Dyscalculia, General Intelligence, and Mathematics Grades in Hungary
library(pacman); p_load(readxl, tidyr, dplyr, tidyverse, psych, ggplot2, cowplot, sandwich, lmtest, ggcorrplot, lavaan, semPlot, lavaanPlot)
HCReg <- function(Formula, Data, HC = "HC5"){
require(sandwich); require(lmtest)
BaseModel <- lm(Formula, Data)
VC <- vcovHC(BaseModel, type = HC)
coeftest_results <- coeftest(BaseModel, vcov = VC)
model_summary <- summary(BaseModel)
r_squared <- model_summary$r.squared
adj_r_squared <- model_summary$adj.r.squared
Output <- list(
coeftest_results = coeftest_results,
r_squared = r_squared,
adj_r_squared = adj_r_squared)
return(Output)}
data <- read_xlsx("SESIncludedData.xlsx")
data$MSZMT_total <- rowSums(data[,62:101]) #MARS Total Score
Transformed <- data %>% gather(Subtest, Score, dpv_tajek:dpv_praktik)
data %>%
summarise_all(list(mean = mean, N = ~sum(!is.na(.)), sd = sd))## Warning: There was 1 warning in `summarise()`.
## ℹ In argument: `SES_mean = (function (x, ...) ...`.
## Caused by warning in `mean.default()`:
## ! argument is not numeric or logical: returning NARationale
The Diszkalkulia Pedagogiai Vizsgalata or DPV is a dyscalculia diagnosis tool used in Hungary. It features 14 subtests which amount to parcels of different numbers of items, in addition to one sumscore for the whole battery (dpv_ossz). Dyscalculia is defined as abnormally low mathematical ability for a person’s chronological age and level of intellectual functioning. Despite this, the DPV may be a measure of general intelligence, and this can be assessed by determining the latent correlation with the g factor from a gold-standard intelligence assessment like the WISC.
DPV Test Details
- Tajek, quality assessment. Binary/boolean indicating if a person has the correct bodily left-right orientation, the correct examiner left-right orientation, understands relations and left-right orientation on a plane, understands relational vocabulary in tenses in time, and relations in time, and understands relationships between numbers and understands relational grammar in numbers.
2.1. Szaml, counting in 10,000s. Five-point scale earned based on a participant’s ability to correctly name numbers, ability to count correctly in ones, tenths, and hundredths in ascending and descending order, ability to correctly place ones, tenths, and hundredths in ascending and descending order, ability to identify numbering rule mistakes for ones, tenths, and hundredths in ascending and descending order, and whether the participant stuttered or slowed their tempo by ones, tenths, or hundredths when going between numbers, in both ascending and descending order.
2.2. Szameml, number memory. Binary/boolean indicating if a person’s number memory appears weak per the examiner’s qualitative judgment. This scale is binary.
2.3. Szamegyz, number name-digit matching in the range of 100,000. Six-point scale earned based on a participant’s ability to avoid making errors when reading and writing five-digit numbers, and to avoid using zero as a placeholder when describing numbers or reading out their digits.
2.4. Rel, quantitative relations between numerical neighbors in the range of 10,000. Four-point scale earned based on a participant’s ability to correctly verbally and visually interpret manufactured quantitative relations, identify the content of a relational signal, and determine whether the neighbors of a given number are correct.
2.5. Helyiert, designation of a local value in the 10,000 range.
3.1. Potlas, substitution, decomposition, addition, and subtraction in numbers of 10 and 20, following arithmetic rules. One hundred-point scale with which points are earned by indicating correct understandings of operations, use of equipment, ability to mathematically abstract, to count in tens, and to switch between different operations without error.
3.2. Muvel, addition and subtraction in 100s, 1000s, analogies, and approximate calculation. Forty-three-point scale with which points are earned by indicating correct readings of specific actions, identifying operation signals and performing with them, properly using devices, correctly interpreting counts, verbally executing operations, performing approximate calculations like rounding and estimating, and avoiding disorientation when switching between operations.
3.3. Szorzoszt, multiplication and inclusion. Nine-point scale with which points are earned by interpreting operations correctly, and interpreting the relationship between multiplication and inclusion correctly.
3.4. Irasbeli, written actions. Thirty-eight-point scale with which points are earned by correctly recording what written operations are, reading them out, identifying operation signals correctly, processing written transactions involving operations, using devices correctly, properly interpreting placeholders during operations, properly interpreting the concept of the remainder, retaining the remainder, obtaining a correct answer, and switching to different operations correctly.
Szoveg, text tasks. 27-point scale with which points are earned by properly state mathematical questions and do so without tools or taking additional actions due to errors.
Logszab, mathematical-logical rules. Nine-point scale with which points are earned by correctly interpreting the terms decreasing and increasing, and by understanding and sticking to defined rules which are used to solve a question that the participant is also scored on.
Muvsorr, higher level mathematical concepts and the order of operations. Twenty-two-point scale with which points are earned by correctly interpreting fractions, reading and writing fractions, performing operations with fractions, relating decimal numbers to fractiosn, reading and writing decimal fractions, identifying operation signals with fractions, understanding when operations are wrong with fractions, processing written transactions with fractions, using devices with fractions, understanding placeholders with decimal fractions, retaining remainders with fractions, switching operations when appropriate, and interpreting negative numbers tied to specific examples like debt and thermometers correctly.
Praktik, practical knowledge. Binary/boolean qualitatively assessing a participant’s ability to identify units of measurement, recall conversion numbers when converting between them, select appropriate operations during unit conversions, and interpret the concepts of districts and areas correctly.
Analyses
Variable Distributions
OrdNames <- list(
"dpv_helyiert" = "Helyiert",
"dpv_irasbeli" = "Irasbeli",
"dpv_logszab" = "Logszab",
"dpv_muvel" = "Muvel",
"dpv_muvsorr" = "Muvsorr",
"dpv_potlas" = "Potlas",
"dpv_praktik" = "Praktik",
"dpv_rel" = "Rel",
"dpv_szamegyz" = "Szamegyz",
"dpv_szameml" = "Szameml",
"dpv_szaml" = "Szaml",
"dpv_szorzoszt"= "Szorzoszt",
"dpv_szoveg" = "Szoveg",
"dpv_tajek" = "Tajek")
TestLabeler <- function(variable, value){
return(OrdNames[value])}
p <- ggplot(Transformed) +
geom_histogram(aes(Score, color = Subtest, fill = Subtest), alpha = .5, binwidth = 1) +
ggplot2::theme_bw() +
theme(legend.position = "none") +
facet_wrap(~ Subtest, scales = "free",
labeller = TestLabeler) +
labs(
x = NULL,
y = NULL)
ggdraw(p) + draw_label(x = .76, y = .15, "Subtests of the DPV")
Correlations
First, some particulars of interest
cor(data$dpv_ossz, data$WISC_TtlQ) #DPV Total Score - FSIQ## [1] 0.6235342cor(data$dpv_ossz, data$osztalyzat) #DPV Total Score - Grades## [1] 0.4969822cor(data$dpv_ossz, data$MSZMT_total) #DPV Total - MARS Total## [1] -0.6455582cor(data$dpv_ossz, as.numeric(data$SES)) #DPV Total - SES## [1] 0.4469441cor(data$WISC_TtlQ, data$osztalyzat) #FSIQ - Grades## [1] 0.7212848cor(data$WISC_TtlQ, data$MSZMT_total) #FSIQ - MARS Total## [1] -0.5050968cor(data$WISC_TtlQ, as.numeric(data$SES)) #FSIQ - SES## [1] 0.7824917and now, the DPV correlation matrix:
VarNames <- list("Tajek", "Szaml", "Szameml", "Szamegyz", "Rel", "Helyiert", "Potlas", "Muvel", "Szorzoszt", "Irasbeli", "Szoveg", "Logszab", "Muvsorr", "Praktik")
ggcorrplot(round(cor(data[42:55]), 4),
hc.order = T,
type = "lower",
outline.col = "white",
ggtheme = ggplot2::theme_bw(),
show.legend = F,
lab = T,
title = "DPV Subtest Intercorrelations",
colors = c("orangered", "gold", "steelblue"),
show.diag = F) +
theme(
plot.title = element_text(hjust = .5)) +
scale_y_discrete(labels = VarNames) +
scale_x_discrete(labels = VarNames)
And now with the WAIS
VarNames <- list("Tajek", "Szaml", "Szameml", "Szamegyz", "Rel", "Helyiert", "Potlas", "Muvel", "Szorzoszt", "Irasbeli", "Szoveg", "Logszab", "Muvsorr", "Praktik", "Szokincs", "Altmegert", "Mozaik", "Kepifog", "Matrix", "Szamterj", "Betuszam", "Kodolas", "Szimbol")
ggcorrplot(round(cor(data[c(42:55, 15, 17, 19, 23, 25, 27, 31, 33, 37, 39)]), 4),
hc.order = F,
type = "lower",
outline.col = "white",
ggtheme = ggplot2::theme_bw(),
show.legend = F,
lab = T,
title = "DPV and WISC Subtest Intercorrelations",
colors = c("orangered", "gold", "steelblue"),
show.diag = F) +
theme(
plot.title = element_text(hjust = .5)) +
scale_y_discrete(labels = VarNames) +
scale_x_discrete(labels = VarNames)
EFA
There is no available theoretical factor structure for the DPV, so exploratory results follow. Since the DPV is supposed to measure one thing, a single-factor structure will be defaulted to unless another can be found. Results from both will be presented regardless.
