- Data Preparation
- Part I: Clean the table
- Part II: Exploratory Factorial Analysis (EFA)
- Part III: Confirmatory Factorial Analysis
- Part IV: Cronbach’s Alpha
- Cronbach’s Alpha
- Discriminant validity
Factor Analysis
Exploratory Factor Analysis and Confirmatory Factor Analysis
Victor Ivamoto
2020/09/24
Data Preparation
Load libraries
library(tidyverse, readxl)## -- Attaching packages --------------------------------------------------- tidyverse 1.3.0 --## v ggplot2 3.3.2 v purrr 0.3.4
## v tibble 3.0.3 v dplyr 1.0.2
## v tidyr 1.1.2 v stringr 1.4.0
## v readr 1.3.1 v forcats 0.5.0## -- Conflicts ------------------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(faraway)
library(mctest, REdaS)
library(psych, corrgram)##
## Attaching package: 'psych'## The following object is masked from 'package:faraway':
##
## logit## The following objects are masked from 'package:ggplot2':
##
## %+%, alphaLoad table
Select one file to import.
tbl <- readxl::read_excel('ORIGINAL.xlsx', col_names = TRUE)
#tbl <- readxl::read_excel('tab_original.xlsx', sheet = 'Smart PLS', col_names = TRUE)
tbl %>% head()## # A tibble: 6 x 39
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3 3 2 3 3 4 3 3 2 3 3 4 2
## 2 1 5 2 1 5 4 2 4 2 4 4 4 3
## 3 3 3 1 2 5 5 2 4 2 5 3 5 1
## 4 3 3 2 3 1 1 5 1 1 5 5 5 1
## 5 2 3 4 2 2 3 3 1 2 4 3 4 2
## 6 1 5 3 1 5 5 3 5 3 5 5 5 3
## # ... with 26 more variables: V14 <dbl>, V15 <dbl>, V16 <dbl>, V17 <dbl>,
## # V18 <dbl>, V19 <dbl>, V20 <dbl>, V21 <dbl>, V22 <dbl>, V23 <dbl>,
## # V24 <dbl>, V25 <dbl>, V26 <dbl>, V27 <dbl>, V28 <dbl>, V29 <dbl>,
## # V30 <dbl>, V31 <dbl>, V32 <dbl>, V33 <dbl>, V34 <dbl>, V35 <dbl>,
## # V36 <dbl>, V37 <dbl>, V38 <dbl>, V39 <dbl>Exclude dichotomous variables
dic <- apply(tbl, 2 , function(x) length(unique(x)))
tbl <- tbl[dic > 2]
tbl %>% head()## # A tibble: 6 x 39
## V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 3 3 2 3 3 4 3 3 2 3 3 4 2
## 2 1 5 2 1 5 4 2 4 2 4 4 4 3
## 3 3 3 1 2 5 5 2 4 2 5 3 5 1
## 4 3 3 2 3 1 1 5 1 1 5 5 5 1
## 5 2 3 4 2 2 3 3 1 2 4 3 4 2
## 6 1 5 3 1 5 5 3 5 3 5 5 5 3
## # ... with 26 more variables: V14 <dbl>, V15 <dbl>, V16 <dbl>, V17 <dbl>,
## # V18 <dbl>, V19 <dbl>, V20 <dbl>, V21 <dbl>, V22 <dbl>, V23 <dbl>,
## # V24 <dbl>, V25 <dbl>, V26 <dbl>, V27 <dbl>, V28 <dbl>, V29 <dbl>,
## # V30 <dbl>, V31 <dbl>, V32 <dbl>, V33 <dbl>, V34 <dbl>, V35 <dbl>,
## # V36 <dbl>, V37 <dbl>, V38 <dbl>, V39 <dbl>Correlation matrix
corrgram::corrgram(tbl)## Registered S3 method overwritten by 'seriation':
## method from
## reorder.hclust gclus
Part I: Clean the table
MSA and KMO tests
| KMO | Reference |
|---|---|
| 0.9 - 1.0 | Marvelous |
| 0.8 - 0.9 | Meritorious |
| 0.7 - 0.8 | Middling |
| 0.6 - 0.7 | Mediocre |
| 0.5 - 0.6 | Miserable |
| less than 0,5 | Unacceptable |
kmos <- REdaS::KMOS(tbl)
kmos##
## Kaiser-Meyer-Olkin Statistics
##
## Call: REdaS::KMOS(x = tbl)
##
## Measures of Sampling Adequacy (MSA):
## V1 V2 V3 V4 V5 V6 V7 V8
## 0.3863221 0.2888696 0.5430261 0.5332195 0.4045718 0.5742530 0.7057292 0.3183750
## V9 V10 V11 V12 V13 V14 V15 V16
## 0.2368494 0.3179444 0.4257270 0.3194953 0.3125138 0.2812793 0.5844332 0.2517149
## V17 V18 V19 V20 V21 V22 V23 V24
## 0.4511708 0.1917775 0.4782174 0.6763129 0.4410895 0.6493593 0.3091503 0.6710117
## V25 V26 V27 V28 V29 V30 V31 V32
## 0.4413103 0.5826637 0.4164522 0.2473532 0.5208505 0.4154455 0.3537410 0.5772935
## V33 V34 V35 V36 V37 V38 V39
## 0.5153674 0.3066627 0.2645096 0.3848108 0.1587135 0.0941182 0.1287547
##
## KMO-Criterion: 0.3942645MSA distribution on each range.
df <- data.frame(Marvelous = round(100*mean(0.9 < kmos$MSA), 2),
Meritorious = round(100*mean(0.8 < kmos$MSA & kmos$MSA <= 0.9), 2),
Middling = round(100*mean(0.7 < kmos$MSA & kmos$MSA <= 0.8), 2),
Mediocre = round(100*mean(0.6 < kmos$MSA & kmos$MSA <= 0.7), 2),
Miserable = round(100*mean(0.5 < kmos$MSA & kmos$MSA <= 0.6), 2),
Unacceptable = round(100*mean(kmos$MSA <= 0.5), 2))
df## Marvelous Meritorious Middling Mediocre Miserable Unacceptable
## 1 0 0 2.56 7.69 20.51 69.23Exclude variables with MSA < 0.50, one variable at time stating with lower KMO.
exclude <- mean(kmos$MSA < 0.5) > 0
while(exclude){
tbl <- tbl[kmos$MSA != min(kmos$MSA)]
kmos <- REdaS::KMOS(tbl)
exclude <- mean(kmos$MSA < 0.5) > 0
}Result after excluding variables.
