EFA and CFA Intro
Dan Isbell
4/17/2021
Get ready by loading some packages:
library(tidyverse)
library(psych)
library(lavaan)
library(semPlot)Part 1: Exploring EFA and CFA
To start off, we’ll use the well-known Holzinger & Swineford (1939) dataset to get familiar with EFA and CFA in R. This data is included in the lavaan package, so we can load it with the data() function.
data(HolzingerSwineford1939)
summary(HolzingerSwineford1939)## id sex ageyr agemo
## Min. : 1.0 Min. :1.000 Min. :11 Min. : 0.000
## 1st Qu.: 82.0 1st Qu.:1.000 1st Qu.:12 1st Qu.: 2.000
## Median :163.0 Median :2.000 Median :13 Median : 5.000
## Mean :176.6 Mean :1.515 Mean :13 Mean : 5.375
## 3rd Qu.:272.0 3rd Qu.:2.000 3rd Qu.:14 3rd Qu.: 8.000
## Max. :351.0 Max. :2.000 Max. :16 Max. :11.000
##
## school grade x1 x2
## Grant-White:145 Min. :7.000 Min. :0.6667 Min. :2.250
## Pasteur :156 1st Qu.:7.000 1st Qu.:4.1667 1st Qu.:5.250
## Median :7.000 Median :5.0000 Median :6.000
## Mean :7.477 Mean :4.9358 Mean :6.088
## 3rd Qu.:8.000 3rd Qu.:5.6667 3rd Qu.:6.750
## Max. :8.000 Max. :8.5000 Max. :9.250
## NA's :1
## x3 x4 x5 x6
## Min. :0.250 Min. :0.000 Min. :1.000 Min. :0.1429
## 1st Qu.:1.375 1st Qu.:2.333 1st Qu.:3.500 1st Qu.:1.4286
## Median :2.125 Median :3.000 Median :4.500 Median :2.0000
## Mean :2.250 Mean :3.061 Mean :4.341 Mean :2.1856
## 3rd Qu.:3.125 3rd Qu.:3.667 3rd Qu.:5.250 3rd Qu.:2.7143
## Max. :4.500 Max. :6.333 Max. :7.000 Max. :6.1429
##
## x7 x8 x9
## Min. :1.304 Min. : 3.050 Min. :2.778
## 1st Qu.:3.478 1st Qu.: 4.850 1st Qu.:4.750
## Median :4.087 Median : 5.500 Median :5.417
## Mean :4.186 Mean : 5.527 Mean :5.374
## 3rd Qu.:4.913 3rd Qu.: 6.100 3rd Qu.:6.083
## Max. :7.435 Max. :10.000 Max. :9.250
## One initial step with any factor analysis is to check the factorability of the data.
KMO(select(HolzingerSwineford1939, x1:x9))## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = select(HolzingerSwineford1939, x1:x9))
## Overall MSA = 0.75
## MSA for each item =
## x1 x2 x3 x4 x5 x6 x7 x8 x9
## 0.81 0.78 0.73 0.76 0.74 0.81 0.59 0.68 0.79cortest.bartlett(select(HolzingerSwineford1939, x1:x9), n = 301)## R was not square, finding R from data## $chisq
## [1] 904.0971
##
## $p.value
## [1] 1.912079e-166
##
## $df
## [1] 36That all looks fine, so we’ll proceed with EFA.
EFA
We’ll use the fa() function from psych and our initial goal is to determine the number of likely factors in the data.