fa.parallel(data[42:55])
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1fa.parallel(sqrt(data[42:55]))
## Parallel analysis suggests that the number of factors = 1 and the number of components = 1print(fa(data[42:55], nfactors = 2), cut = .3, sort = T)## Loading required namespace: GPArotation## Factor Analysis using method = minres
## Call: fa(r = data[42:55], nfactors = 2)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 h2 u2 com
## dpv_praktik 14 0.90 0.59 0.41 1.1
## dpv_muvsorr 13 0.88 0.68 0.32 1.0
## dpv_szorzoszt 9 0.84 0.77 0.23 1.0
## dpv_muvel 8 0.71 0.82 0.18 1.3
## dpv_logszab 12 0.68 0.77 0.23 1.3
## dpv_szoveg 11 0.59 0.35 0.74 0.26 1.6
## dpv_irasbeli 10 0.56 0.42 0.58 1.1
## dpv_szamegyz 4 0.50 0.42 0.71 0.29 1.9
## dpv_potlas 7 0.46 0.36 0.57 0.43 1.9
## dpv_szameml 3 0.44 0.23 0.77 1.0
## dpv_szaml 2 0.85 0.75 0.25 1.0
## dpv_helyiert 6 0.63 0.41 0.59 1.0
## dpv_rel 5 0.61 0.47 0.53 1.1
## dpv_tajek 1 0.55 0.45 0.55 1.2
##
## MR1 MR2
## SS loadings 5.29 3.09
## Proportion Var 0.38 0.22
## Cumulative Var 0.38 0.60
## Proportion Explained 0.63 0.37
## Cumulative Proportion 0.63 1.00
##
## With factor correlations of
## MR1 MR2
## MR1 1.00 0.66
## MR2 0.66 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 91 and the objective function was 11.63 with Chi Square of 1110.67
## The degrees of freedom for the model are 64 and the objective function was 2.03
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 102 with the empirical chi square 53.42 with prob < 0.82
## The total number of observations was 102 with Likelihood Chi Square = 191.38 with prob < 1.3e-14
##
## Tucker Lewis Index of factoring reliability = 0.82
## RMSEA index = 0.139 and the 90 % confidence intervals are 0.118 0.163
## BIC = -104.62
## Fit based upon off diagonal values = 0.99
## Measures of factor score adequacy
## MR1 MR2
## Correlation of (regression) scores with factors 0.97 0.94
## Multiple R square of scores with factors 0.94 0.89
## Minimum correlation of possible factor scores 0.89 0.78print(fa(data[42:55], nfactors = 3), cut = .3, sort = T)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully## Factor Analysis using method = minres
## Call: fa(r = data[42:55], nfactors = 3)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR3 MR2 h2 u2 com
## dpv_muvsorr 13 0.89 0.67 0.32571 1.0
## dpv_szorzoszt 9 0.86 0.78 0.21982 1.0
## dpv_praktik 14 0.86 0.60 0.39933 1.1
## dpv_muvel 8 0.75 0.84 0.15858 1.2
## dpv_logszab 12 0.67 0.76 0.23610 1.3
## dpv_szoveg 11 0.60 0.74 0.26015 1.5
## dpv_irasbeli 10 0.56 0.48 0.52124 1.7
## dpv_szamegyz 4 0.55 0.72 0.28451 1.7
## dpv_potlas 7 0.48 0.56 0.43552 1.7
## dpv_szameml 3 0.44 0.23 0.76578 1.1
## dpv_szaml 2 0.89 0.82 0.17701 1.0
## dpv_tajek 1 0.71 0.55 0.44662 1.1
## dpv_helyiert 6 0.51 0.39 0.61362 1.2
## dpv_rel 5 0.96 1.00 -0.00037 1.0
##
## MR1 MR3 MR2
## SS loadings 5.29 2.41 1.45
## Proportion Var 0.38 0.17 0.10
## Cumulative Var 0.38 0.55 0.65
## Proportion Explained 0.58 0.26 0.16
## Cumulative Proportion 0.58 0.84 1.00
##
## With factor correlations of
## MR1 MR3 MR2
## MR1 1.00 0.65 0.44
## MR3 0.65 1.00 0.49
## MR2 0.44 0.49 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 91 and the objective function was 11.63 with Chi Square of 1110.67
## The degrees of freedom for the model are 52 and the objective function was 1.56
##
## The root mean square of the residuals (RMSR) is 0.04
## The df corrected root mean square of the residuals is 0.06
##
## The harmonic number of observations is 102 with the empirical chi square 33.62 with prob < 0.98
## The total number of observations was 102 with Likelihood Chi Square = 146.04 with prob < 7.3e-11
##
## Tucker Lewis Index of factoring reliability = 0.835
## RMSEA index = 0.133 and the 90 % confidence intervals are 0.108 0.16
## BIC = -94.46
## Fit based upon off diagonal values = 0.99print(fa(data[42:55], nfactors = 4), cut = .3, sort = T)## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.## Factor Analysis using method = minres
## Call: fa(r = data[42:55], nfactors = 4)
## Standardized loadings (pattern matrix) based upon correlation matrix
## item MR1 MR2 MR4 MR3 h2 u2 com
## dpv_praktik 14 0.89 0.76 0.2398 1.1
## dpv_muvsorr 13 0.59 0.67 0.3345 1.6
## dpv_logszab 12 0.55 0.30 0.80 0.1969 2.0
## dpv_szoveg 11 0.41 0.32 0.75 0.2476 2.8
## dpv_szameml 3 0.38 0.25 0.7505 1.4
## dpv_rel 5 0.83 0.73 0.2737 1.1
## dpv_szamegyz 4 0.58 0.76 0.2378 1.6
## dpv_muvel 8 0.41 0.52 0.85 0.1502 2.1
## dpv_potlas 7 0.56 0.4392 3.6
## dpv_tajek 1 0.78 0.67 0.3347 1.1
## dpv_szaml 2 0.68 0.76 0.2392 1.4
## dpv_helyiert 6 0.39 0.39 0.6065 2.5
## dpv_irasbeli 10 1.01 1.00 0.0034 1.0
## dpv_szorzoszt 9 0.39 0.39 0.41 0.81 0.1888 3.1
##
## MR1 MR2 MR4 MR3
## SS loadings 2.97 2.76 2.11 1.91
## Proportion Var 0.21 0.20 0.15 0.14
## Cumulative Var 0.21 0.41 0.56 0.70
## Proportion Explained 0.30 0.28 0.22 0.20
## Cumulative Proportion 0.30 0.59 0.80 1.00
##
## With factor correlations of
## MR1 MR2 MR4 MR3
## MR1 1.00 0.47 0.44 0.54
## MR2 0.47 1.00 0.52 0.39
## MR4 0.44 0.52 1.00 0.43
## MR3 0.54 0.39 0.43 1.00
##
## Mean item complexity = 1.9
## Test of the hypothesis that 4 factors are sufficient.
##
## The degrees of freedom for the null model are 91 and the objective function was 11.63 with Chi Square of 1110.67
## The degrees of freedom for the model are 41 and the objective function was 1.07
##
## The root mean square of the residuals (RMSR) is 0.03
## The df corrected root mean square of the residuals is 0.05
##
## The harmonic number of observations is 102 with the empirical chi square 18.39 with prob < 1
## The total number of observations was 102 with Likelihood Chi Square = 99.03 with prob < 1e-06
##
## Tucker Lewis Index of factoring reliability = 0.87
## RMSEA index = 0.117 and the 90 % confidence intervals are 0.089 0.148
## BIC = -90.6
## Fit based upon off diagonal values = 1The 4-factor models fit best, but none of these look good at all.
ModBi4 <- '
g =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik
F1 =~ dpv_muvsorr + dpv_praktik
F2 =~ dpv_rel + dpv_irasbeli
F3 =~ dpv_szaml + dpv_tajek'
ModGF4 <- '
F1 =~ dpv_praktik + dpv_muvsorr + dpv_logszab + dpv_szoveg + dpv_szameml + dpv_muvel + dpv_szorzoszt
F2 =~ dpv_szoveg + dpv_rel + dpv_szamegyz + dpv_muvel + dpv_szorzoszt
F3 =~ dpv_logszab + dpv_tajek + dpv_szaml + dpv_helyiert
F4 =~ dpv_irasbeli + dpv_szorzoszt
dpv_szamegyz ~~ 0*dpv_szamegyz
dpv_szorzoszt ~~ 0*dpv_szorzoszt'
FitBi4 <- cfa(ModBi4, std.lv = T, meanstructure = T, orthogonal = T, data, estimator = "DWLS", ordered = c("dpv_szaml", "dpv_szamegyz", "dpv_rel", "dpv_potlas", "dpv_muvel", "dpv_szorzoszt", "dpv_irasbeli", "dpv_szoveg", "dpv_logszab", "dpv_muvsorr"), check.gradient = F, control=list(rel.tol=1e-4))## Warning in lav_data_full(data = data, group = group, cluster = cluster, :
## lavaan WARNING: some ordered categorical variable(s) have more than 12 levels:
## dpv_potlas dpv_muvel dpv_szoveg## Warning in muthen1984(Data = X[[g]], wt = WT[[g]], ov.names = ov.names[[g]], :
## lavaan WARNING: trouble constructing W matrix; used generalized inverse for A11
## submatrix## Warning in lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats, : lavaan WARNING:
## Could not compute standard errors! The information matrix could
## not be inverted. This may be a symptom that the model is not
## identified.## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negativeFitGF4 <- cfa(ModGF4, std.lv = T, meanstructure = T, orthogonal = F, data, estimator = "DWLS", ordered = c("dpv_szaml", "dpv_szamegyz", "dpv_rel", "dpv_potlas", "dpv_muvel", "dpv_szorzoszt", "dpv_irasbeli", "dpv_szoveg", "dpv_logszab", "dpv_muvsorr"), check.gradient = F, control=list(rel.tol=1e-4))## Warning in lav_data_full(data = data, group = group, cluster = cluster, :
## lavaan WARNING: some ordered categorical variable(s) have more than 12 levels:
## dpv_szoveg dpv_muvel## Warning in muthen1984(Data = X[[g]], wt = WT[[g]], ov.names = ov.names[[g]], :
## lavaan WARNING: trouble constructing W matrix; used generalized inverse for A11
## submatrix## Warning in lav_object_post_check(object): lavaan WARNING: some estimated ov
## variances are negativesummary(FitBi4, stand = T, fit = T)## lavaan 0.6.14 ended normally after 50 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 120
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 68.690
## Degrees of freedom 71
## P-value (Chi-square) 0.556
##
## Model Test Baseline Model:
##
## Test statistic 9338.384
## Degrees of freedom 91
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.054
## P-value H_0: RMSEA <= 0.050 0.926
## P-value H_0: RMSEA >= 0.080 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.060
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g =~