df <- data.frame(Marvelous = round(100*mean(0.9 < kmos$MSA), 2),
Meritorious = round(100*mean(0.8 < kmos$MSA & kmos$MSA <= 0.9), 2),
Middling = round(100*mean(0.7 < kmos$MSA & kmos$MSA <= 0.8), 2),
Mediocre = round(100*mean(0.6 < kmos$MSA & kmos$MSA <= 0.7), 2),
Miserable = round(100*mean(0.5 < kmos$MSA & kmos$MSA <= 0.6), 2),
Unacceptable = round(100*mean(kmos$MSA <= 0.5), 2))
df## Marvelous Meritorious Middling Mediocre Miserable Unacceptable
## 1 3.33 13.33 33.33 33.33 16.67 0Variance Inflation Factor (VIF)
Exclude variables with values larger than 10.
# Build formula
fml <- paste0(colnames(tbl)[1],' ~ ', paste(colnames(tbl)[-1], collapse = " + "))
fml <- as.formula(fml)
model <- lm(fml, data = tbl)
imc <- imcdiag(model, method = "VIF", vif = 10)[[1]][,1]
exclude <- mean(imc > 10) > 0
while(exclude){
# Exclude column with largest VIF
i <- imc %>% sort(decreasing = TRUE)
ii <- colnames(tbl) %in% names(i)[1]
tbl <- tbl[!ii]
cat('Variable removed:', names(i)[1])
# Build formula
fml <- paste0(colnames(tbl)[1],' ~ ', paste(colnames(tbl)[-1], collapse = " + "))
fml <- as.formula(fml)
# Create model
model <- lm(fml, data = tbl)
# Measure colinearity
imc <- imcdiag(model, method = "VIF", vif = 10)[[1]][,1]
exclude <- mean(imc > 10) > 0
}## Variable removed: V32Variable removed: V26After removing the variables, there’s no co-linearity.
imcdiag(model, method = "VIF", vif = 10)##
## Call:
## imcdiag(mod = model, method = "VIF", vif = 10)
##
##
## VIF Multicollinearity Diagnostics
##
## VIF detection
## V2 3.8602 0
## V3 2.8566 0
## V4 6.1227 0
## V5 4.5287 0
## V6 3.1706 0
## V7 3.4121 0
## V10 3.7700 0
## V11 3.7743 0
## V13 2.8579 0
## V14 3.6790 0
## V15 4.5054 0
## V16 3.7317 0
## V17 3.6933 0
## V19 3.2066 0
## V20 3.6005 0
## V21 7.0210 0
## V22 3.9780 0
## V23 3.9217 0
## V24 3.2466 0
## V25 3.6634 0
## V27 8.5060 0
## V29 4.7419 0
## V30 3.9918 0
## V31 4.2783 0
## V33 5.1438 0
## V35 4.4911 0
## V36 5.6376 0
##
## NOTE: VIF Method Failed to detect multicollinearity
##
##
## 0 --> COLLINEARITY is not detected by the test
##
## ===================================Bartlett’s Test of Sphericity
REdaS::bart_spher(tbl)## Bartlett's Test of Sphericity
##
## Call: REdaS::bart_spher(x = tbl)
##
## X2 = 802.684
## df = 378
## p-value < 2.22e-16Part II: Exploratory Factorial Analysis (EFA)
Correlation matrix compared to random “parallel” matrices
nfactors <- fa.parallel(tbl, plot = FALSE)## Parallel analysis suggests that the number of factors = 3 and the number of components = 3nfactors## Call: fa.parallel(x = tbl, plot = FALSE)
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3
##
## Eigen Values of
## Original factors Resampled data Simulated data Original components
## 1 9.12 2.01 2.08 9.73
## 2 2.29 1.60 1.64 3.02
## 3 2.06 1.34 1.36 2.78
## Resampled components Simulated components
## 1 2.84 2.90
## 2 2.55 2.59
## 3 2.28 2.30Correlation matrix
corMat <- cor(tbl)Factor analysis
nfact <- nfactors$nfact
fa <- factanal(tbl, factors=nfact, scores="regression")
