  0.004  0.011  0.045  0.017 -0.080  0.107  0.089 -0.026 -0.014  0.028
## HL13  0.005 -0.091 -0.023 -0.143 -0.158 -0.077  0.034  0.038  0.026 -0.069
## HL14 -0.142 -0.117 -0.013 -0.037 -0.159 -0.032 -0.011 -0.166 -0.084 -0.008
## HL15 -0.060 -0.087  0.034 -0.068 -0.042 -0.035  0.067 -0.039 -0.096 -0.052
## HL16  0.038  0.017 -0.054 -0.128 -0.060 -0.098  0.049 -0.076 -0.093  0.022
## HL17  0.026  0.144 -0.051 -0.093 -0.025  0.146 -0.149 -0.061 -0.099  0.058
## HL18 -0.002  0.068  0.020 -0.106 -0.102 -0.036  0.032  0.053 -0.065  0.066
## HL19 -0.073 -0.141  0.027 -0.143 -0.041 -0.116  0.079 -0.028  0.054 -0.041
## HL20 -0.035 -0.019 -0.035 -0.098 -0.008 -0.049 -0.010 -0.028  0.031  0.001
## HL21 -0.018 -0.038 -0.060 -0.092  0.024 -0.017  0.033 -0.036 -0.051 -0.089
## HL22 -0.101 -0.224 -0.064 -0.004 -0.060 -0.050  0.052  0.017 -0.050 -0.072
## HL23 -0.083 -0.038 -0.090 -0.045 -0.055 -0.045 -0.085 -0.058 -0.064 -0.035
## HL24  0.058 -0.149 -0.033  0.004 -0.018 -0.122  0.013  0.049  0.001 -0.037
## HL25 -0.168 -0.208 -0.042  0.056 -0.020 -0.078  0.016 -0.001 -0.002 -0.093
##      HL11   HL12   HL13   HL14   HL15   HL16   HL17   HL18   HL19   HL20  
## HL1                                                                       
## HL2                                                                       
## HL3                                                                       
## HL4                                                                       
## HL5                                                                       
## HL6                                                                       
## HL7                                                                       
## HL8                                                                       
## HL9                                                                       
## HL10                                                                      
## HL11  0.000                                                               
## HL12  0.088  0.000                                                        
## HL13 -0.057  0.055  0.000                                                 
## HL14  0.008 -0.058 -0.113  0.000                                          
## HL15  0.035 -0.065  0.108  0.191  0.000                                   
## HL16 -0.056  0.023  0.133 -0.058  0.088  0.000                            
## HL17  0.039 -0.054 -0.027  0.081  0.044  0.099  0.000                     
## HL18  0.013  0.007 -0.115  0.013 -0.058  0.062  0.109  0.000              
## HL19 -0.111  0.017  0.047 -0.107 -0.080  0.017 -0.101 -0.012  0.000       
## HL20 -0.041 -0.055 -0.093 -0.049 -0.075  0.000  0.032  0.031  0.026  0.000
## HL21 -0.042  0.002  0.062 -0.078  0.009  0.035 -0.114 -0.081  0.055  0.069
## HL22 -0.066 -0.056  0.005 -0.007 -0.051 -0.107 -0.065 -0.035 -0.027  0.061
## HL23 -0.037 -0.014  0.041 -0.076 -0.006 -0.030 -0.033 -0.091  0.077  0.022
## HL24 -0.048 -0.067 -0.055  0.024  0.001 -0.055 -0.042  0.052  0.053 -0.018
## HL25 -0.157 -0.070 -0.065  0.192  0.057 -0.072  0.000 -0.046 -0.050 -0.027
##      HL21   HL22   HL23   HL24   HL25  
## HL1                                    
## HL2                                    
## HL3                                    
## HL4                                    
## HL5                                    
## HL6                                    
## HL7                                    
## HL8                                    
## HL9                                    
## HL10                                   
## HL11                                   
## HL12                                   
## HL13                                   
## HL14                                   
## HL15                                   
## HL16                                   
## HL17                                   
## HL18                                   
## HL19                                   
## HL20                                   
## HL21  0.000                            
## HL22  0.063  0.000                     
## HL23  0.027  0.162  0.000              
## HL24 -0.032 -0.044  0.038  0.000       
## HL25 -0.076  0.058  0.024  0.131  0.000

Pre prehladnejšiu vizualizáciu, matica reziduí s vyznačenými reziduálnymi hodnotami > .1 (štandardizované z-reziduá je možné odhadnúť iba v prípade použitia estimátora z rodiny maximum likelihood. Arbitrárna hodnota .1 preto, lebo neumožní produkt dvoch nábojov > .3)

Počet premenných

p = 25

Ak máme v matici (p(p+1)/2 - p) = 300 elementov, tak

(p*(p+1)/2 - p)*.05
## [1] 15

z nich môže byť signifikantných na hladine alfa = .05

HRUBÁ APROXIMÁCIA - približne toľko elementov môže byť > .1 Diag = diagonála, >.1 = reziduálna hodnota vyššia ako .1