## dpv_tajek 0.160 NA 0.160 0.497
## dpv_szaml 0.848 NA 0.848 0.848
## dpv_szameml 0.306 NA 0.306 0.617
## dpv_szamegyz 0.885 NA 0.885 0.885
## dpv_rel 0.761 NA 0.761 0.761
## dpv_helyiert 0.129 NA 0.129 0.434
## dpv_potlas 0.814 NA 0.814 0.814
## dpv_muvel 0.933 NA 0.933 0.933
## dpv_szorzoszt 0.935 NA 0.935 0.935
## dpv_irasbeli 0.853 NA 0.853 0.853
## dpv_szoveg 0.894 NA 0.894 0.894
## dpv_logszab 0.920 NA 0.920 0.920
## dpv_muvsorr 0.876 NA 0.876 0.876
## dpv_praktik 0.255 NA 0.255 0.621
## F1 =~
## dpv_muvsorr 0.702 NA 0.702 0.702
## dpv_praktik 0.089 NA 0.089 0.216
## F2 =~
## dpv_rel 0.864 NA 0.864 0.864
## dpv_irasbeli -0.173 NA -0.173 -0.173
## F3 =~
## dpv_szaml 0.711 NA 0.711 0.711
## dpv_tajek 0.066 NA 0.066 0.206
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## F1 0.000 0.000 0.000
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
## F1 ~~
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
## F2 ~~
## F3 0.000 0.000 0.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_tajek 0.882 NA 0.882 2.738
## .dpv_szaml 0.000 0.000 0.000
## .dpv_szameml 0.559 NA 0.559 1.125
## .dpv_szamegyz 0.000 0.000 0.000
## .dpv_rel 0.000 0.000 0.000
## .dpv_helyiert 0.902 NA 0.902 3.034
## .dpv_potlas 0.000 0.000 0.000
## .dpv_muvel 0.000 0.000 0.000
## .dpv_szorzoszt 0.000 0.000 0.000
## .dpv_irasbeli 0.000 0.000 0.000
## .dpv_szoveg 0.000 0.000 0.000
## .dpv_logszab 0.000 0.000 0.000
## .dpv_muvsorr 0.000 0.000 0.000
## .dpv_praktik 0.784 NA 0.784 1.906
## g 0.000 0.000 0.000
## F1 0.000 0.000 0.000
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_szaml|t1 -2.334 NA -2.334 -2.334
## dpv_szaml|t2 -1.565 NA -1.565 -1.565
## dpv_szaml|t3 -1.293 NA -1.293 -1.293
## dpv_szamgyz|t1 -2.334 NA -2.334 -2.334
## dpv_szamgyz|t2 -2.062 NA -2.062 -2.062
## dpv_szamgyz|t3 -1.565 NA -1.565 -1.565
## dpv_szamgyz|t4 -1.238 NA -1.238 -1.238
## dpv_szamgyz|t5 -0.967 NA -0.967 -0.967
## dpv_rel|t1 -2.062 NA -2.062 -2.062
## dpv_rel|t2 -1.093 NA -1.093 -1.093
## dpv_potlas|t1 -2.334 NA -2.334 -2.334
## dpv_potlas|t2 -2.062 NA -2.062 -2.062
## dpv_potlas|t3 -1.890 NA -1.890 -1.890
## dpv_potlas|t4 -1.760 NA -1.760 -1.760
## dpv_potlas|t5 -1.654 NA -1.654 -1.654
## dpv_potlas|t6 -1.565 NA -1.565 -1.565
## dpv_potlas|t7 -1.416 NA -1.416 -1.416
## dpv_potlas|t8 -1.352 NA -1.352 -1.352
## dpv_potlas|t9 -1.187 NA -1.187 -1.187
## dpv_potlas|t10 -1.093 NA -1.093 -1.093
## dpv_potlas|t11 -1.049 NA -1.049 -1.049
## dpv_potlas|t12 -1.007 NA -1.007 -1.007
## dpv_potlas|t13 -0.929 NA -0.929 -0.929
## dpv_potlas|t14 -0.892 NA -0.892 -0.892
## dpv_potlas|t15 -0.821 NA -0.821 -0.821
## dpv_potlas|t16 -0.754 NA -0.754 -0.754
## dpv_potlas|t17 -0.690 NA -0.690 -0.690
## dpv_potlas|t18 -0.659 NA -0.659 -0.659
## dpv_muvel|t1 -2.334 NA -2.334 -2.334
## dpv_muvel|t2 -2.062 NA -2.062 -2.062
## dpv_muvel|t3 -1.890 NA -1.890 -1.890
## dpv_muvel|t4 -1.760 NA -1.760 -1.760
## dpv_muvel|t5 -1.654 NA -1.654 -1.654
## dpv_muvel|t6 -1.416 NA -1.416 -1.416
## dpv_muvel|t7 -1.293 NA -1.293 -1.293
## dpv_muvel|t8 -1.238 NA -1.238 -1.238
## dpv_muvel|t9 -1.139 NA -1.139 -1.139
## dpv_muvel|t10 -0.967 NA -0.967 -0.967
## dpv_muvel|t11 -0.929 NA -0.929 -0.929
## dpv_muvel|t12 -0.856 NA -0.856 -0.856
## dpv_muvel|t13 -0.690 NA -0.690 -0.690
## dpv_muvel|t14 -0.377 NA -0.377 -0.377
## dpv_muvel|t15 -0.325 NA -0.325 -0.325
## dpv_muvel|t16 -0.299 NA -0.299 -0.299
## dpv_szrzszt|t1 -1.890 NA -1.890 -1.890
## dpv_szrzszt|t2 -1.760 NA -1.760 -1.760
## dpv_szrzszt|t3 -1.486 NA -1.486 -1.486
## dpv_szrzszt|t4 -1.352 NA -1.352 -1.352
## dpv_szrzszt|t5 -1.187 NA -1.187 -1.187
## dpv_szrzszt|t6 -1.007 NA -1.007 -1.007
## dpv_szrzszt|t7 -0.754 NA -0.754 -0.754
## dpv_irasbel|t1 -2.334 NA -2.334 -2.334
## dpv_irasbel|t2 -2.062 NA -2.062 -2.062
## dpv_irasbel|t3 -1.890 NA -1.890 -1.890
## dpv_irasbel|t4 -1.486 NA -1.486 -1.486
## dpv_irasbel|t5 -1.238 NA -1.238 -1.238
## dpv_irasbel|t6 -1.187 NA -1.187 -1.187
## dpv_irasbel|t7 -1.139 NA -1.139 -1.139
## dpv_irasbel|t8 -0.967 NA -0.967 -0.967
## dpv_szoveg|t1 -2.334 NA -2.334 -2.334
## dpv_szoveg|t2 -2.062 NA -2.062 -2.062
## dpv_szoveg|t3 -1.890 NA -1.890 -1.890
## dpv_szoveg|t4 -1.760 NA -1.760 -1.760
## dpv_szoveg|t5 -1.654 NA -1.654 -1.654
## dpv_szoveg|t6 -1.565 NA -1.565 -1.565
## dpv_szoveg|t7 -1.486 NA -1.486 -1.486
## dpv_szoveg|t8 -1.352 NA -1.352 -1.352
## dpv_szoveg|t9 -1.293 NA -1.293 -1.293
## dpv_szoveg|t10 -1.238 NA -1.238 -1.238
## dpv_szoveg|t11 -1.139 NA -1.139 -1.139
## dpv_szoveg|t12 -1.093 NA -1.093 -1.093
## dpv_szoveg|t13 -1.007 NA -1.007 -1.007
## dpv_szoveg|t14 -0.929 NA -0.929 -0.929
## dpv_szoveg|t15 -0.787 NA -0.787 -0.787
## dpv_logszab|t1 -2.334 NA -2.334 -2.334
## dpv_logszab|t2 -2.062 NA -2.062 -2.062
## dpv_logszab|t3 -1.565 NA -1.565 -1.565
## dpv_logszab|t4 -1.293 NA -1.293 -1.293
## dpv_logszab|t5 -1.139 NA -1.139 -1.139
## dpv_logszab|t6 -0.821 NA -0.821 -0.821
## dpv_logszab|t7 -0.690 NA -0.690 -0.690
## dpv_muvsorr|t1 -2.334 NA -2.334 -2.334
## dpv_muvsorr|t2 -2.062 NA -2.062 -2.062
## dpv_muvsorr|t3 -1.890 NA -1.890 -1.890
## dpv_muvsorr|t4 -1.654 NA -1.654 -1.654
## dpv_muvsorr|t5 -1.486 NA -1.486 -1.486
## dpv_muvsorr|t6 -1.416 NA -1.416 -1.416
## dpv_muvsorr|t7 -1.352 NA -1.352 -1.352
## dpv_muvsorr|t8 -1.187 NA -1.187 -1.187
## dpv_muvsorr|t9 -1.093 NA -1.093 -1.093
## dpv_muvsrr|t10 -1.007 NA -1.007 -1.007
## dpv_muvsrr|t11 -0.967 NA -0.967 -0.967
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_tajek 0.074 NA 0.074 0.710
## .dpv_szaml -0.225 -0.225 -0.225
## .dpv_szameml 0.153 NA 0.153 0.619
## .dpv_szamegyz 0.216 0.216 0.216
## .dpv_rel -0.325 -0.325 -0.325
## .dpv_helyiert 0.072 NA 0.072 0.812
## .dpv_potlas 0.338 0.338 0.338
## .dpv_muvel 0.130 0.130 0.130
## .dpv_szorzoszt 0.125 0.125 0.125
## .dpv_irasbeli 0.242 0.242 0.242
## .dpv_szoveg 0.201 0.201 0.201
## .dpv_logszab 0.153 0.153 0.153
## .dpv_muvsorr -0.260 -0.260 -0.260
## .dpv_praktik 0.096 NA 0.096 0.568
## g 1.000 1.000 1.000
## F1 1.000 1.000 1.000
## F2 1.000 1.000 1.000
## F3 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_szaml 1.000 1.000 1.000
## dpv_szamegyz 1.000 1.000 1.000
## dpv_rel 1.000 1.000 1.000
## dpv_potlas 1.000 1.000 1.000
## dpv_muvel 1.000 1.000 1.000
## dpv_szorzoszt 1.000 1.000 1.000
## dpv_irasbeli 1.000 1.000 1.000
## dpv_szoveg 1.000 1.000 1.000
## dpv_logszab 1.000 1.000 1.000
## dpv_muvsorr 1.000 1.000 1.000summary(FitGF4, stand = T, fit = T)## lavaan 0.6.14 ended normally after 80 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 106
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 35.729
## Degrees of freedom 54
## P-value (Chi-square) 0.974
##
## Model Test Baseline Model:
##
## Test statistic 7819.135
## Degrees of freedom 78
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.003
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 0.999
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.053
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## dpv_praktik 0.268 0.012 22.486 0.000 0.268 0.651
## dpv_muvsorr 0.903 0.024 36.956 0.000 0.903 0.903
## dpv_logszab 0.645 0.155 4.153 0.000 0.645 0.645
## dpv_szoveg 0.088 0.485 0.181 0.856 0.088 0.088
## dpv_szameml 0.312 0.016 19.562 0.000 0.312 0.629
## dpv_muvel 1.839 0.945 1.945 0.052 1.839 1.839
## dpv_szorzoszt 1.722 6.452 0.267 0.790 1.722 1.722
## F2 =~
## dpv_szoveg 0.820 0.483 1.700 0.089 0.820 0.820
## dpv_rel 0.752 0.034 22.365 0.000 0.752 0.752
## dpv_szamegyz 0.903 0.031 28.796 0.000 0.903 0.903
## dpv_muvel -0.910 0.948 -0.959 0.337 -0.910 -0.910
## dpv_szorzoszt -0.909 1.802 -0.505 0.614 -0.909 -0.909
## F3 =~
## dpv_logszab 0.332 0.178 1.867 0.062 0.332 0.332
## dpv_tajek 0.193 0.011 17.110 0.000 0.193 0.598
## dpv_szaml 0.976 0.052 18.827 0.000 0.976 0.976
## dpv_helyiert 0.147 0.010 14.493 0.000 0.147 0.495
## F4 =~
## dpv_irasbeli 1.348 41.162 0.033 0.974 1.348 1.348
## dpv_szorzoszt 0.140 9.017 0.016 0.988 0.140 0.140
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 0.975 0.028 34.365 0.000 0.975 0.975
## F3 0.809 0.061 13.333 0.000 0.809 0.809
## F4 0.598 18.250 0.033 0.974 0.598 0.598
## F2 ~~
## F3 0.907 0.064 14.253 0.000 0.907 0.907
## F4 0.585 17.870 0.033 0.974 0.585 0.585
## F3 ~~
## F4 0.501 15.287 0.033 0.974 0.501 0.501
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_praktik 0.784 0.011 73.298 0.000 0.784 1.907