fa##
## Call:
## factanal(x = tbl, factors = nfact, scores = "regression")
##
## Uniquenesses:
## V1 V2 V3 V4 V5 V6 V7 V10 V11 V13 V14 V15 V16
## 0.213 0.560 0.471 0.252 0.478 0.673 0.601 0.498 0.527 0.813 0.727 0.361 0.758
## V17 V19 V20 V21 V22 V23 V24 V25 V27 V29 V30 V31 V33
## 0.343 0.820 0.437 0.361 0.367 0.643 0.444 0.709 0.220 0.342 0.680 0.441 0.357
## V35 V36
## 0.658 0.401
##
## Loadings:
## Factor1 Factor2 Factor3
## V1 -0.814 -0.298 -0.188
## V2 0.576 0.328
## V3 0.658 0.134 0.278
## V4 -0.814 -0.220 -0.191
## V5 0.648 0.220 0.232
## V6 0.467 0.288 0.163
## V7 0.249 0.384 0.435
## V10 0.648 0.285
## V11 0.202 0.612 0.239
## V13 0.422
## V14 0.495 0.158
## V15 0.788 0.109
## V16 0.492
## V17 0.213 0.780
## V19 0.379 -0.138 0.130
## V20 0.527 0.368 0.388
## V21 0.448 0.651 0.123
## V22 0.235 0.752 0.109
## V23 0.544 0.237
## V24 0.732 0.125
## V25 0.522 0.116
## V27 0.319 -0.143 0.811
## V29 0.302 0.241 0.713
## V30 0.237 0.512
## V31 0.332 0.316 0.591
## V33 0.172 0.179 0.763
## V35 0.111 0.573
## V36 0.302 0.711
##
## Factor1 Factor2 Factor3
## SS loadings 5.225 4.613 4.005
## Proportion Var 0.187 0.165 0.143
## Cumulative Var 0.187 0.351 0.494
##
## Test of the hypothesis that 3 factors are sufficient.
## The chi square statistic is 326.54 on 297 degrees of freedom.
## The p-value is 0.115Exploratory factor analysis using minimum residual.
N <- nrow(tbl)
faPC <- fa(r = corMat, nfactors = nfact, n.obs = N, rotate = "varimax")
print(faPC)## Factor Analysis using method = minres
## Call: fa(r = corMat, nfactors = nfact, n.obs = N, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR1 MR2 MR3 h2 u2 com
## V1 -0.64 -0.38 -0.29 0.63 0.37 2.1
## V2 0.49 0.36 0.07 0.37 0.63 1.9
## V3 0.51 0.19 0.36 0.43 0.57 2.1
## V4 -0.64 -0.29 -0.29 0.58 0.42 1.8
## V5 0.61 0.26 0.27 0.52 0.48 1.8
## V6 0.51 0.30 0.15 0.37 0.63 1.8
## V7 0.22 0.39 0.41 0.37 0.63 2.5
## V10 0.05 0.63 0.25 0.46 0.54 1.3
## V11 0.27 0.61 0.17 0.47 0.53 1.6
## V13 0.52 0.03 0.09 0.27 0.73 1.1
## V14 0.62 0.16 0.01 0.41 0.59 1.1
## V15 0.04 0.78 0.11 0.62 0.38 1.0
## V16 0.65 -0.03 -0.03 0.43 0.57 1.0
## V17 0.21 0.78 0.07 0.66 0.34 1.2
## V19 0.56 -0.18 0.10 0.35 0.65 1.3
## V20 0.52 0.37 0.42 0.59 0.41 2.8
## V21 0.37 0.68 0.17 0.63 0.37 1.7
## V22 0.21 0.76 0.11 0.63 0.37 1.2
## V23 0.57 0.24 0.12 0.39 0.61 1.5
## V24 -0.04 0.75 0.16 0.60 0.40 1.1
## V25 0.64 0.09 0.04 0.42 0.58 1.0
## V27 0.33 -0.12 0.78 0.74 0.26 1.4
## V29 0.26 0.25 0.72 0.64 0.36 1.5
## V30 -0.07 0.22 0.55 0.35 0.65 1.3
## V31 0.28 0.33 0.60 0.55 0.45 2.0
## V33 0.12 0.18 0.77 0.64 0.36 1.2
## V35 -0.04 0.08 0.61 0.38 0.62 1.0
## V36 0.22 0.08 0.74 0.61 0.39 1.2
##
## MR1 MR2 MR3
## SS loadings 5.02 4.85 4.26
## Proportion Var 0.18 0.17 0.15
## Cumulative Var 0.18 0.35 0.50
## Proportion Explained 0.36 0.34 0.30
## Cumulative Proportion 0.36 0.70 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 378 and the objective function was 24.45 with Chi Square of 802.68