ifelse(residuals.m2 == 0, "Diag", ifelse(residuals.m2 > .1, ">.1", "."))
##      HL1    HL2    HL3    HL4    HL5    HL6    HL7    HL8    HL9    HL10  
## HL1  "Diag" ">.1"  "."    "."    "."    "."    "."    "."    "."    "."   
## HL2  ">.1"  "Diag" ">.1"  "."    ">.1"  ">.1"  "."    "."    "."    "."   
## HL3  "."    ">.1"  "Diag" "."    "."    "."    "."    "."    "."    "."   
## HL4  "."    "."    "."    "Diag" ">.1"  ">.1"  "."    "."    "."    ">.1" 
## HL5  "."    ">.1"  "."    ">.1"  "Diag" ">.1"  "."    "."    "."    "."   
## HL6  "."    ">.1"  "."    ">.1"  ">.1"  "Diag" "."    "."    "."    "."   
## HL7  "."    "."    "."    "."    "."    "."    "Diag" "."    "."    "."   
## HL8  "."    "."    "."    "."    "."    "."    "."    "Diag" ">.1"  "."   
## HL9  "."    "."    "."    "."    "."    "."    "."    ">.1"  "Diag" "."   
## HL10 "."    "."    "."    ">.1"  "."    "."    "."    "."    "."    "Diag"
## HL11 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL12 "."    "."    "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL13 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL14 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL15 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL16 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL17 "."    ">.1"  "."    "."    "."    ">.1"  "."    "."    "."    "."   
## HL18 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL19 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL20 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL21 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL22 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL23 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL24 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL25 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
##      HL11   HL12   HL13   HL14   HL15   HL16   HL17   HL18   HL19   HL20  
## HL1  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL2  "."    "."    "."    "."    "."    "."    ">.1"  "."    "."    "."   
## HL3  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL4  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL5  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL6  "."    ">.1"  "."    "."    "."    "."    ">.1"  "."    "."    "."   
## HL7  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL8  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL9  "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL10 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL11 "Diag" "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL12 "."    "Diag" "."    "."    "."    "."    "."    "."    "."    "."   
## HL13 "."    "."    "Diag" "."    ">.1"  ">.1"  "."    "."    "."    "."   
## HL14 "."    "."    "."    "Diag" ">.1"  "."    "."    "."    "."    "."   
## HL15 "."    "."    ">.1"  ">.1"  "Diag" "."    "."    "."    "."    "."   
## HL16 "."    "."    ">.1"  "."    "."    "Diag" "."    "."    "."    "."   
## HL17 "."    "."    "."    "."    "."    "."    "Diag" ">.1"  "."    "."   
## HL18 "."    "."    "."    "."    "."    "."    ">.1"  "Diag" "."    "."   
## HL19 "."    "."    "."    "."    "."    "."    "."    "."    "Diag" "."   
## HL20 "."    "."    "."    "."    "."    "."    "."    "."    "."    "Diag"
## HL21 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL22 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL23 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL24 "."    "."    "."    "."    "."    "."    "."    "."    "."    "."   
## HL25 "."    "."    "."    ">.1"  "."    "."    "."    "."    "."    "."   
##      HL21   HL22   HL23   HL24   HL25  
## HL1  "."    "."    "."    "."    "."   
## HL2  "."    "."    "."    "."    "."   
## HL3  "."    "."    "."    "."    "."   
## HL4  "."    "."    "."    "."    "."   
## HL5  "."    "."    "."    "."    "."   
## HL6  "."    "."    "."    "."    "."   
## HL7  "."    "."    "."    "."    "."   
## HL8  "."    "."    "."    "."    "."   
## HL9  "."    "."    "."    "."    "."   
## HL10 "."    "."    "."    "."    "."   
## HL11 "."    "."    "."    "."    "."   
## HL12 "."    "."    "."    "."    "."   
## HL13 "."    "."    "."    "."    "."   
## HL14 "."    "."    "."    "."    ">.1" 
## HL15 "."    "."    "."    "."    "."   
## HL16 "."    "."    "."    "."    "."   
## HL17 "."    "."    "."    "."    "."   
## HL18 "."    "."    "."    "."    "."   
## HL19 "."    "."    "."    "."    "."   
## HL20 "."    "."    "."    "."    "."   
## HL21 "Diag" "."    "."    "."    "."   
## HL22 "."    "Diag" ">.1"  "."    "."   
## HL23 "."    ">.1"  "Diag" "."    "."   
## HL24 "."    "."    "."    "Diag" ">.1" 
## HL25 "."    "."    "."    ">.1"  "Diag"

Odhad reliability

Odhad internej konzistencie - Cronbachova alfa

alpha(rel.HLQ.na.rm[,1:25])$total$std.alpha # pre jednofaktorovu (25 polozkovu) skalu
## [1] 0.9310071

Odhad stability v čase

Výpočet sumárneho skóre HLQ

rel.HLQ.na.rm$HLQ_sum <- rowMeans(rel.HLQ.na.rm[,c("HL1", "HL2", "HL3", "HL4", "HL5", "HL6", "HL7", "HL8", "HL9",
                                                   "HL10", "HL11", "HL12", "HL13", "HL14", "HL15", "HL16", "HL17",
                                                   "HL18", "HL19", "HL20", "HL21", "HL22", "HL23", "HL24", "HL25")], na.rm = TRUE)

Výpočet sumárného skóre retestu RHLQ

#rel.HLQ.na.rm$RHLQ_sum <- rowMeans(rel.HLQ.na.rm[,c("RHL1", "RHL2", "RHL3", "RHL4", "RHL5", "RHL6", "RHL7", "RHL8", "RHL9",
#                                                    "RHL10", "RHL11", "RHL12", "RHL13", "RHL14", "RHL15", "RHL16", "RHL17",
#                                                    "RHL18", "RHL19", "RHL20", "RHL21", "RHL22", "RHL23", "RHL24", "RHL25")], na.rm = TRUE)

Test-retest korelácia

#with(rel.HLQ.na.rm, cor.test(HLQ_sum, RHLQ_sum))$estimate # pre jednofaktorovu (25 polozkovu) skalu