## .dpv_muvsorr 0.000 0.000 0.000
## .dpv_logszab 0.000 0.000 0.000
## .dpv_szoveg 0.000 0.000 0.000
## .dpv_szameml 0.559 0.047 11.955 0.000 0.559 1.125
## .dpv_muvel 0.000 0.000 0.000
## .dpv_szorzoszt 0.000 0.000 0.000
## .dpv_rel 0.000 0.000 0.000
## .dpv_szamegyz 0.000 0.000 0.000
## .dpv_tajek 0.882 0.002 400.922 0.000 0.882 2.739
## .dpv_szaml 0.000 0.000 0.000
## .dpv_helyiert 0.902 0.001 660.347 0.000 0.902 3.033
## .dpv_irasbeli 0.000 0.000 0.000
## F1 0.000 0.000 0.000
## F2 0.000 0.000 0.000
## F3 0.000 0.000 0.000
## F4 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_muvsorr|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_muvsorr|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_muvsorr|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_muvsorr|t4 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_muvsorr|t5 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_muvsorr|t6 -1.416 0.183 -7.750 0.000 -1.416 -1.416
## dpv_muvsorr|t7 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_muvsorr|t8 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_muvsorr|t9 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_muvsrr|t10 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_muvsrr|t11 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_logszab|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_logszab|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_logszab|t3 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_logszab|t4 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_logszab|t5 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_logszab|t6 -0.821 0.141 -5.811 0.000 -0.821 -0.821
## dpv_logszab|t7 -0.690 0.136 -5.069 0.000 -0.690 -0.690
## dpv_szoveg|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szoveg|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_szoveg|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_szoveg|t4 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_szoveg|t5 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_szoveg|t6 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szoveg|t7 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_szoveg|t8 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_szoveg|t9 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_szoveg|t10 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_szoveg|t11 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_szoveg|t12 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_szoveg|t13 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_szoveg|t14 -0.929 0.146 -6.346 0.000 -0.929 -0.929
## dpv_szoveg|t15 -0.787 0.140 -5.628 0.000 -0.787 -0.787
## dpv_muvel|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_muvel|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_muvel|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_muvel|t4 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_muvel|t5 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_muvel|t6 -1.416 0.183 -7.750 0.000 -1.416 -1.416
## dpv_muvel|t7 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_muvel|t8 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_muvel|t9 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_muvel|t10 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_muvel|t11 -0.929 0.146 -6.346 0.000 -0.929 -0.929
## dpv_muvel|t12 -0.856 0.143 -5.992 0.000 -0.856 -0.856
## dpv_muvel|t13 -0.690 0.136 -5.069 0.000 -0.690 -0.690
## dpv_muvel|t14 -0.377 0.128 -2.949 0.003 -0.377 -0.377
## dpv_muvel|t15 -0.325 0.127 -2.557 0.011 -0.325 -0.325
## dpv_muvel|t16 -0.299 0.127 -2.361 0.018 -0.299 -0.299
## dpv_szrzszt|t1 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_szrzszt|t2 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_szrzszt|t3 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_szrzszt|t4 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_szrzszt|t5 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_szrzszt|t6 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_szrzszt|t7 -0.754 0.138 -5.443 0.000 -0.754 -0.754
## dpv_rel|t1 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_rel|t2 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_szamgyz|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szamgyz|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_szamgyz|t3 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szamgyz|t4 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_szamgyz|t5 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_szaml|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szaml|t2 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szaml|t3 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_irasbel|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_irasbel|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_irasbel|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_irasbel|t4 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_irasbel|t5 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_irasbel|t6 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_irasbel|t7 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_irasbel|t8 -0.967 0.148 -6.518 0.000 -0.967 -0.967
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_szamegyz 0.184 0.184 0.184
## .dpv_szorzoszt 0.103 0.103 0.103
## .dpv_praktik 0.097 0.019 5.105 0.000 0.097 0.576
## .dpv_muvsorr 0.185 0.185 0.185
## .dpv_logszab 0.128 0.128 0.128
## .dpv_szoveg 0.179 0.179 0.179
## .dpv_szameml 0.149 0.015 9.950 0.000 0.149 0.604
## .dpv_muvel 0.055 0.055 0.055
## .dpv_rel 0.434 0.434 0.434
## .dpv_tajek 0.067 0.009 7.248 0.000 0.067 0.642
## .dpv_szaml 0.048 0.048 0.048
## .dpv_helyiert 0.067 0.007 9.683 0.000 0.067 0.755
## .dpv_irasbeli -0.818 -0.818 -0.818
## F1 1.000 1.000 1.000
## F2 1.000 1.000 1.000
## F3 1.000 1.000 1.000
## F4 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_muvsorr 1.000 1.000 1.000
## dpv_logszab 1.000 1.000 1.000
## dpv_szoveg 1.000 1.000 1.000
## dpv_muvel 1.000 1.000 1.000
## dpv_szorzoszt 1.000 1.000 1.000
## dpv_rel 1.000 1.000 1.000
## dpv_szamegyz 1.000 1.000 1.000
## dpv_szaml 1.000 1.000 1.000
## dpv_irasbeli 1.000 1.000 1.000Both fail to converge and simpler models aren’t much better. A single-factor model will be used.
CFAs
WISC first, using the theoretical model that was desired in its construction.
ModWISC <- '
wm =~ betuszam_ertek + szamterj_ertek
vc =~ szokincs_ertek + kozjel_ertek + altmegert_ertek
ps =~ kodolas_ertek + szimbol_ertek
pr =~ kepifog_ertek + mozaik_ertek + matrix_ertek
g =~ wm + vc + ps + pr'
FitWISC <- cfa(ModWISC, std.lv = T, meanstructure = T, data)
summary(FitWISC, stand = T, fit = T)## lavaan 0.6.14 ended normally after 41 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 34
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 36.401
## Degrees of freedom 31
## P-value (Chi-square) 0.232
##
## Model Test Baseline Model:
##
## Test statistic 629.440
## Degrees of freedom 45
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.991
## Tucker-Lewis Index (TLI) 0.987
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2042.468
## Loglikelihood unrestricted model (H1) -2024.267
##
## Akaike (AIC) 4152.935
## Bayesian (BIC) 4242.184
## Sample-size adjusted Bayesian (SABIC) 4134.791
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.041
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.088
## P-value H_0: RMSEA <= 0.050 0.573
## P-value H_0: RMSEA >= 0.080 0.097
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.048
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wm =~
## betuszam_ertek 0.898 0.200 4.491 0.000 2.029 0.873
## szamterj_ertek 1.048 0.234 4.479 0.000 2.367 0.880
## vc =~
## szokincs_ertek 1.204 0.164 7.339 0.000 1.834 0.802
## kozjel_ertek 1.158 0.157 7.366 0.000 1.765 0.806
## altmegert_ertk 1.328 0.174 7.644 0.000 2.023 0.850
## ps =~
## kodolas_ertek 1.690 0.405 4.174 0.000 2.681 0.959
## szimbol_ertek 0.600 0.125 4.807 0.000 0.952 0.514
## pr =~
## kepifog_ertek 1.140 0.164 6.937 0.000 1.945 0.806
## mozaik_ertek 1.344 0.182 7.384 0.000 2.294 0.912
## matrix_ertek 1.271 0.182 6.971 0.000 2.168 0.812
## g =~
## wm 2.026 0.545 3.717 0.000 0.897 0.897
## vc 1.149 0.222 5.171 0.000 0.754 0.754
## ps 1.231 0.340 3.620 0.000 0.776 0.776
## pr 1.382 0.268 5.159 0.000 0.810 0.810
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .betuszam_ertek 10.951 0.230 47.596 0.000 10.951 4.713
## .szamterj_ertek 9.176 0.266 34.435 0.000 9.176 3.410
## .szokincs_ertek 12.461 0.226 55.035 0.000 12.461 5.449
## .kozjel_ertek 12.706 0.217 58.597 0.000 12.706 5.802
## .altmegert_ertk 11.235 0.236 47.653 0.000 11.235 4.718
## .kodolas_ertek 10.451 0.277 37.754 0.000 10.451 3.738
## .szimbol_ertek 11.275 0.183 61.443 0.000 11.275 6.084
## .kepifog_ertek 12.078 0.239 50.576 0.000 12.078 5.008
## .mozaik_ertek 10.588 0.249 42.535 0.000 10.588 4.212
## .matrix_ertek 10.196 0.265 38.543 0.000 10.196 3.816
## .wm 0.000 0.000 0.000
## .vc 0.000 0.000 0.000
## .ps 0.000 0.000 0.000
## .pr 0.000 0.000 0.000
## g 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .betuszam_ertek 1.284 0.326 3.941 0.000 1.284 0.238
## .szamterj_ertek 1.639 0.435 3.765 0.000 1.639 0.226
## .szokincs_ertek 1.864 0.357 5.220 0.000 1.864 0.357
## .kozjel_ertek 1.682 0.325 5.167 0.000 1.682 0.351
## .altmegert_ertk 1.577 0.360 4.382 0.000 1.577 0.278
## .kodolas_ertek 0.627 1.267 0.495 0.620 0.627 0.080
## .szimbol_ertek 2.528 0.388 6.512 0.000 2.528 0.736
## .kepifog_ertek 2.035 0.360 5.645 0.000 2.035 0.350
## .mozaik_ertek 1.059 0.317 3.344 0.001 1.059 0.168
## .matrix_ertek 2.437 0.437 5.581 0.000 2.437 0.341
## .wm 1.000 0.196 0.196
## .vc 1.000 0.431 0.431
## .ps 1.000 0.397 0.397
## .pr 1.000 0.344 0.344
## g 1.000 1.000 1.000DPV next, single-factor, as suggested might work by the parallel analysis, however poor that appeared.