## The degrees of freedom for the model are 297 and the objective function was 10.69
##
## The root mean square of the residuals (RMSR) is 0.08
## The df corrected root mean square of the residuals is 0.09
##
## The harmonic number of observations is 44 with the empirical chi square 209.31 with prob < 1
## The total number of observations was 44 with Likelihood Chi Square = 329.62 with prob < 0.094
##
## Tucker Lewis Index of factoring reliability = 0.89
## RMSEA index = 0.044 and the 90 % confidence intervals are 0 0.08
## BIC = -794.28
## Fit based upon off diagonal values = 0.95
## Measures of factor score adequacy
## MR1 MR2 MR3
## Correlation of (regression) scores with factors 0.93 0.95 0.94
## Multiple R square of scores with factors 0.87 0.90 0.89
## Minimum correlation of possible factor scores 0.74 0.79 0.78Remove variables with low commonalities (h2 < 0.40).
h2 <- faPC$communality # Column h2
exclui <- mean(h2 < 0.40) > 0 # TRUE se houver h2 < 0.40
while(exclui){
tbl <- tbl[!(h2 == min(h2))] # Exclui variavel com menor h2
nfactors <- fa.parallel(tbl, plot = FALSE) # Recalcula nfactors
nfact <- nfactors$nfact # Number of factors
N <- nrow(tbl) # Number of rows in new table
corMat <- cor(tbl) # Recompute correlation
faPC <- fa(r = corMat, nfactors = nfact, n.obs = N, rotate = "varimax")
h2 <- faPC$communality # Column h2
exclui <- mean(h2 < 0.40) > 0 # Continue while h2 < 0.40
}## Parallel analysis suggests that the number of factors = 3 and the number of components = 3## 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## Parallel analysis suggests that the number of factors = 3 and the number of components = 3
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2## 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.## Parallel analysis suggests that the number of factors = 3 and the number of components = 3
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2
## Parallel analysis suggests that the number of factors = 3 and the number of components = 2
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3print(faPC)## Factor Analysis using method = minres
## Call: fa(r = corMat, nfactors = nfact, n.obs = N, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## MR2 MR1 MR3 h2 u2 com
## V1 -0.27 -0.86 -0.09 0.83 0.17 1.2
## V3 0.08 0.74 0.18 0.58 0.42 1.1
## V4 -0.20 -0.83 -0.12 0.74 0.26 1.2
## V5 0.25 0.58 0.22 0.44 0.56 1.7
## V10 0.69 0.02 0.31 0.58 0.42 1.4
## V11 0.62 0.24 0.15 0.47 0.53 1.4
## V15 0.79 0.10 0.10 0.64 0.36 1.1
## V17 0.76 0.23 0.04 0.64 0.36 1.2
## V20 0.37 0.54 0.36 0.55 0.45 2.6
## V21 0.63 0.51 0.03 0.66 0.34 1.9
## V22 0.76 0.26 0.06 0.65 0.35 1.2
## V24 0.70 0.12 0.14 0.52 0.48 1.1
## V27 -0.12 0.41 0.73 0.71 0.29 1.6
## V29 0.21 0.46 0.59 0.61 0.39 2.2
## V30 0.25 -0.08 0.67 0.52 0.48 1.3
## V31 0.29 0.47 0.48 0.53 0.47 2.6
## V33 0.15 0.34 0.65 0.56 0.44 1.6
## V35 0.13 -0.03 0.71 0.52 0.48 1.1
## V36 0.05 0.36 0.70 0.62 0.38 1.5
##
## MR2 MR1 MR3
## SS loadings 4.12 3.91 3.36
## Proportion Var 0.22 0.21 0.18
## Cumulative Var 0.22 0.42 0.60
## Proportion Explained 0.36 0.34 0.30
## Cumulative Proportion 0.36 0.70 1.00
##
## Mean item complexity = 1.5
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 171 and the objective function was 14.69 with Chi Square of 526.21
## The degrees of freedom for the model are 117 and the objective function was 3.48
##
## The root mean square of the residuals (RMSR) is 0.06
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 44 with the empirical chi square 46.96 with prob < 1
## The total number of observations was 44 with Likelihood Chi Square = 117.61 with prob < 0.47
##
## Tucker Lewis Index of factoring reliability = 0.997
## RMSEA index = 0 and the 90 % confidence intervals are 0 0.077
## BIC = -325.14
## Fit based upon off diagonal values = 0.98
## Measures of factor score adequacy
## MR2 MR1 MR3
## Correlation of (regression) scores with factors 0.94 0.95 0.93
## Multiple R square of scores with factors 0.89 0.90 0.86
## Minimum correlation of possible factor scores 0.78 0.79 0.72Scree plot
fa.parallel(tbl)
## Parallel analysis suggests that the number of factors = 3 and the number of components = 3Graph factor loading matrices. Identify factors with corresponding variables.
fa.diagram(faPC)
Apply the Very Simple Structure, MAP, and other criteria to determine the appropriate number of factors.
vss(tbl, n.obs=N, rotate='varimax')
##
## Very Simple Structure
## Call: vss(x = tbl, rotate = "varimax", n.obs = N)
## VSS complexity 1 achieves a maximimum of 0.8 with 1 factors
## VSS complexity 2 achieves a maximimum of 0.89 with 2 factors
##
## The Velicer MAP achieves a minimum of 0.04 with 4 factors
## BIC achieves a minimum of -325.14 with 3 factors
## Sample Size adjusted BIC achieves a minimum of -5.09 with 8 factors
##
## Statistics by number of factors
## vss1 vss2 map dof chisq prob sqresid fit RMSEA BIC SABIC complex
## 1 0.80 0.00 0.069 152 277 2.3e-09 15.6 0.80 0.135 -298 178.49 1.0
## 2 0.67 0.89 0.048 134 183 3.1e-03 8.2 0.89 0.088 -324 95.94 1.3
## 3 0.58 0.89 0.040 117 118 4.7e-01 4.3 0.94 0.000 -325 41.49 1.5
## 4 0.56 0.82 0.037 101 84 8.8e-01 3.2 0.96 0.000 -298 18.77 1.6
## 5 0.51 0.77 0.042 86 63 9.7e-01 2.6 0.97 0.000 -262 7.53 1.7
## 6 0.49 0.73 0.045 72 47 9.9e-01 2.1 0.97 0.000 -226 -0.33 1.9
## 7 0.47 0.74 0.049 59 35 9.9e-01 1.7 0.98 0.000 -188 -3.17 2.0
## 8 0.47 0.71 0.056 47 25 1.0e+00 1.4 0.98 0.000 -152 -5.09 2.1
## eChisq SRMR eCRMS eBIC
## 1 355.9 0.154 0.163 -219
## 2 143.6 0.098 0.110 -363
## 3 47.0 0.056 0.068 -396
## 4 25.7 0.041 0.054 -357
## 5 17.7 0.034 0.048 -308
## 6 10.3 0.026 0.040 -262
## 7 6.4 0.021 0.035 -217
## 8 3.5 0.015 0.029 -174Part III: Confirmatory Factorial Analysis
Build the model for future use.
library(lavaan, semPlot)## This is lavaan 0.6-7## lavaan is BETA software! Please report any bugs.##
## Attaching package: 'lavaan'## The following object is masked from 'package:psych':
##
## cor2covlibrary(qlcMatrix)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loading required package: slam## Loading required package: sparsesvd##
## Attaching package: 'qlcMatrix'## The following object is masked from 'package:purrr':
##
## nonefaResult <- data.frame(faPC$Structure %>% head(nrow(tbl)))
MR <- apply(faResult, 1, function(x) colnames(faResult[which.max(x)]))
create_fml <- function(x) {
varNames <- names(MR[MR == x])
vars <- str_c(varNames, collapse = ' + ')
fml <- paste0(x, " =~ ", vars)
return(fml)
}
# Model
mdl <- str_c(sapply(unique(MR), create_fml))
print(mdl)## [1] "MR3 =~ V1 + V4 + V27 + V29 + V30 + V31 + V33 + V35 + V36"