hs.efa <- fa(select(HolzingerSwineford1939, x1:x9), nfactors = 8,
rotate = "none", fm = "ml")
hs.efa## Factor Analysis using method = ml
## Call: fa(r = select(HolzingerSwineford1939, x1:x9), nfactors = 8, rotate = "none",
## fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML2 ML4 ML3 ML5 ML6 ML7 ML8 h2 u2 com
## x1 0.37 0.48 0.33 -0.21 -0.12 -0.18 -0.07 -0.09 0.58 0.420 3.9
## x2 0.18 0.25 0.37 -0.17 -0.01 0.13 0.21 0.09 0.33 0.671 4.0
## x3 0.14 0.51 0.39 -0.19 -0.03 0.22 -0.05 -0.07 0.52 0.480 2.9
## x4 0.83 0.14 -0.24 -0.32 -0.13 0.00 0.03 0.01 0.88 0.123 1.6
## x5 0.97 -0.12 0.05 0.11 -0.02 0.01 0.00 0.00 0.96 0.038 1.1
## x6 0.80 0.13 -0.03 -0.21 0.34 -0.02 -0.02 0.02 0.82 0.182 1.6
## x7 0.15 0.49 -0.42 0.35 0.01 0.11 -0.11 -0.03 0.59 0.406 3.3
## x8 0.17 0.59 -0.09 0.43 0.07 -0.07 0.17 -0.06 0.62 0.384 2.4
## x9 0.27 0.58 0.15 0.23 -0.09 -0.06 -0.08 0.19 0.54 0.456 2.3
##
## ML1 ML2 ML4 ML3 ML5 ML6 ML7 ML8
## SS loadings 2.56 1.54 0.66 0.63 0.17 0.12 0.10 0.06
## Proportion Var 0.28 0.17 0.07 0.07 0.02 0.01 0.01 0.01
## Cumulative Var 0.28 0.46 0.53 0.60 0.62 0.63 0.64 0.65
## Proportion Explained 0.44 0.26 0.11 0.11 0.03 0.02 0.02 0.01
## Cumulative Proportion 0.44 0.70 0.82 0.92 0.95 0.97 0.99 1.00
##
## Mean item complexity = 2.6
## Test of the hypothesis that 8 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3.05 with Chi Square of 904.1
## The degrees of freedom for the model are -8 and the objective function was 0
##
## The root mean square of the residuals (RMSR) is 0
## The df corrected root mean square of the residuals is NA
##
## The harmonic number of observations is 301 with the empirical chi square 0 with prob < NA
## The total number of observations was 301 with Likelihood Chi Square = 0 with prob < NA
##
## Tucker Lewis Index of factoring reliability = 1.042
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML2 ML4 ML3 ML5
## Correlation of (regression) scores with factors 0.99 0.90 0.80 0.85 0.68
## Multiple R square of scores with factors 0.97 0.80 0.65 0.72 0.47
## Minimum correlation of possible factor scores 0.94 0.61 0.29 0.44 -0.07
## ML6 ML7 ML8
## Correlation of (regression) scores with factors 0.45 0.41 0.35
## Multiple R square of scores with factors 0.20 0.17 0.12
## Minimum correlation of possible factor scores -0.60 -0.66 -0.75Two approaches to determining number of factors are a screeplot and parallel analysis. First, the screeplot of eigenvalues:
plot(hs.efa$e.values)
It looks like there are at least 3 factors - maybe 4.
Let’s try the parallel analysis:
fa.parallel(select(HolzingerSwineford1939, x1:x9), fa = "fa", fm = "ml")
## Parallel analysis suggests that the number of factors = 3 and the number of components = NAThis indicates that we have 3 factors which are above the level of random noise. 3 seems like a good number to go with.
Now we fit a 3-factor solution and rotate it - we’ll use an oblique rotation that allows the factors to correlate.