ModDPV <- '
dpv =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik'
FitDPV <- sem(ModDPV, std.lv = T, meanstructure = T, data, estimator = "DWLS", ordered = c("dpv_szaml", "dpv_szamegyz", "dpv_rel", "dpv_potlas", "dpv_muvel", "dpv_szorzoszt", "dpv_irasbeli", "dpv_szoveg", "dpv_logszab", "dpv_muvsorr"))
summary(FitDPV, stand = T, fit = T)## lavaan 0.6.14 ended normally after 45 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 114
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 79.354
## Degrees of freedom 77
## P-value (Chi-square) 0.405
##
## Model Test Baseline Model:
##
## Test statistic 9338.384
## Degrees of freedom 91
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.017
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.060
## P-value H_0: RMSEA <= 0.050 0.873
## P-value H_0: RMSEA >= 0.080 0.002
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv =~
## dpv_tajek 0.165 0.008 20.929 0.000 0.165 0.512
## dpv_szaml 0.860 0.029 29.559 0.000 0.860 0.860
## dpv_szameml 0.306 0.014 21.206 0.000 0.306 0.616
## dpv_szamegyz 0.883 0.024 36.173 0.000 0.883 0.883
## dpv_rel 0.750 0.029 25.521 0.000 0.750 0.750
## dpv_helyiert 0.129 0.007 17.285 0.000 0.129 0.433
## dpv_potlas 0.813 0.021 37.836 0.000 0.813 0.813
## dpv_muvel 0.932 0.018 50.612 0.000 0.932 0.932
## dpv_szorzoszt 0.934 0.020 45.752 0.000 0.934 0.934
## dpv_irasbeli 0.843 0.028 30.428 0.000 0.843 0.843
## dpv_szoveg 0.893 0.020 44.386 0.000 0.893 0.893
## dpv_logszab 0.917 0.022 41.781 0.000 0.917 0.917
## dpv_muvsorr 0.888 0.022 39.582 0.000 0.888 0.888
## dpv_praktik 0.266 0.011 24.006 0.000 0.266 0.647
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_tajek 0.882 0.002 400.922 0.000 0.882 2.739
## .dpv_szaml 0.000 0.000 0.000
## .dpv_szameml 0.559 0.047 11.955 0.000 0.559 1.125
## .dpv_szamegyz 0.000 0.000 0.000
## .dpv_rel 0.000 0.000 0.000
## .dpv_helyiert 0.902 0.001 660.347 0.000 0.902 3.033
## .dpv_potlas 0.000 0.000 0.000
## .dpv_muvel 0.000 0.000 0.000
## .dpv_szorzoszt 0.000 0.000 0.000
## .dpv_irasbeli 0.000 0.000 0.000
## .dpv_szoveg 0.000 0.000 0.000
## .dpv_logszab 0.000 0.000 0.000
## .dpv_muvsorr 0.000 0.000 0.000
## .dpv_praktik 0.784 0.011 73.298 0.000 0.784 1.907
## dpv 0.000 0.000 0.000
##
## Thresholds:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_szaml|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szaml|t2 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szaml|t3 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_szamgyz|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szamgyz|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_szamgyz|t3 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szamgyz|t4 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_szamgyz|t5 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_rel|t1 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_rel|t2 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_potlas|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_potlas|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_potlas|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_potlas|t4 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_potlas|t5 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_potlas|t6 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_potlas|t7 -1.416 0.183 -7.750 0.000 -1.416 -1.416
## dpv_potlas|t8 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_potlas|t9 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_potlas|t10 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_potlas|t11 -1.049 0.153 -6.850 0.000 -1.049 -1.049
## dpv_potlas|t12 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_potlas|t13 -0.929 0.146 -6.346 0.000 -0.929 -0.929
## dpv_potlas|t14 -0.892 0.145 -6.170 0.000 -0.892 -0.892
## dpv_potlas|t15 -0.821 0.141 -5.811 0.000 -0.821 -0.821
## dpv_potlas|t16 -0.754 0.138 -5.443 0.000 -0.754 -0.754
## dpv_potlas|t17 -0.690 0.136 -5.069 0.000 -0.690 -0.690
## dpv_potlas|t18 -0.659 0.135 -4.880 0.000 -0.659 -0.659
## dpv_muvel|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_muvel|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_muvel|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_muvel|t4 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_muvel|t5 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_muvel|t6 -1.416 0.183 -7.750 0.000 -1.416 -1.416
## dpv_muvel|t7 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_muvel|t8 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_muvel|t9 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_muvel|t10 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_muvel|t11 -0.929 0.146 -6.346 0.000 -0.929 -0.929
## dpv_muvel|t12 -0.856 0.143 -5.992 0.000 -0.856 -0.856
## dpv_muvel|t13 -0.690 0.136 -5.069 0.000 -0.690 -0.690
## dpv_muvel|t14 -0.377 0.128 -2.949 0.003 -0.377 -0.377
## dpv_muvel|t15 -0.325 0.127 -2.557 0.011 -0.325 -0.325
## dpv_muvel|t16 -0.299 0.127 -2.361 0.018 -0.299 -0.299
## dpv_szrzszt|t1 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_szrzszt|t2 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_szrzszt|t3 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_szrzszt|t4 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_szrzszt|t5 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_szrzszt|t6 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_szrzszt|t7 -0.754 0.138 -5.443 0.000 -0.754 -0.754
## dpv_irasbel|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_irasbel|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_irasbel|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_irasbel|t4 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_irasbel|t5 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_irasbel|t6 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_irasbel|t7 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_irasbel|t8 -0.967 0.148 -6.518 0.000 -0.967 -0.967
## dpv_szoveg|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_szoveg|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_szoveg|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_szoveg|t4 -1.760 0.228 -7.726 0.000 -1.760 -1.760
## dpv_szoveg|t5 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_szoveg|t6 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_szoveg|t7 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_szoveg|t8 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_szoveg|t9 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_szoveg|t10 -1.238 0.166 -7.436 0.000 -1.238 -1.238
## dpv_szoveg|t11 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_szoveg|t12 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_szoveg|t13 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_szoveg|t14 -0.929 0.146 -6.346 0.000 -0.929 -0.929
## dpv_szoveg|t15 -0.787 0.140 -5.628 0.000 -0.787 -0.787
## dpv_logszab|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_logszab|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_logszab|t3 -1.565 0.200 -7.839 0.000 -1.565 -1.565
## dpv_logszab|t4 -1.293 0.171 -7.558 0.000 -1.293 -1.293
## dpv_logszab|t5 -1.139 0.159 -7.159 0.000 -1.139 -1.139
## dpv_logszab|t6 -0.821 0.141 -5.811 0.000 -0.821 -0.821
## dpv_logszab|t7 -0.690 0.136 -5.069 0.000 -0.690 -0.690
## dpv_muvsorr|t1 -2.334 0.374 -6.236 0.000 -2.334 -2.334
## dpv_muvsorr|t2 -2.062 0.290 -7.116 0.000 -2.062 -2.062
## dpv_muvsorr|t3 -1.890 0.251 -7.523 0.000 -1.890 -1.890
## dpv_muvsorr|t4 -1.654 0.212 -7.818 0.000 -1.654 -1.654
## dpv_muvsorr|t5 -1.486 0.190 -7.812 0.000 -1.486 -1.486
## dpv_muvsorr|t6 -1.416 0.183 -7.750 0.000 -1.416 -1.416
## dpv_muvsorr|t7 -1.352 0.176 -7.664 0.000 -1.352 -1.352
## dpv_muvsorr|t8 -1.187 0.163 -7.303 0.000 -1.187 -1.187
## dpv_muvsorr|t9 -1.093 0.156 -7.008 0.000 -1.093 -1.093
## dpv_muvsrr|t10 -1.007 0.151 -6.686 0.000 -1.007 -1.007
## dpv_muvsrr|t11 -0.967 0.148 -6.518 0.000 -0.967 -0.967
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .dpv_tajek 0.077 0.009 8.992 0.000 0.077 0.738