## [2] "MR1 =~ V3 + V5 + V20"
## [3] "MR2 =~ V10 + V11 + V15 + V17 + V21 + V22 + V24"Fit confirmatory factor analysis models.
fit<- lavaan::cfa(mdl,data= tbl)
summary(fit, fit.measures=TRUE)## lavaan 0.6-7 ended normally after 43 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 41
##
## Number of observations 44
##
## Model Test User Model:
##
## Test statistic 258.141
## Degrees of freedom 149
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 646.140
## Degrees of freedom 171
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.770
## Tucker-Lewis Index (TLI) 0.736
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1037.766
## Loglikelihood unrestricted model (H1) -908.696
##
## Akaike (AIC) 2157.532
## Bayesian (BIC) 2230.684
## Sample-size adjusted Bayesian (BIC) 2102.206
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.129
## 90 Percent confidence interval - lower 0.102
## 90 Percent confidence interval - upper 0.155
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.117
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## MR3 =~
## V1 1.000
## V4 1.093 0.292 3.742 0.000
## V27 -1.150 0.271 -4.248 0.000
## V29 -0.917 0.199 -4.605 0.000
## V30 -0.730 0.268 -2.724 0.006
## V31 -0.804 0.190 -4.243 0.000
## V33 -1.104 0.254 -4.347 0.000
## V35 -0.701 0.241 -2.905 0.004
## V36 -1.288 0.306 -4.214 0.000
## MR1 =~
## V3 1.000
## V5 0.961 0.258 3.724 0.000
## V20 1.087 0.253 4.306 0.000
## MR2 =~
## V10 1.000
## V11 1.447 0.330 4.386 0.000
## V15 1.228 0.262 4.687 0.000
## V17 1.414 0.294 4.815 0.000
## V21 1.412 0.305 4.630 0.000
## V22 1.457 0.293 4.966 0.000
## V24 1.108 0.255 4.339 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## MR3 ~~
## MR1 -0.585 0.206 -2.834 0.005
## MR2 -0.201 0.088 -2.277 0.023
## MR1 ~~
## MR2 0.263 0.104 2.527 0.012
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .V1 0.882 0.203 4.352 0.000
## .V4 1.154 0.263 4.382 0.000
## .V27 0.719 0.174 4.140 0.000
## .V29 0.273 0.072 3.764 0.000
## .V30 1.401 0.306 4.577 0.000
## .V31 0.354 0.085 4.144 0.000
## .V33 0.582 0.143 4.063 0.000
## .V35 1.082 0.237 4.555 0.000
## .V36 0.942 0.226 4.163 0.000
## .V3 0.876 0.215 4.070 0.000
## .V5 0.841 0.205 4.094 0.000
## .V20 0.494 0.152 3.256 0.001
## .V10 0.266 0.063 4.227 0.000
## .V11 0.514 0.123 4.190 0.000
## .V15 0.272 0.068 4.005 0.000
## .V17 0.311 0.080 3.896 0.000
## .V21 0.382 0.094 4.047 0.000
## .V22 0.274 0.073 3.731 0.000
## .V24 0.316 0.075 4.213 0.000
## MR3 0.654 0.278 2.348 0.019
## MR1 0.681 0.295 2.312 0.021
## MR2 0.253 0.099 2.559 0.010Plot path diagram for SEM models.
semPlot::semPaths(fit, 'par', edge.label.cex=1.2,fade=FALSE)## Registered S3 methods overwritten by 'huge':
## method from
## plot.sim BDgraph
## print.sim BDgraph
Parameter estimates of a latent variable model.
parameterEstimates(fit, standardized=TRUE)## lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all
## 1 MR3 =~ V1 1.000 0.000 NA NA 1.000 1.000 0.808 0.653
## 2 MR3 =~ V4 1.093 0.292 3.742 0.000 0.521 1.666 0.884 0.635
## 3 MR3 =~ V27 -1.150 0.271 -4.248 0.000 -1.680 -0.619 -0.929 -0.739
## 4 MR3 =~ V29 -0.917 0.199 -4.605 0.000 -1.307 -0.527 -0.741 -0.818
## 5 MR3 =~ V30 -0.730 0.268 -2.724 0.006 -1.256 -0.205 -0.590 -0.446
## 6 MR3 =~ V31 -0.804 0.190 -4.243 0.000 -1.176 -0.433 -0.650 -0.738
## 7 MR3 =~ V33 -1.104 0.254 -4.347 0.000 -1.601 -0.606 -0.892 -0.760
## 8 MR3 =~ V35 -0.701 0.241 -2.905 0.004 -1.174 -0.228 -0.567 -0.479
## 9 MR3 =~ V36 -1.288 0.306 -4.214 0.000 -1.887 -0.689 -1.042 -0.732
## 10 MR1 =~ V3 1.000 0.000 NA NA 1.000 1.000 0.825 0.661
## 11 MR1 =~ V5 0.961 0.258 3.724 0.000 0.455 1.467 0.794 0.654
## 12 MR1 =~ V20 1.087 0.253 4.306 0.000 0.592 1.582 0.898 0.787
## 13 MR2 =~ V10 1.000 0.000 NA NA 1.000 1.000 0.503 0.698
## 14 MR2 =~ V11 1.447 0.330 4.386 0.000 0.800 2.093 0.727 0.712
## 15 MR2 =~ V15 1.228 0.262 4.687 0.000 0.715 1.742 0.617 0.764
## 16 MR2 =~ V17 1.414 0.294 4.815 0.000 0.838 1.989 0.710 