hs.efa3 <- fa(select(HolzingerSwineford1939, x1:x9), nfactors = 3, rotate = "oblimin", fm = "ml")## Loading required namespace: GPArotationhs.efa3## Factor Analysis using method = ml
## Call: fa(r = select(HolzingerSwineford1939, x1:x9), nfactors = 3, rotate = "oblimin",
## fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML1 ML3 ML2 h2 u2 com
## x1 0.19 0.60 0.03 0.49 0.51 1.2
## x2 0.04 0.51 -0.12 0.25 0.75 1.1
## x3 -0.07 0.69 0.02 0.46 0.54 1.0
## x4 0.84 0.02 0.01 0.72 0.28 1.0
## x5 0.89 -0.07 0.01 0.76 0.24 1.0
## x6 0.81 0.08 -0.01 0.69 0.31 1.0
## x7 0.04 -0.15 0.72 0.50 0.50 1.1
## x8 -0.03 0.10 0.70 0.53 0.47 1.0
## x9 0.03 0.37 0.46 0.46 0.54 1.9
##
## ML1 ML3 ML2
## SS loadings 2.24 1.34 1.28
## Proportion Var 0.25 0.15 0.14
## Cumulative Var 0.25 0.40 0.54
## Proportion Explained 0.46 0.28 0.26
## Cumulative Proportion 0.46 0.74 1.00
##
## With factor correlations of
## ML1 ML3 ML2
## ML1 1.00 0.33 0.22
## ML3 0.33 1.00 0.27
## ML2 0.22 0.27 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 3.05 with Chi Square of 904.1
## The degrees of freedom for the model are 12 and the objective function was 0.08
##
## The root mean square of the residuals (RMSR) is 0.02
## The df corrected root mean square of the residuals is 0.03
##
## The harmonic number of observations is 301 with the empirical chi square 8.03 with prob < 0.78
## The total number of observations was 301 with Likelihood Chi Square = 22.38 with prob < 0.034
##
## Tucker Lewis Index of factoring reliability = 0.964
## RMSEA index = 0.053 and the 90 % confidence intervals are 0.015 0.088
## BIC = -46.11
## Fit based upon off diagonal values = 1
## Measures of factor score adequacy
## ML1 ML3 ML2
## Correlation of (regression) scores with factors 0.94 0.84 0.85
## Multiple R square of scores with factors 0.89 0.71 0.72
## Minimum correlation of possible factor scores 0.78 0.42 0.45CFA
Now we’ll use the same data to run a CFA. We’ll be aiming for a 3 factor solution based on the theory behind the various measures in this dataset.
It’s important to note that it is not good practice to use a CFA to ‘confirm’ the findings of an EFA - it’s better to use an EFA to help determine the number of factors, but then to collect more data to test one or more competing models based on that general factorization.
As you’ll see in Step 1 below, our CFA model is much more restricted than the EFA model.
Step 1: Specify the Model
hs.mod <- 'visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9'Step 2: Estimate (fit) the model
hs.fit <- cfa(hs.mod, data = HolzingerSwineford1939)Step 3: Model Fit and Step 4: Interpret
summary(hs.fit, fit.measures = TRUE)## lavaan 0.6-7 ended normally after 35 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 21
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 85.306
## Degrees of freedom 24
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 918.852
## Degrees of freedom 36
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.931
## Tucker-Lewis Index (TLI) 0.896
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -3737.745
## Loglikelihood unrestricted model (H1) -3695.092
##
## Akaike (AIC) 7517.490
## Bayesian (BIC) 7595.339
## Sample-size adjusted Bayesian (BIC) 7528.739
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.092