## .dpv_szaml 0.261 0.261 0.261
## .dpv_szameml 0.153 0.014 10.759 0.000 0.153 0.621
## .dpv_szamegyz 0.220 0.220 0.220
## .dpv_rel 0.437 0.437 0.437
## .dpv_helyiert 0.072 0.006 11.058 0.000 0.072 0.813
## .dpv_potlas 0.340 0.340 0.340
## .dpv_muvel 0.132 0.132 0.132
## .dpv_szorzoszt 0.128 0.128 0.128
## .dpv_irasbeli 0.289 0.289 0.289
## .dpv_szoveg 0.202 0.202 0.202
## .dpv_logszab 0.158 0.158 0.158
## .dpv_muvsorr 0.212 0.212 0.212
## .dpv_praktik 0.098 0.019 5.196 0.000 0.098 0.581
## dpv 1.000 1.000 1.000
##
## Scales y*:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## dpv_szaml 1.000 1.000 1.000
## dpv_szamegyz 1.000 1.000 1.000
## dpv_rel 1.000 1.000 1.000
## dpv_potlas 1.000 1.000 1.000
## dpv_muvel 1.000 1.000 1.000
## dpv_szorzoszt 1.000 1.000 1.000
## dpv_irasbeli 1.000 1.000 1.000
## dpv_szoveg 1.000 1.000 1.000
## dpv_logszab 1.000 1.000 1.000
## dpv_muvsorr 1.000 1.000 1.000And then both at once.
ModBoth <- '
wm =~ betuszam_ertek + szamterj_ertek
vc =~ szokincs_ertek + kozjel_ertek + altmegert_ertek
ps =~ kodolas_ertek + szimbol_ertek
pr =~ kepifog_ertek + mozaik_ertek + matrix_ertek
g =~ wm + vc + ps + pr
dpv =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik'
FitBoth <- cfa(ModBoth, std.lv = T, meanstructure = T, data, estimator = "DWLS")
summary(FitBoth, stand = T, fit = T)## lavaan 0.6.14 ended normally after 118 iterations
##
## Estimator DWLS
## Optimization method NLMINB
## Number of model parameters 77
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 96.465
## Degrees of freedom 247
## P-value (Chi-square) 1.000
##
## Model Test Baseline Model:
##
## Test statistic 2834.805
## Degrees of freedom 276
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.066
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 1.000
## P-value H_0: RMSEA >= 0.080 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.074
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Unstructured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## wm =~
## betuszam_ertek 0.747 0.515 1.450 0.147 2.038 0.873
## szamterj_ertek 0.872 0.601 1.450 0.147 2.380 0.880
## vc =~
## szokincs_ertek 1.182 0.138 8.589 0.000 1.635 0.712
## kozjel_ertek 1.426 0.158 9.000 0.000 1.972 0.896
## altmegert_ertk 1.436 0.160 8.961 0.000 1.986 0.830
## ps =~
## kodolas_ertek 1.698 0.614 2.766 0.006 2.762 0.983
## szimbol_ertek 0.574 0.198 2.895 0.004 0.934 0.501
## pr =~
## kepifog_ertek 0.967 0.216 4.472 0.000 1.978 0.816
## mozaik_ertek 1.078 0.242 4.450 0.000 2.203 0.872
## matrix_ertek 1.104 0.249 4.443 0.000 2.258 0.841
## g =~
## wm 2.539 1.795 1.415 0.157 0.930 0.930
## vc 0.955 0.118 8.115 0.000 0.691 0.691
## ps 1.283 0.473 2.709 0.007 0.789 0.789
## pr 1.783 0.435 4.096 0.000 0.872 0.872
## dpv =~
## dpv_tajek 0.226 0.017 12.995 0.000 0.226 0.698
## dpv_szaml 0.422 0.036 11.665 0.000 0.422 0.771
## dpv_szameml 0.256 0.016 15.779 0.000 0.256 0.513
## dpv_szamegyz 0.754 0.060 12.569 0.000 0.754 0.801
## dpv_rel 0.251 0.024 10.438 0.000 0.251 0.602
## dpv_helyiert 0.173 0.016 10.788 0.000 0.173 0.578
## dpv_potlas 6.829 0.547 12.493 0.000 6.829 0.732
## dpv_muvel 4.615 0.365 12.649 0.000 4.615 0.838
## dpv_szorzoszt 1.439 0.114 12.676 0.000 1.439 0.755
## dpv_irasbeli 2.173 0.208 10.438 0.000 2.173 0.557
## dpv_szoveg 4.120 0.326 12.640 0.000 4.120 0.806
## dpv_logszab 1.474 0.100 14.755 0.000 1.474 0.883
## dpv_muvsorr 1.843 0.154 11.935 0.000 1.843 0.671
## dpv_praktik 0.283 0.018 15.434 0.000 0.283 0.685
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## dpv 0.777 0.032 24.352 0.000 0.777 0.777
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .betuszam_ertek 10.951 0.231 47.362 0.000 10.951 4.690
## .szamterj_ertek 9.176 0.268 34.266 0.000 9.176 3.393
## .szokincs_ertek 12.461 0.228 54.765 0.000 12.461 5.423
## .kozjel_ertek 12.706 0.218 58.309 0.000 12.706 5.773
## .altmegert_ertk 11.235 0.237 47.419 0.000 11.235 4.695
## .kodolas_ertek 10.451 0.278 37.568 0.000 10.451 3.720
## .szimbol_ertek 11.275 0.184 61.141 0.000 11.275 6.054
## .kepifog_ertek 12.078 0.240 50.328 0.000 12.078 4.983
## .mozaik_ertek 10.588 0.250 42.326 0.000 10.588 4.191
## .matrix_ertek 10.196 0.266 38.353 0.000 10.196 3.798
## .dpv_tajek 0.882 0.032 27.523 0.000 0.882 2.725
## .dpv_szaml 4.833 0.054 89.319 0.000 4.833 8.844
## .dpv_szameml 0.559 0.049 11.311 0.000 0.559 1.120
## .dpv_szamegyz 5.637 0.093 60.454 0.000 5.637 5.986
## .dpv_rel 3.843 0.041 93.272 0.000 3.843 9.235
## .dpv_helyiert 0.902 0.030 30.483 0.000 0.902 3.018
## .dpv_potlas 95.402 0.923 103.326 0.000 95.402 10.231
## .dpv_muvel 40.206 0.545 73.764 0.000 40.206 7.304
## .dpv_szorzoszt 8.206 0.189 43.496 0.000 8.206 4.307
## .dpv_irasbeli 36.755 0.386 95.099 0.000 36.755 9.416
## .dpv_szoveg 24.951 0.506 49.300 0.000 24.951 4.881
## .dpv_logszab 8.216 0.165 49.723 0.000 8.216 4.923
## .dpv_muvsorr 21.000 0.272 77.215 0.000 21.000 7.645
## .dpv_praktik 0.784 0.041 19.164 0.000 0.784 1.898
## .wm 0.000 0.000 0.000
## .vc 0.000 0.000 0.000
## .ps 0.000 0.000 0.000
## .pr 0.000 0.000 0.000
## g 0.000 0.000 0.000
## dpv 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .betuszam_ertek 1.301 1.064 1.223 0.221 1.301 0.239
## .szamterj_ertek 1.650 1.498 1.101 0.271 1.650 0.225
## .szokincs_ertek 2.607 0.821 3.175 0.001 2.607 0.494
## .kozjel_ertek 0.956 0.780 1.226 0.220 0.956 0.197
## .altmegert_ertk 1.782 0.943 1.889 0.059 1.782 0.311
## .kodolas_ertek 0.268 2.394 0.112 0.911 0.268 0.034
## .szimbol_ertek 2.597 0.494 5.255 0.000 2.597 0.749
## .kepifog_ertek 1.964 0.885 2.219 0.026 1.964 0.334
## .mozaik_ertek 1.530 0.944 1.621 0.105 1.530 0.240
## .matrix_ertek 2.112 1.080 1.955 0.051 2.112 0.293
## .dpv_tajek 0.054 0.026 2.085 0.037 0.054 0.512
## .dpv_szaml 0.121 0.110 1.104 0.270 0.121 0.405
## .dpv_szameml 0.183 0.010 18.105 0.000 0.183 0.737
## .dpv_szamegyz 0.318 0.291 1.092 0.275 0.318 0.359
## .dpv_rel 0.110 0.052 2.129 0.033 0.110 0.637
## .dpv_helyiert 0.059 0.024 2.434 0.015 0.059 0.666
## .dpv_potlas 40.318 23.091 1.746 0.081 40.318 0.464
## .dpv_muvel 9.001 12.317 0.731 0.465 9.001 0.297
## .dpv_szorzoszt 1.560 1.074 1.453 0.146 1.560 0.430
## .dpv_irasbeli 10.517 8.434 1.247 0.212 10.517 0.690
## .dpv_szoveg 9.154 8.820 1.038 0.299 9.154 0.350
## .dpv_logszab 0.613 0.837 0.733 0.464 0.613 0.220
## .dpv_muvsorr 4.149 2.740 1.514 0.130 4.149 0.550
## .dpv_praktik 0.091 0.025 3.561 0.000 0.091 0.531
## .wm 1.000 0.134 0.134
## .vc 1.000 0.523 0.523
## .ps 1.000 0.378 0.378
## .pr 1.000 0.239 0.239
## g 1.000 1.000 1.000
## dpv 1.000 1.000 1.000Plots
lavaanPlot(model = FitBoth, node_options = list(shape = "box", fontname = "Helvetica"), edge_options = list(color = "grey"), coefs = TRUE, covs = TRUE, stars = TRUE, stand = T, digits = 1)DPVLats <- list(
DPV = c("dpv_tajek", "dpv_szaml", "dpv_szameml", "dpv_szamegyz", "dpv_rel", "dpv_helyiert", "dpv_potlas", "dpv_muvel", "dpv_szorzoszt", "dpv_irasbeli", "dpv_szoveg", "dpv_logszab", "dpv_muvsorr", "dpv_praktik"),
wm = c("betuszam_ertek", "szamterj_ertek"),
vc = c("szokincs_ertek", "kozjel_ertek", "altmegert_ertek"),
ps = c("kodolas_ertek", "szimbol_ertek"),
pr = c("kepifog_ertek", "mozaik_ertek", "matrix_ertek"))
semPaths(FitBoth, "model", "std", title = F, residuals = F,
groups = "DPVLats", pastel = T, mar = c(2, 1, 3, 1),
bifactor = c("dpv", "g"),
layout = "tree",
exoCov = T, intercepts = F)
Standard Regressions
Standard: Unstandardized
summary(lm(osztalyzat ~ WISC_TtlQ, data))##
## Call:
## lm(formula = osztalyzat ~ WISC_TtlQ, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.33473 -0.38533 -0.08454 0.46569 1.46587
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.619763 0.522974 -3.097 0.00254 **
## WISC_TtlQ 0.050038 0.004805 10.414 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6544 on 100 degrees of freedom
## Multiple R-squared: 0.5203, Adjusted R-squared: 0.5155
## F-statistic: 108.4 on 1 and 100 DF, p-value: < 2.2e-16summary(lm(osztalyzat ~ dpv_ossz, data))##
## Call:
## lm(formula = osztalyzat ~ dpv_ossz, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.03552 -0.78556 -0.01857 0.96448 1.52371
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.489153 0.750575 -0.652 0.516
## dpv_ossz 0.016946 0.002959 5.727 1.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8198 on 100 degrees of freedom
## Multiple R-squared: 0.247, Adjusted R-squared: 0.2395
## F-statistic: 32.8 on 1 and 100 DF, p-value: 1.077e-07summary(lm(osztalyzat ~ as.numeric(SES), data))##
## Call:
## lm(formula = osztalyzat ~ as.numeric(SES), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9875 -0.4885 -0.1657 0.5123 1.7676
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.78431 0.07773 48.686 < 2e-16 ***
## as.numeric(SES) 0.17712 0.02645 6.696 1.27e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.785 on 100 degrees of freedom
## Multiple R-squared: 0.3095, Adjusted R-squared: 0.3026
## F-statistic: 44.83 on 1 and 100 DF, p-value: 1.268e-09summary(lm(osztalyzat ~ MSZMT_total, data))##
## Call:
## lm(formula = osztalyzat ~ MSZMT_total, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.01716 -0.45088 -0.00269 0.64821 1.87684
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.801508 0.178504 26.899 < 2e-16 ***
## MSZMT_total -0.008434 0.001327 -6.354 6.28e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7974 on 100 degrees of freedom
## Multiple R-squared: 0.2876, Adjusted R-squared: 0.2805
## F-statistic: 40.37 on 1 and 100 DF, p-value: 6.276e-09summary(lm(osztalyzat ~ WISC_TtlQ + dpv_ossz, data))##
## Call:
## lm(formula = osztalyzat ~ WISC_TtlQ + dpv_ossz, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3370 -0.3983 -0.1022 0.4404 1.4338
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.923267 0.628894 -3.058 0.00286 **
## WISC_TtlQ 0.046695 0.006154 7.588 1.81e-11 ***
## dpv_ossz 0.002635 0.003025 0.871 0.38571
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6552 on 99 degrees of freedom
## Multiple R-squared: 0.5239, Adjusted R-squared: 0.5143
## F-statistic: 54.47 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(osztalyzat ~ WISC_TtlQ + as.numeric(SES), data)) ##
## Call:
## lm(formula = osztalyzat ~ WISC_TtlQ + as.numeric(SES), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3395 -0.3953 -0.1051 0.4689 1.4510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.741182 0.840011 -2.073 0.0408 *
## WISC_TtlQ 0.051162 0.007754 6.598 2.07e-09 ***
## as.numeric(SES) -0.006593 0.035586 -0.185 0.8534
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6576 on 99 degrees of freedom
## Multiple R-squared: 0.5204, Adjusted R-squared: 0.5107
## F-statistic: 53.71 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(osztalyzat ~ WISC_TtlQ + MSZMT_total, data))##
## Call:
## lm(formula = osztalyzat ~ WISC_TtlQ + MSZMT_total, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.3944 -0.4128 -0.1110 0.4351 1.2885
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.308215 0.667830 -0.462 0.64544