0.787
## 17 MR2 =~ V21 1.412 0.305 4.630 0.000 0.814 2.010 0.710 0.754
## 18 MR2 =~ V22 1.457 0.293 4.966 0.000 0.882 2.032 0.732 0.814
## 19 MR2 =~ V24 1.108 0.255 4.339 0.000 0.607 1.608 0.557 0.704
## 20 V1 ~~ V1 0.882 0.203 4.352 0.000 0.485 1.279 0.882 0.574
## 21 V4 ~~ V4 1.154 0.263 4.382 0.000 0.638 1.670 1.154 0.596
## 22 V27 ~~ V27 0.719 0.174 4.140 0.000 0.379 1.059 0.719 0.454
## 23 V29 ~~ V29 0.273 0.072 3.764 0.000 0.131 0.415 0.273 0.332
## 24 V30 ~~ V30 1.401 0.306 4.577 0.000 0.801 2.001 1.401 0.801
## 25 V31 ~~ V31 0.354 0.085 4.144 0.000 0.187 0.522 0.354 0.456
## 26 V33 ~~ V33 0.582 0.143 4.063 0.000 0.301 0.863 0.582 0.422
## 27 V35 ~~ V35 1.082 0.237 4.555 0.000 0.616 1.547 1.082 0.771
## 28 V36 ~~ V36 0.942 0.226 4.163 0.000 0.499 1.386 0.942 0.465
## 29 V3 ~~ V3 0.876 0.215 4.070 0.000 0.454 1.298 0.876 0.563
## 30 V5 ~~ V5 0.841 0.205 4.094 0.000 0.439 1.244 0.841 0.572
## 31 V20 ~~ V20 0.494 0.152 3.256 0.001 0.196 0.791 0.494 0.380
## 32 V10 ~~ V10 0.266 0.063 4.227 0.000 0.142 0.389 0.266 0.513
## 33 V11 ~~ V11 0.514 0.123 4.190 0.000 0.274 0.755 0.514 0.493
## 34 V15 ~~ V15 0.272 0.068 4.005 0.000 0.139 0.405 0.272 0.416
## 35 V17 ~~ V17 0.311 0.080 3.896 0.000 0.155 0.467 0.311 0.381
## 36 V21 ~~ V21 0.382 0.094 4.047 0.000 0.197 0.568 0.382 0.432
## 37 V22 ~~ V22 0.274 0.073 3.731 0.000 0.130 0.418 0.274 0.338
## 38 V24 ~~ V24 0.316 0.075 4.213 0.000 0.169 0.463 0.316 0.505
## 39 MR3 ~~ MR3 0.654 0.278 2.348 0.019 0.108 1.199 1.000 1.000
## 40 MR1 ~~ MR1 0.681 0.295 2.312 0.021 0.104 1.259 1.000 1.000
## 41 MR2 ~~ MR2 0.253 0.099 2.559 0.010 0.059 0.446 1.000 1.000
## 42 MR3 ~~ MR1 -0.585 0.206 -2.834 0.005 -0.989 -0.180 -0.876 -0.876
## 43 MR3 ~~ MR2 -0.201 0.088 -2.277 0.023 -0.374 -0.028 -0.494 -0.494
## 44 MR1 ~~ MR2 0.263 0.104 2.527 0.012 0.059 0.467 0.634 0.634
## std.nox
## 1 0.653
## 2 0.635
## 3 -0.739
## 4 -0.818
## 5 -0.446
## 6 -0.738
## 7 -0.760
## 8 -0.479
## 9 -0.732
## 10 0.661
## 11 0.654
## 12 0.787
## 13 0.698
## 14 0.712
## 15 0.764
## 16 0.787
## 17 0.754
## 18 0.814
## 19 0.704
## 20 0.574
## 21 0.596
## 22 0.454
## 23 0.332
## 24 0.801
## 25 0.456
## 26 0.422
## 27 0.771
## 28 0.465
## 29 0.563
## 30 0.572
## 31 0.380
## 32 0.513
## 33 0.493
## 34 0.416
## 35 0.381
## 36 0.432
## 37 0.338
## 38 0.505
## 39 1.000
## 40 1.000
## 41 1.000
## 42 -0.876
## 43 -0.494
## 44 0.634Part IV: Cronbach’s Alpha
Alfa_R.pdf
2a Methodology: Method 1: see CFA_Plot1.pdf (page 11) (α ≥ 0,7 better if ≥0,9)
factor1 <- select(tbl, nep1, nep6, nep11) #subset data using dplyr
factor2 <- select(tbl, nep2, nep7, nep12)(
alpha(factor1) #function from psych package to calculate cronbach's alpha Method 2: see CReliability.pdf Correlation data frame
library(corrr)
tbl %>% correlate()##
## Correlation method: 'pearson'
## Missing treated using: 'pairwise.complete.obs'## # A tibble: 19 x 20
## rowname V1 V3 V4 V5 V10 V11 V15 V17 V20
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 V1 NA -0.697 0.855 -0.638 -0.231 -0.355 -0.314 -0.370 -0.533
## 2 V3 -0.697 NA -0.650 0.463 0.0621 0.209 0.207 0.288 0.517
## 3 V4 0.855 -0.650 NA -0.626 -0.264 -0.239 -0.294 -0.309 -0.614
## 4 V5 -0.638 0.463 -0.626 NA 0.265 0.369 0.261 0.351 0.502
## 5 V10 -0.231 0.0621 -0.264 0.265 NA 0.557 0.618 0.489 0.371
## 6 V11 -0.355 0.209 -0.239 0.369 0.557 NA 0.521 0.545 0.392
## 7 V15 -0.314 0.207 -0.294 0.261 0.618 0.521 NA 0.657 0.406
## 8 V17 -0.370 0.288 -0.309 0.351 0.489 0.545 0.657 NA 0.462
## 9 V20 -0.533 0.517 -0.614 0.502 0.371 0.392 0.406 0.462 NA
## 10 V21 -0.610 0.448 -0.517 0.404 0.438 0.536 0.440 0.651 0.534
## 11 V22 -0.434 0.237 -0.366 0.273 0.606 0.609 0.591 0.569 0.439
## 12 V24 -0.381 0.128 -0.271 0.327 0.477 0.428 0.646 0.597 0.274
## 13 V27 -0.354 0.372 -0.366 0.389 0.233 0.259 -0.0467 0.00727 0.409
## 14 V29 -0.463 0.444 -0.419 0.468 0.310 0.379 0.290 0.293 0.522
## 15 V30 -0.129 0.140 -0.102 0.216 0.396 0.104 0.271 0.225 0.327
## 16 V31 -0.477 