## 90 Percent confidence interval - lower 0.071
## 90 Percent confidence interval - upper 0.114
## P-value RMSEA <= 0.05 0.001
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## visual =~
## x1 1.000
## x2 0.554 0.100 5.554 0.000
## x3 0.729 0.109 6.685 0.000
## textual =~
## x4 1.000
## x5 1.113 0.065 17.014 0.000
## x6 0.926 0.055 16.703 0.000
## speed =~
## x7 1.000
## x8 1.180 0.165 7.152 0.000
## x9 1.082 0.151 7.155 0.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## visual ~~
## textual 0.408 0.074 5.552 0.000
## speed 0.262 0.056 4.660 0.000
## textual ~~
## speed 0.173 0.049 3.518 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .x1 0.549 0.114 4.833 0.000
## .x2 1.134 0.102 11.146 0.000
## .x3 0.844 0.091 9.317 0.000
## .x4 0.371 0.048 7.779 0.000
## .x5 0.446 0.058 7.642 0.000
## .x6 0.356 0.043 8.277 0.000
## .x7 0.799 0.081 9.823 0.000
## .x8 0.488 0.074 6.573 0.000
## .x9 0.566 0.071 8.003 0.000
## visual 0.809 0.145 5.564 0.000
## textual 0.979 0.112 8.737 0.000
## speed 0.384 0.086 4.451 0.000semPaths(hs.fit, "std", layout = "tree", intercepts = F, residuals = T, nDigits = 2,
label.cex = 1, edge.label.cex=.95, fade = F)
Part 2: Working with some measures of L2 morphosyntax
d <- read_csv("cfa_data.csv")
summary(d)## SPRt_s WMTt OPr EIr
## Min. :-0.60412 Min. :-0.67012 Min. :0.3750 Min. :0.700
## 1st Qu.:-0.17407 1st Qu.:-0.12850 1st Qu.:0.7265 1st Qu.:1.300
## Median : 0.07328 Median : 0.06882 Median :0.8400 Median :1.550
## Mean : 0.05501 Mean : 0.04815 Mean :0.8176 Mean :1.529
## 3rd Qu.: 0.24032 3rd Qu.: 0.20718 3rd Qu.:0.9384 3rd Qu.:1.800
## Max. : 0.92267 Max. : 0.66606 Max. :1.0000 Max. :2.100
## NA's :26 NA's :31 NA's :28 NA's :44
## TAGJT TWGJT UAGJT_ug UWGJT_ug
## Min. :0.2083 Min. :0.1250 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.4896 1st Qu.:0.5417 1st Qu.:0.3333 1st Qu.:0.4167
## Median :0.5417 Median :0.5833 Median :0.4167 Median :0.6667
## Mean :0.5687 Mean :0.6083 Mean :0.4476 Mean :0.6194
## 3rd Qu.:0.6250 3rd Qu.:0.7083 3rd Qu.:0.5833 3rd Qu.:0.7708
## Max. :1.0000 Max. :0.9583 Max. :1.0000 Max. :1.0000
## NA's :8 NA's :36 NA's :8 NA's :36
## MKT
## Min. :0.2083
## 1st Qu.:0.5417
## Median :0.6667
## Mean :0.6401
## 3rd Qu.:0.7500
## Max. :1.0000
## NA's :21Factorability:
KMO(d)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = d)
## Overall MSA = 0.77
## MSA for each item =
## SPRt_s WMTt OPr EIr TAGJT TWGJT UAGJT_ug UWGJT_ug
## 0.70 0.51 0.81 0.83 0.79 0.77 0.78 0.75
## MKT
## 0.76cortest.bartlett(cor(d, use = "pairwise.complete.obs"), n = 156)## $chisq
## [1] 243.5961
##
## $p.value
## [1] 1.183665e-32
##
## $df
## [1] 36EFA
EFA <- fa(d, nfactors = 8, rotate = "none", fm = "ml")
summary(EFA)##
## Factor analysis with Call: fa(r = d, nfactors = 8, rotate = "none", fm = "ml")
##
## Test of the hypothesis that 8 factors are sufficient.
## The degrees of freedom for the model is -8 and the objective function was 0
## The number of observations was 156 with Chi Square = 0 with prob < NA
##
## The root mean square of the residuals (RMSA) is 0
## The df corrected root mean square of the residuals is NA
##
## Tucker Lewis Index of factoring reliability = 1.181plot(EFA$e.values)
fa.parallel(d, fa = "fa", fm = "ml") 
## Parallel analysis suggests that the number of factors = 1 and the number of components = NAEFA2 <- fa(d, nfactors = 2, rotate = "oblimin", fm = "ml")