## WISC_TtlQ 0.041948 0.005359 7.828 5.6e-12 ***
## MSZMT_total -0.003631 0.001215 -2.989 0.00353 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6299 on 99 degrees of freedom
## Multiple R-squared: 0.56, Adjusted R-squared: 0.5511
## F-statistic: 62.99 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(osztalyzat ~ WISC_TtlQ + dpv_ossz + as.numeric(SES) + MSZMT_total, data))##
## Call:
## lm(formula = osztalyzat ~ WISC_TtlQ + dpv_ossz + as.numeric(SES) +
## MSZMT_total, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.36543 -0.40715 -0.08392 0.48102 1.29570
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.181756 1.056015 -0.172 0.86371
## WISC_TtlQ 0.047002 0.008587 5.473 3.46e-07 ***
## dpv_ossz -0.002403 0.003394 -0.708 0.48057
## as.numeric(SES) -0.018938 0.034805 -0.544 0.58762
## MSZMT_total -0.004180 0.001418 -2.948 0.00401 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.634 on 97 degrees of freedom
## Multiple R-squared: 0.5631, Adjusted R-squared: 0.5451
## F-statistic: 31.26 on 4 and 97 DF, p-value: < 2.2e-16Standard: Standardized
summary(lm(scale(osztalyzat) ~ scale(WISC_TtlQ), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(WISC_TtlQ), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.41983 -0.40990 -0.08993 0.49538 1.55934
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.467e-16 6.892e-02 0.00 1
## scale(WISC_TtlQ) 7.213e-01 6.926e-02 10.41 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6961 on 100 degrees of freedom
## Multiple R-squared: 0.5203, Adjusted R-squared: 0.5155
## F-statistic: 108.4 on 1 and 100 DF, p-value: < 2.2e-16summary(lm(scale(osztalyzat) ~ scale(dpv_ossz), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(dpv_ossz), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.16531 -0.83565 -0.01976 1.02598 1.62087
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.189e-16 8.635e-02 0.000 1
## scale(dpv_ossz) 4.970e-01 8.678e-02 5.727 1.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8721 on 100 degrees of freedom
## Multiple R-squared: 0.247, Adjusted R-squared: 0.2395
## F-statistic: 32.8 on 1 and 100 DF, p-value: 1.077e-07summary(lm(scale(osztalyzat) ~ scale(as.numeric(SES)), data)) ##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(as.numeric(SES)), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.1143 -0.5196 -0.1762 0.5450 1.8803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.504e-16 8.269e-02 0.000 1
## scale(as.numeric(SES)) 5.564e-01 8.309e-02 6.696 1.27e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8351 on 100 degrees of freedom
## Multiple R-squared: 0.3095, Adjusted R-squared: 0.3026
## F-statistic: 44.83 on 1 and 100 DF, p-value: 1.268e-09summary(lm(scale(osztalyzat) ~ scale(MSZMT_total), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(MSZMT_total), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.14577 -0.47963 -0.00286 0.68955 1.99651
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.258e-16 8.399e-02 0.000 1
## scale(MSZMT_total) -5.363e-01 8.440e-02 -6.354 6.28e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8482 on 100 degrees of freedom
## Multiple R-squared: 0.2876, Adjusted R-squared: 0.2805
## F-statistic: 40.37 on 1 and 100 DF, p-value: 6.276e-09summary(lm(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz),
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4223 -0.4237 -0.1087 0.4685 1.5252
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.856e-16 6.901e-02 0.000 1.000
## scale(WISC_TtlQ) 6.731e-01 8.870e-02 7.588 1.81e-11 ***
## scale(dpv_ossz) 7.728e-02 8.870e-02 0.871 0.386
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6969 on 99 degrees of freedom
## Multiple R-squared: 0.5239, Adjusted R-squared: 0.5143
## F-statistic: 54.47 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(as.numeric(SES)), data)) ##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(as.numeric(SES)),
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4249 -0.4205 -0.1118 0.4988 1.5435
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.484e-16 6.926e-02 0.000 1.000
## scale(WISC_TtlQ) 7.375e-01 1.118e-01 6.598 2.07e-09 ***
## scale(as.numeric(SES)) -2.071e-02 1.118e-01 -0.185 0.853
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6995 on 99 degrees of freedom
## Multiple R-squared: 0.5204, Adjusted R-squared: 0.5107
## F-statistic: 53.71 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(MSZMT_total), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(MSZMT_total),
## data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4833 -0.4392 -0.1181 0.4628 1.3706
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.287e-16 6.634e-02 0.000 1.00000
## scale(WISC_TtlQ) 6.047e-01 7.725e-02 7.828 5.6e-12 ***
## scale(MSZMT_total) -2.309e-01 7.725e-02 -2.989 0.00353 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.67 on 99 degrees of freedom
## Multiple R-squared: 0.56, Adjusted R-squared: 0.5511
## F-statistic: 62.99 on 2 and 99 DF, p-value: < 2.2e-16summary(lm(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz) + scale(as.numeric(SES)) + scale(MSZMT_total), data))##
## Call:
## lm(formula = scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz) +
## scale(as.numeric(SES)) + scale(MSZMT_total), data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.45249 -0.43311 -0.08927 0.51170 1.37832
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.867e-16 6.678e-02 0.000 1.00000
## scale(WISC_TtlQ) 6.775e-01 1.238e-01 5.473 3.46e-07 ***
## scale(dpv_ossz) -7.048e-02 9.952e-02 -0.708 0.48057
## scale(as.numeric(SES)) -5.949e-02 1.093e-01 -0.544 0.58762
## scale(MSZMT_total) -2.658e-01 9.016e-02 -2.948 0.00401 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6745 on 97 degrees of freedom
## Multiple R-squared: 0.5631, Adjusted R-squared: 0.5451
## F-statistic: 31.26 on 4 and 97 DF, p-value: < 2.2e-16Robust Regressions
Robust: Unstandardized
HCReg(osztalyzat ~ WISC_TtlQ, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.6197626 0.4052548 -3.9969 0.0001229 ***
## WISC_TtlQ 0.0500377 0.0036845 13.5807 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5202518
##
## $adj_r_squared
## [1] 0.5154544HCReg(osztalyzat ~ dpv_ossz, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4891530 0.9255660 -0.5285 0.5983
## dpv_ossz 0.0169463 0.0036395 4.6562 9.922e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.2469913
##
## $adj_r_squared
## [1] 0.2394612HCReg(osztalyzat ~ as.numeric(SES), data) ## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.784314 0.077357 48.9200 < 2.2e-16 ***
## as.numeric(SES) 0.177123 0.024884 7.1179 1.694e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.3095473
##
## $adj_r_squared
## [1] 0.3026428HCReg(osztalyzat ~ MSZMT_total, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.8015079 0.1725471 27.8272 < 2.2e-16 ***
## MSZMT_total -0.0084339 0.0012048 -7.0005 2.977e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.2875992
##
## $adj_r_squared
## [1] 0.2804752HCReg(osztalyzat ~ WISC_TtlQ + dpv_ossz, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.9232675 0.4603108 -4.1782 6.340e-05 ***
## WISC_TtlQ 0.0466947 0.0049572 9.4196 2.019e-15 ***
## dpv_ossz 0.0026353 0.0023766 1.1088 0.2702
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5239025
##
## $adj_r_squared
## [1] 0.5142843HCReg(osztalyzat ~ WISC_TtlQ + as.numeric(SES), data) ## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7411817 0.7887485 -2.2075 0.02959 *
## WISC_TtlQ 0.0511620 0.0072983 7.0101 2.949e-10 ***
## as.numeric(SES) -0.0065933 0.0386462 -0.1706 0.86488
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5204181
##
## $adj_r_squared
## [1] 0.5107296HCReg(osztalyzat ~ WISC_TtlQ + MSZMT_total, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3082146 0.6401389 -0.4815 0.631237
## WISC_TtlQ 0.0419483 0.0048491 8.6507 9.499e-14 ***
## MSZMT_total -0.0036307 0.0012031 -3.0177 0.003239 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5599519
##
## $adj_r_squared
## [1] 0.551062HCReg(osztalyzat ~ WISC_TtlQ + dpv_ossz + as.numeric(SES) + MSZMT_total, data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.1817559 0.8888797 -0.2045 0.838409
## WISC_TtlQ 0.0470020 0.0078425 5.9932 3.507e-08 ***
## dpv_ossz -0.0024031 0.0024254 -0.9908 0.324245
## as.numeric(SES) -0.0189378 0.0365354 -0.5183 0.605401
## MSZMT_total -0.0041800 0.0013200 -3.1666 0.002062 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5631072
##
## $adj_r_squared
## [1] 0.545091Robust: Standardized
HCReg(scale(osztalyzat) ~ scale(WISC_TtlQ), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.4672e-16 6.8537e-02 0.000 1
## scale(WISC_TtlQ) 7.2128e-01 5.3111e-02 13.581 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5202518
##
## $adj_r_squared
## [1] 0.5154544HCReg(scale(osztalyzat) ~ scale(dpv_ossz), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.1886e-16 8.7201e-02 0.0000 1
## scale(dpv_ossz) 4.9698e-01 1.0674e-01 4.6562 9.922e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.2469913
##
## $adj_r_squared
## [1] 0.2394612HCReg(scale(osztalyzat) ~ scale(as.numeric(SES)), data) ## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.5044e-16 8.2290e-02 0.0000 1
## scale(as.numeric(SES)) 5.5637e-01 7.8165e-02 7.1179 1.694e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.3095473
##
## $adj_r_squared
## [1] 0.3026428HCReg(scale(osztalyzat) ~ scale(MSZMT_total), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.2575e-16 8.3624e-02 0.0000 1
## scale(MSZMT_total) -5.3628e-01 7.6607e-02 -7.0005 2.977e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.2875992
##
## $adj_r_squared
## [1] 0.2804752HCReg(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.8557e-16 6.8438e-02 0.0000 1.0000
## scale(WISC_TtlQ) 6.7310e-01 7.1457e-02 9.4196 2.019e-15 ***
## scale(dpv_ossz) 7.7284e-02 6.9698e-02 1.1088 0.2702
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5239025
##
## $adj_r_squared
## [1] 0.5142843HCReg(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(as.numeric(SES)), data) ## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.4843e-16 6.8760e-02 0.0000 1.0000
## scale(WISC_TtlQ) 7.3749e-01 1.0520e-01 7.0101 2.949e-10 ***
## scale(as.numeric(SES)) -2.0711e-02 1.2139e-01 -0.1706 0.8649
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5204181