0.456 -0.413 0.354 0.319 0.415 0.267 0.387 0.537
## 17 V33 -0.355 0.423 -0.366 0.254 0.302 0.263 0.338 0.174 0.487
## 18 V35 -0.106 0.126 -0.125 0.210 0.302 0.102 0.112 0.140 0.319
## 19 V36 -0.439 0.395 -0.416 0.373 0.213 0.220 0.151 0.141 0.417
## # ... with 10 more variables: V21 <dbl>, V22 <dbl>, V24 <dbl>, V27 <dbl>,
## # V29 <dbl>, V30 <dbl>, V31 <dbl>, V33 <dbl>, V35 <dbl>, V36 <dbl>psych::alpha(tbl) ## Warning in psych::alpha(tbl): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( V1 V4 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = tbl)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.81 0.84 0.94 0.22 5.3 0.038 3.1 0.52 0.3
##
## lower alpha upper 95% confidence boundaries
## 0.73 0.81 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## V1 0.85 0.88 0.94 0.28 7.1 0.029 0.083 0.33
## V3 0.80 0.84 0.94 0.22 5.1 0.040 0.122 0.30
## V4 0.86 0.87 0.94 0.28 7.0 0.028 0.087 0.33
## V5 0.79 0.83 0.93 0.22 4.9 0.041 0.124 0.29
## V10 0.79 0.82 0.93 0.21 4.7 0.040 0.128 0.29
## V11 0.79 0.83 0.93 0.21 4.7 0.041 0.127 0.29
## V15 0.79 0.83 0.93 0.21 4.8 0.040 0.126 0.30
## V17 0.79 0.83 0.93 0.21 4.7 0.041 0.125 0.30
## V20 0.78 0.82 0.93 0.21 4.6 0.043 0.122 0.27
## V21 0.79 0.83 0.93 0.21 4.7 0.041 0.121 0.29
## V22 0.79 0.83 0.93 0.21 4.7 0.041 0.124 0.30
## V24 0.79 0.83 0.93 0.21 4.8 0.040 0.127 0.30
## V27 0.79 0.83 0.93 0.21 4.9 0.042 0.125 0.30
## V29 0.78 0.82 0.93 0.20 4.6 0.043 0.123 0.27
## V30 0.79 0.83 0.93 0.21 4.9 0.041 0.131 0.31
## V31 0.78 0.82 0.93 0.20 4.6 0.042 0.123 0.29
## V33 0.78 0.82 0.93 0.21 4.7 0.043 0.125 0.29
## V35 0.79 0.83 0.93 0.22 4.9 0.041 0.131 0.31
## V36 0.78 0.83 0.93 0.21 4.8 0.043 0.125 0.30
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## V1 44 -0.49 -0.52 -0.55 -0.58 2.3 1.25
## V3 44 0.48 0.47 0.45 0.37 2.8 1.26
## V4 44 -0.44 -0.47 -0.50 -0.54 2.3 1.41
## V5 44 0.54 0.54 0.51 0.44 3.7 1.23
## V10 44 0.62 0.67 0.66 0.58 4.4 0.73
## V11 44 0.61 0.65 0.63 0.54 3.8 1.03
## V15 44 0.57 0.63 0.63 0.51 4.3 0.82
## V17 44 0.60 0.65 0.64 0.53 4.2 0.91
## V20 44 0.70 0.70 0.68 0.63 3.3 1.15
## V21 44 0.60 0.65 0.65 0.53 3.5 0.95
## V22 44 0.59 0.65 0.64 0.53 4.1 0.91
## V24 44 0.55 0.60 0.58 0.49 4.3 0.80
## V27 44 0.61 0.55 0.55 0.52 2.1 1.27
## V29 44 0.74 0.73 0.73 0.70 1.6 0.92
## V30 44 0.62 0.58 0.56 0.53 3.0 1.34
## V31 44 0.72 0.72 0.71 0.67 1.6 0.89
## V33 44 0.70 0.67 0.67 0.63 2.4 1.19
## V35 44 0.59 0.54 0.52 0.51 2.8 1.20
## V36 44 0.67 0.62 0.61 0.58 2.9 1.44
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## V1 0.36 0.18 0.30 0.09 0.07 0
## V3 0.16 0.27 0.30 0.14 0.14 0
## V4 0.45 0.11 0.20 0.14 0.09 0
## V5 0.09 0.07 0.16 0.39 0.30 0
## V10 0.00 0.00 0.14 0.30 0.57 0
## V11 0.02 0.02 0.41 0.18 0.36 0
## V15 0.00 0.00 0.23 0.27 0.50 0
## V17 0.02 0.00 0.20 0.34 0.43 0
## V20 0.09 0.11 0.36 0.27 0.16 0
## V21 0.02 0.05 0.52 0.20 0.20 0
## V22 0.00 0.02 0.30 0.25 0.43 0
## V24 0.00 0.00 0.20 0.27 0.52 0
## V27 0.48 0.16 0.23 0.07 0.07 0
## V29 0.64 0.11 0.23 0.02 0.00 0
## V30 0.18 0.16 0.27 0.23 0.16 0
## V31 0.59 0.23 0.14 0.05 0.00 0
## V33 0.27 0.30 0.23 0.16 0.05 0
## V35 0.18 0.23 0.30 0.23 0.07 0
## V36 0.23 0.23 0.18 0.18 0.18 0psych::alpha(tbl, check.keys = TRUE)$total$std.alpha## Warning in psych::alpha(tbl, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.## [1] 0.91847633b Reliability - see “reliability function.pdf” Calculate reliability values of factors
semTools::reliability(fit)## MR3 MR1 MR2
## alpha 0.6497646 0.7440909 0.8958109
## omega 0.6518882 0.7412252 0.8988574
## omega2 0.6518882 0.7412252 0.8988574
## omega3 0.4424298 0.7374587 0.9003546
## avevar 0.4407139 0.4891054 0.5636193Cronbach’s Alpha
psych::alpha(tbl) ## Warning in psych::alpha(tbl): Some items were negatively correlated with the total scale and probably
## should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option## Some items ( V1 V4 ) were negatively correlated with the total scale and