EFA2## Factor Analysis using method = ml
## Call: fa(r = d, nfactors = 2, rotate = "oblimin", fm = "ml")
## Standardized loadings (pattern matrix) based upon correlation matrix
## ML2 ML1 h2 u2 com
## SPRt_s 0.19 0.01 0.037 0.96 1.0
## WMTt 0.20 -0.20 0.039 0.96 2.0
## OPr 0.56 -0.02 0.300 0.70 1.0
## EIr 0.63 -0.05 0.365 0.63 1.0
## TAGJT 0.63 -0.05 0.365 0.63 1.0
## TWGJT 0.74 0.07 0.605 0.39 1.0
## UAGJT_ug 0.24 0.04 0.071 0.93 1.1
## UWGJT_ug 0.00 0.99 0.980 0.02 1.0
## MKT 0.27 0.37 0.312 0.69 1.8
##
## ML2 ML1
## SS loadings 1.88 1.20
## Proportion Var 0.21 0.13
## Cumulative Var 0.21 0.34
## Proportion Explained 0.61 0.39
## Cumulative Proportion 0.61 1.00
##
## With factor correlations of
## ML2 ML1
## ML2 1.00 0.51
## ML1 0.51 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 factors are sufficient.
##
## The degrees of freedom for the null model are 36 and the objective function was 1.61 with Chi Square of 243.6
## The degrees of freedom for the model are 19 and the objective function was 0.14
##
## The root mean square of the residuals (RMSR) is 0.05
## The df corrected root mean square of the residuals is 0.07
##
## The harmonic number of observations is 112 with the empirical chi square 20.95 with prob < 0.34
## The total number of observations was 156 with Likelihood Chi Square = 21.65 with prob < 0.3
##
## Tucker Lewis Index of factoring reliability = 0.976
## RMSEA index = 0.029 and the 90 % confidence intervals are 0 0.079
## BIC = -74.3
## Fit based upon off diagonal values = 0.96
## Measures of factor score adequacy
## ML2 ML1
## Correlation of (regression) scores with factors 0.89 0.99
## Multiple R square of scores with factors 0.79 0.98
## Minimum correlation of possible factor scores 0.57 0.96CFA
Two models - we’ll compare a 1 and 2 factor model.
One <- '
# latent variable definitions
language =~ EIr + OPr + UWGJT_ug + MKT + TWGJT + MKT + SPRt_s + WMTt + TAGJT + UAGJT_ug
'
Two <- '
# latent variable definitions
implicit =~ EIr + OPr + TWGJT + TAGJT + WMTt + SPRt_s
explicit =~ UWGJT_ug + UAGJT_ug + MKT
# covariances
implicit~~explicit
'And then fit them both:
fitOne <- cfa(One, data = d, missing = "fiml", estimator = "MLR")
fitTwo <- cfa(Two, data = d, missing = "fiml", estimator = "MLR")And compare…
lavaan::summary(fitOne, estimates = T, standardized = T, fit.measures = T)## lavaan 0.6-7 ended normally after 84 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 27
##
## Number of observations 156
## Number of missing patterns 26
##
## Model Test User Model:
## Standard Robust
## Test Statistic 30.458 29.942
## Degrees of freedom 27 27
## P-value (Chi-square) 0.294 0.317
## Scaling correction factor 1.017
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 183.271 176.306
## Degrees of freedom 36 36
## P-value 0.000 0.000
## Scaling correction factor 1.040
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.977 0.979
## Tucker-Lewis Index (TLI) 0.969 0.972
##
## Robust Comparative Fit Index (CFI) 0.979
## Robust Tucker-Lewis Index (TLI) 0.973
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 274.605 274.605
## Scaling correction factor 1.010
## for the MLR correction
## Loglikelihood unrestricted model (H1) 289.834 289.834
## Scaling correction factor 1.014
## for the MLR correction
##
## Akaike (AIC) -495.211 -495.211
## Bayesian (BIC) -412.865 -412.865
## Sample-size adjusted Bayesian (BIC) -498.328 -498.328
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.029 0.026
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.071 0.070
## P-value RMSEA <= 0.05 0.753 0.774
##
## Robust RMSEA 0.027
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.070
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.059 0.059
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## language =~
## EIr 1.000 0.183 0.591
## OPr 0.433 0.091 4.785 0.000 0.079 0.526
## UWGJT_ug 0.723 0.167 4.325 0.000 0.132 0.556
## MKT 0.459 0.101 4.550 0.000 0.084 0.491
## TWGJT 0.594 0.099 6.005 0.000 0.109 0.787
## SPRt_s 0.385 0.179 2.150 0.032 0.071 0.234
## WMTt 0.104 0.133 0.782 0.434 0.019 0.074
## TAGJT 0.453 0.095 4.765 0.000 0.083 0.565
## UAGJT_ug 0.348 0.131 2.664 0.008 0.064 0.287
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .EIr 1.529 0.028 54.086 0.000 1.529 4.936