##
## $adj_r_squared
## [1] 0.5107296HCReg(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(MSZMT_total), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.2875e-16 6.5854e-02 0.0000 1.000000
## scale(WISC_TtlQ) 6.0468e-01 6.9899e-02 8.6507 9.499e-14 ***
## scale(MSZMT_total) -2.3086e-01 7.6504e-02 -3.0177 0.003239 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5599519
##
## $adj_r_squared
## [1] 0.551062HCReg(scale(osztalyzat) ~ scale(WISC_TtlQ) + scale(dpv_ossz) + scale(as.numeric(SES)) + scale(MSZMT_total), data)## $coeftest_results
##
## t test of coefficients:
##
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.8671e-16 6.5888e-02 0.0000 1.000000
## scale(WISC_TtlQ) 6.7753e-01 1.1305e-01 5.9932 3.507e-08 ***
## scale(dpv_ossz) -7.0475e-02 7.1129e-02 -0.9908 0.324245
## scale(as.numeric(SES)) -5.9486e-02 1.1476e-01 -0.5183 0.605401
## scale(MSZMT_total) -2.6579e-01 8.3936e-02 -3.1666 0.002062 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## $r_squared
## [1] 0.5631072
##
## $adj_r_squared
## [1] 0.545091SAM Models
WISCSAM <- '
g =~ betuszam_ertek + szamterj_ertek + szokincs_ertek + kozjel_ertek + altmegert_ertek + kodolas_ertek + szimbol_ertek + kepifog_ertek + mozaik_ertek + matrix_ertek
osztalyzat ~ g'
DPVSAM <- '
dpv =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik
osztalyzat ~ dpv'
SESSAM <- '
osztalyzat ~ SES'
MARSSAM <- '
MARS =~ mszmt1 + mszmt2 + mszmt3 + mszmt4 + mszmt5 + mszmt6 + mszmt7 + mszmt8 + mszmt9 + mszmt10 + mszmt11 + mszmt12 + mszmt13 + mszmt14 + mszmt15 + mszmt16 + mszmt17 + mszmt18 + mszmt19 + mszmt20 + mszmt21 + mszmt22 + mszmt23 + mszmt24 + mszmt25 + mszmt26 + mszmt27 + mszmt28 + mszmt29 + mszmt30 + mszmt31 + mszmt32 + mszmt33 + mszmt34 + mszmt35 + mszmt36 + mszmt37 + mszmt38 + mszmt39 + mszmt40
osztalyzat ~ MARS'
WISCDPVSAM <- '
g =~ betuszam_ertek + szamterj_ertek + szokincs_ertek + kozjel_ertek + altmegert_ertek + kodolas_ertek + szimbol_ertek + kepifog_ertek + mozaik_ertek + matrix_ertek
dpv =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik
g ~~ dpv
osztalyzat ~ g + dpv'
WISCSESSAM <- '
g =~ betuszam_ertek + szamterj_ertek + szokincs_ertek + kozjel_ertek + altmegert_ertek + kodolas_ertek + szimbol_ertek + kepifog_ertek + mozaik_ertek + matrix_ertek
g ~~ SES
osztalyzat ~ g + SES'
WISCMARSSAM <- '
g =~ betuszam_ertek + szamterj_ertek + szokincs_ertek + kozjel_ertek + altmegert_ertek + kodolas_ertek + szimbol_ertek + kepifog_ertek + mozaik_ertek + matrix_ertek
MARS =~ mszmt1 + mszmt2 + mszmt3 + mszmt4 + mszmt5 + mszmt6 + mszmt7 + mszmt8 + mszmt9 + mszmt10 + mszmt11 + mszmt12 + mszmt13 + mszmt14 + mszmt15 + mszmt16 + mszmt17 + mszmt18 + mszmt19 + mszmt20 + mszmt21 + mszmt22 + mszmt23 + mszmt24 + mszmt25 + mszmt26 + mszmt27 + mszmt28 + mszmt29 + mszmt30 + mszmt31 + mszmt32 + mszmt33 + mszmt34 + mszmt35 + mszmt36 + mszmt37 + mszmt38 + mszmt39 + mszmt40
g ~~ MARS
osztalyzat ~ g + MARS'
WISCDPVSESMARSSAM <- '
g =~ betuszam_ertek + szamterj_ertek + szokincs_ertek + kozjel_ertek + altmegert_ertek + kodolas_ertek + szimbol_ertek + kepifog_ertek + mozaik_ertek + matrix_ertek
dpv =~ dpv_tajek + dpv_szaml + dpv_szameml + dpv_szamegyz + dpv_rel + dpv_helyiert + dpv_potlas + dpv_muvel + dpv_szorzoszt + dpv_irasbeli + dpv_szoveg + dpv_logszab + dpv_muvsorr + dpv_praktik
MARS =~ mszmt1 + mszmt2 + mszmt3 + mszmt4 + mszmt5 + mszmt6 + mszmt7 + mszmt8 + mszmt9 + mszmt10 + mszmt11 + mszmt12 + mszmt13 + mszmt14 + mszmt15 + mszmt16 + mszmt17 + mszmt18 + mszmt19 + mszmt20 + mszmt21 + mszmt22 + mszmt23 + mszmt24 + mszmt25 + mszmt26 + mszmt27 + mszmt28 + mszmt29 + mszmt30 + mszmt31 + mszmt32 + mszmt33 + mszmt34 + mszmt35 + mszmt36 + mszmt37 + mszmt38 + mszmt39 + mszmt40
g ~~ dpv + SES + MARS
dpv ~~ SES + MARS
SES ~~ MARS
osztalyzat ~ g + dpv + SES + MARS'
WISCSAMFit <- sam(WISCSAM, data)
DPVSAMFit <- sam(DPVSAM, data)
SESSAMFit <- sem(SESSAM, data)
MARSSAMFit <- sam(MARSSAM, data)
WISCDPVSAMFit <- sam(WISCDPVSAM, data)
WISCSESSAMFit <- sam(WISCSESSAM, data)
WISCMARSSAMFit <- sam(WISCMARSSAM, data)
WISCDPVSESMARSSAMFit <- sam(WISCDPVSESMARSSAM, data)
summary(WISCSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 1
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 g 10 147.897 35
##
## Model-based reliability latent variables:
##
## g osztalyzat
## 0.917 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## g 0.425 0.056 7.578 0.000 0.716 0.766
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.362 0.057 6.327 0.000 0.362 0.414
## g 2.845 0.689 4.132 0.000 1.000 1.000summary(DPVSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 1
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 dpv 14 267.038 77
##
## Model-based reliability latent variables:
##
## dpv osztalyzat
## 0.959 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## dpv 2.573 0.521 4.936 0.000 0.510 0.545
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.615 0.088 7.014 0.000 0.615 0.703
## dpv 0.039 0.012 3.392 0.001 1.000 1.000summary(SESSAMFit, stand = T, fit = T)## lavaan 0.6.14 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 2
##
## Number of observations 102
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 9.965
## Degrees of freedom 1
## P-value 0.002
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -132.942
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 269.884
## Bayesian (BIC) 275.134
## Sample-size adjusted Bayesian (SABIC) 268.817
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## SES 0.020 0.006 3.235 0.001 0.020 0.305
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.794 0.111 7.141 0.000 0.794 0.907summary(MARSSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 1
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 MARS 40 2355.196 740
##
## Model-based reliability latent variables:
##
## MARS osztalyzat
## 0.985 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## MARS -0.439 0.085 -5.194 0.000 -0.551 -0.589
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.572 0.081 7.084 0.000 0.572 0.654
## MARS 1.574 0.479 3.283 0.001 1.000 1.000summary(WISCDPVSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 2
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 g 10 147.897 35
## 2 dpv 14 267.038 77
##
## Model-based reliability latent variables:
##
## g dpv osztalyzat
## 0.917 0.959 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## g 0.418 0.070 5.937 0.000 0.706 0.754
## dpv 0.077 0.486 0.157 0.875 0.015 0.016
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## dpv 0.234 0.056 4.163 0.000 0.701 0.701
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.362 0.057 6.348 0.000 0.362 0.414
## g 2.845 0.689 4.132 0.000 1.000 1.000
## dpv 0.039 0.012 3.392 0.001 1.000 1.000summary(WISCSESSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 1
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 g 10 147.897 35
##
## Model-based reliability latent variables:
##
## g osztalyzat SES
## 0.917 1 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## g 0.466 0.064 7.242 0.000 0.787 0.841
## SES -0.009 0.005 -1.742 0.081 -0.009 -0.141
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## SES 12.719 3.024 4.206 0.000 7.541 0.531
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.349 0.057 6.151 0.000 0.349 0.399
## SES 201.680 28.241 7.141 0.000 201.680 1.000
## g 2.845 0.689 4.132 0.000 1.000 1.000summary(WISCMARSSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 2
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 g 10 147.897 35
## 2 MARS 40 2355.196 740
##
## Model-based reliability latent variables:
##
## g MARS osztalyzat
## 0.917 0.985 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## g 0.357 0.058 6.103 0.000 0.601 0.643
## MARS -0.154 0.065 -2.360 0.018 -0.194 -0.207
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## MARS -1.256 0.327 -3.848 0.000 -0.594 -0.594
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.338 0.052 6.499 0.000 0.338 0.386
## g 2.845 0.689 4.132 0.000 1.000 1.000
## MARS 1.574 0.479 3.283 0.001 1.000 1.000summary(WISCDPVSESMARSSAMFit, stand = T, fit = T)## Warning in lav_object_summary(object = object, header = header, fit.measures = fit.measures, : lavaan WARNING: fit measures not available if test = "none"## This is lavaan 0.6.14 -- using the SAM approach to SEM
##
## SAM method LOCAL
## Mapping matrix M method ML
## Number of measurement blocks 3
## Estimator measurement part ML
## Estimator structural part ML
##
## Number of observations 102
##
## Summary Information Measurement + Structural:
##
## Block Latent Nind Chisq Df
## 1 g 10 147.897 35
## 2 dpv 14 267.038 77
## 3 MARS 40 2355.196 740
##
## Model-based reliability latent variables:
##
## g dpv MARS osztalyzat SES
## 0.917 0.959 0.985 1 1
##
## Summary Information Structural part:
##
## chisq df cfi rmsea srmr
## 0 0 1 0 0
##
## Parameter Estimates:
##
## Standard errors Twostep
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## osztalyzat ~
## g 0.457 0.085 5.371 0.000 0.770 0.823
## dpv -0.949 0.595 -1.597 0.110 -0.188 -0.201
## SES -0.010 0.006 -1.693 0.090 -0.010 -0.145
## MARS -0.202 0.078 -2.580 0.010 -0.253 -0.270
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## g ~~
## dpv 0.234 0.056 4.163 0.000 0.701 0.701
## SES 12.719 3.024 4.206 0.000 7.541 0.531
## MARS -1.256 0.327 -3.848 0.000 -0.594 -0.594
## dpv ~~
## SES 0.494 0.296 1.670 0.095 2.490 0.175
## MARS -0.179 0.045 -3.940 0.000 -0.719 -0.719
## MARS ~~
## SES -3.177 1.855 -1.712 0.087 -2.532 -0.178
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .osztalyzat 0.319 0.053 6.067 0.000 0.319 0.364
## SES 201.680 28.241 7.141 0.000 201.680 1.000
## g 2.845 0.689 4.132 0.000 1.000 1.000
## dpv 0.039 0.012 3.392 0.001 1.000 1.000
## MARS 1.574 0.479 3.283 0.001 1.000 1.000Discussion
The DPV measures a g that is highly similar to the g measured by the WISC (r = .78), which is very similar to the r = .72 result achieved by Zaboski, Kranzler & Gage (2018). This is likely attenuated because of psychometric sampling error, since the DPV is purely concerned with mathematics and the g factor from the WISC is a higher-order g factor that is much less colored by a particular form of content.
References
Zaboski, B. A., Kranzler, J. H., & Gage, N. A. (2018). Meta-analysis of the relationship between academic achievement and broad abilities of the Cattell-horn-Carroll theory. Journal of School Psychology, 71, 42–56. https://doi.org/10.1016/j.jsp.2018.10.001
sessionInfo()## R version 4.2.2 (2022-10-31 ucrt)
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## Running under: Windows 10 x64 (build 19045)
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## [13] purrr_1.0.1 readr_2.1.4 tibble_3.1.8 ggplot2_3.4.1
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## [4] htmlTable_2.4.1 corpcor_1.6.10 base64enc_0.1-3
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## [40] nlme_3.1-160 lisrelToR_0.1.5 xfun_0.37
## [43] openxlsx_4.2.5.2 lme4_1.1-31 timechange_0.2.0
## [46] lifecycle_1.0.3 gtools_3.9.4 XML_3.99-0.13
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