## probably should be reversed.
## To do this, run the function again with the 'check.keys=TRUE' option##
## Reliability analysis
## Call: psych::alpha(x = tbl)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.81 0.84 0.94 0.22 5.3 0.038 3.1 0.52 0.3
##
## lower alpha upper 95% confidence boundaries
## 0.73 0.81 0.88
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## V1 0.85 0.88 0.94 0.28 7.1 0.029 0.083 0.33
## V3 0.80 0.84 0.94 0.22 5.1 0.040 0.122 0.30
## V4 0.86 0.87 0.94 0.28 7.0 0.028 0.087 0.33
## V5 0.79 0.83 0.93 0.22 4.9 0.041 0.124 0.29
## V10 0.79 0.82 0.93 0.21 4.7 0.040 0.128 0.29
## V11 0.79 0.83 0.93 0.21 4.7 0.041 0.127 0.29
## V15 0.79 0.83 0.93 0.21 4.8 0.040 0.126 0.30
## V17 0.79 0.83 0.93 0.21 4.7 0.041 0.125 0.30
## V20 0.78 0.82 0.93 0.21 4.6 0.043 0.122 0.27
## V21 0.79 0.83 0.93 0.21 4.7 0.041 0.121 0.29
## V22 0.79 0.83 0.93 0.21 4.7 0.041 0.124 0.30
## V24 0.79 0.83 0.93 0.21 4.8 0.040 0.127 0.30
## V27 0.79 0.83 0.93 0.21 4.9 0.042 0.125 0.30
## V29 0.78 0.82 0.93 0.20 4.6 0.043 0.123 0.27
## V30 0.79 0.83 0.93 0.21 4.9 0.041 0.131 0.31
## V31 0.78 0.82 0.93 0.20 4.6 0.042 0.123 0.29
## V33 0.78 0.82 0.93 0.21 4.7 0.043 0.125 0.29
## V35 0.79 0.83 0.93 0.22 4.9 0.041 0.131 0.31
## V36 0.78 0.83 0.93 0.21 4.8 0.043 0.125 0.30
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## V1 44 -0.49 -0.52 -0.55 -0.58 2.3 1.25
## V3 44 0.48 0.47 0.45 0.37 2.8 1.26
## V4 44 -0.44 -0.47 -0.50 -0.54 2.3 1.41
## V5 44 0.54 0.54 0.51 0.44 3.7 1.23
## V10 44 0.62 0.67 0.66 0.58 4.4 0.73
## V11 44 0.61 0.65 0.63 0.54 3.8 1.03
## V15 44 0.57 0.63 0.63 0.51 4.3 0.82
## V17 44 0.60 0.65 0.64 0.53 4.2 0.91
## V20 44 0.70 0.70 0.68 0.63 3.3 1.15
## V21 44 0.60 0.65 0.65 0.53 3.5 0.95
## V22 44 0.59 0.65 0.64 0.53 4.1 0.91
## V24 44 0.55 0.60 0.58 0.49 4.3 0.80
## V27 44 0.61 0.55 0.55 0.52 2.1 1.27
## V29 44 0.74 0.73 0.73 0.70 1.6 0.92
## V30 44 0.62 0.58 0.56 0.53 3.0 1.34
## V31 44 0.72 0.72 0.71 0.67 1.6 0.89
## V33 44 0.70 0.67 0.67 0.63 2.4 1.19
## V35 44 0.59 0.54 0.52 0.51 2.8 1.20
## V36 44 0.67 0.62 0.61 0.58 2.9 1.44
##
## Non missing response frequency for each item
## 1 2 3 4 5 miss
## V1 0.36 0.18 0.30 0.09 0.07 0
## V3 0.16 0.27 0.30 0.14 0.14 0
## V4 0.45 0.11 0.20 0.14 0.09 0
## V5 0.09 0.07 0.16 0.39 0.30 0
## V10 0.00 0.00 0.14 0.30 0.57 0
## V11 0.02 0.02 0.41 0.18 0.36 0
## V15 0.00 0.00 0.23 0.27 0.50 0
## V17 0.02 0.00 0.20 0.34 0.43 0
## V20 0.09 0.11 0.36 0.27 0.16 0
## V21 0.02 0.05 0.52 0.20 0.20 0
## V22 0.00 0.02 0.30 0.25 0.43 0
## V24 0.00 0.00 0.20 0.27 0.52 0
## V27 0.48 0.16 0.23 0.07 0.07 0
## V29 0.64 0.11 0.23 0.02 0.00 0
## V30 0.18 0.16 0.27 0.23 0.16 0
## V31 0.59 0.23 0.14 0.05 0.00 0
## V33 0.27 0.30 0.23 0.16 0.05 0
## V35 0.18 0.23 0.30 0.23 0.07 0
## V36 0.23 0.23 0.18 0.18 0.18 0Discriminant validity
Assessing discriminant validity using Heterotrait-Monotrait Ratio
semTools::htmt(mdl, tbl, sample.cov = NULL, missing = 'listwise', ordered = NULL, absolute = TRUE)## MR3 MR1 MR2
## MR3 1.000
## MR1 0.902 1.000
## MR2 0.526 0.608 1.000Multitrait Multimethod approach of scale validation
y <- psy::mtmm(tbl,list(c("V15","V22","V17","V24","V10","V21","V11"),
c("V1","V4","V3","V5","V20"),
c("V27","V36","V33","V29","V31")),
#y <- psy::mtmm(tbl,list(c('V3', 'V5', 'V20'),
# c('V10', 'V11', 'V15', 'V17', 'V21', 'V22', 'V24'),
# c('V1', 'V4', 'V27', 'V29', 'V30', 'V31', 'V33', 'V35', 'V36')),
color=TRUE,
itemTot=TRUE,
graphItem=FALSE,
stripChart=FALSE,
namesDim=NULL)
y<-psy::mtmm(tbl,list(c("V15","V22","V17","V24","V10","V21","V11"),c("V1","V4","V3","V5","V20"),c("V27","V35","V36","V30","V33","V29","V31")),color=TRUE,itemTot=TRUE,graphItem=FALSE,stripChart=FALSE,namesDim=NULL)