## .OPr 0.818 0.013 62.349 0.000 0.818 5.424
## .UWGJT_ug 0.617 0.021 28.925 0.000 0.617 2.590
## .MKT 0.640 0.015 43.732 0.000 0.640 3.738
## .TWGJT 0.606 0.012 50.090 0.000 0.606 4.381
## .SPRt_s 0.052 0.026 1.991 0.046 0.052 0.173
## .WMTt 0.046 0.023 2.000 0.046 0.046 0.180
## .TAGJT 0.567 0.012 47.599 0.000 0.567 3.861
## .UAGJT_ug 0.446 0.018 24.347 0.000 0.446 2.008
## language 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .EIr 0.062 0.010 6.195 0.000 0.062 0.650
## .OPr 0.016 0.002 7.497 0.000 0.016 0.723
## .UWGJT_ug 0.039 0.006 6.864 0.000 0.039 0.691
## .MKT 0.022 0.003 7.190 0.000 0.022 0.759
## .TWGJT 0.007 0.002 3.471 0.001 0.007 0.381
## .SPRt_s 0.086 0.010 8.765 0.000 0.086 0.945
## .WMTt 0.065 0.008 8.034 0.000 0.065 0.994
## .TAGJT 0.015 0.003 5.669 0.000 0.015 0.681
## .UAGJT_ug 0.045 0.006 7.231 0.000 0.045 0.918
## language 0.034 0.010 3.385 0.001 1.000 1.000lavaan::summary(fitTwo, estimates = T, standardized = T, fit.measures = T)## lavaan 0.6-7 ended normally after 95 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of free parameters 28
##
## Number of observations 156
## Number of missing patterns 26
##
## Model Test User Model:
## Standard Robust
## Test Statistic 21.043 21.508
## Degrees of freedom 26 26
## P-value (Chi-square) 0.740 0.715
## Scaling correction factor 0.978
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 183.271 176.306
## Degrees of freedom 36 36
## P-value 0.000 0.000
## Scaling correction factor 1.040
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000 1.000
## Tucker-Lewis Index (TLI) 1.047 1.044
##
## Robust Comparative Fit Index (CFI) 1.000
## Robust Tucker-Lewis Index (TLI) 1.042
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) 279.313 279.313
## Scaling correction factor 1.047
## for the MLR correction
## Loglikelihood unrestricted model (H1) 289.834 289.834
## Scaling correction factor 1.014
## for the MLR correction
##
## Akaike (AIC) -502.625 -502.625
## Bayesian (BIC) -417.229 -417.229
## Sample-size adjusted Bayesian (BIC) -505.858 -505.858
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000 0.000
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.047 0.049
## P-value RMSEA <= 0.05 0.961 0.953
##
## Robust RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.048
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.052 0.052
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## implicit =~
## EIr 1.000 0.182 0.586
## OPr 0.436 0.089 4.906 0.000 0.079 0.524
## TWGJT 0.626 0.116 5.392 0.000 0.114 0.821
## TAGJT 0.465 0.101 4.618 0.000 0.084 0.575
## WMTt 0.107 0.131 0.813 0.416 0.019 0.076
## SPRt_s 0.367 0.175 2.099 0.036 0.067 0.221
## explicit =~
## UWGJT_ug 1.000 0.180 0.752
## UAGJT_ug 0.328 0.179 1.830 0.067 0.059 0.265
## MKT 0.607 0.123 4.944 0.000 0.109 0.636
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## implicit ~~
## explicit 0.022 0.006 4.006 0.000 0.685 0.685
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .EIr 1.530 0.028 54.065 0.000 1.530 4.935
## .OPr 0.819 0.013 62.390 0.000 0.819 5.423
## .TWGJT 0.607 0.012 50.156 0.000 0.607 4.384
## .TAGJT 0.567 0.012 47.636 0.000 0.567 3.862
## .WMTt 0.046 0.023 2.005 0.045 0.046 0.180
## .SPRt_s 0.052 0.026 1.994 0.046 0.052 0.173
## .UWGJT_ug 0.616 0.021 29.071 0.000 0.616 2.583
## .UAGJT_ug 0.446 0.018 24.223 0.000 0.446 2.008
## .MKT 0.638 0.015 43.185 0.000 0.638 3.725
## implicit 0.000 0.000 0.000
## explicit 0.000 0.000 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .EIr 0.063 0.011 5.922 0.000 0.063 0.657
## .OPr 0.017 0.002 7.407 0.000 0.017 0.725
## .TWGJT 0.006 0.002 2.838 0.005 0.006 0.325
## .TAGJT 0.014 0.003 5.644 0.000 0.014 0.669
## .WMTt 0.065 0.008 8.008 0.000 0.065 0.994
## .SPRt_s 0.086 0.010 8.767 0.000 0.086 0.951
## .UWGJT_ug 0.025 0.007 3.355 0.001 0.025 0.434
## .UAGJT_ug 0.046 0.007 6.657 0.000 0.046 0.930
## .MKT 0.018 0.003 5.083 0.000 0.018 0.596
## implicit 0.033 0.010 3.247 0.001 1.000 1.000
## explicit 0.032 0.010 3.365 0.001 1.000 1.000