set.seed(5212023)
library(tidyverse)
library(lavaan)
library(psych)
library(semTools)
library(semPlot)
data <- psych::bfi[,16:25]
cfa_data <- data[sample(nrow(data),300),]
sem_data <- lavaan::PoliticalDemocracy %>% na.omit()data using sample() function
PoliticalDemocracy data set from the lavaan package. Omit missing data using the na.omit() function
# Create CFA Model
cfa_model <- 'nfactor =~ N1 + N2 + N3 + N4 + N5
ofactor =~ O1 + O2 + O3 + O4 + O5'
fit_cfa <- cfa(cfa_model, data = cfa_data)
summary(fit_cfa, fit.measures = TRUE)
semPaths(fit_cfa,'std')cfa() function
summary() function with the fit.measures argument set to TRUE
semPaths() function with standardized coefficients using the std argument
lavaan 0.6.15 ended normally after 39 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Used Total
Number of observations 284 300
Model Test User Model:
Test statistic 126.828
Degrees of freedom 34
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 785.605
Degrees of freedom 45
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.875
Tucker-Lewis Index (TLI) 0.834
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4737.244
Loglikelihood unrestricted model (H1) -4673.830
Akaike (AIC) 9516.489
Bayesian (BIC) 9593.117
Sample-size adjusted Bayesian (SABIC) 9526.525
Root Mean Square Error of Approximation:
RMSEA 0.098
90 Percent confidence interval - lower 0.080
90 Percent confidence interval - upper 0.117
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.952
Standardized Root Mean Square Residual:
SRMR 0.084
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
nfactor =~
N1 1.000
N2 0.979 0.067 14.513 0.000
N3 0.809 0.071 11.478 0.000
N4 0.794 0.070 11.382 0.000
N5 0.746 0.076 9.796 0.000
ofactor =~
O1 1.000
O2 -0.580 0.159 -3.635 0.000
O3 1.314 0.250 5.249 0.000
O4 0.266 0.125 2.134 0.033
O5 -0.799 0.158 -5.051 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
nfactor ~~
ofactor -0.070 0.072 -0.967 0.333
Variances:
Estimate Std.Err z-value P(>|z|)
.N1 0.838 0.109 7.720 0.000
.N2 0.759 0.101 7.491 0.000
.N3 1.442 0.139 10.387 0.000
.N4 1.424 0.137 10.427 0.000
.N5 1.921 0.175 10.953 0.000
.O1 0.879 0.115 7.630 0.000
.O2 2.025 0.177 11.468 0.000
.O3 0.595 0.158 3.769 0.000
.O4 1.415 0.120 11.787 0.000
.O5 1.583 0.147 10.733 0.000
nfactor 1.779 0.224 7.947 0.000
ofactor 0.491 0.125 3.932 0.000For SEM and CFA models, the =~ syntax is used. You can interpret it as an “equals” sign more or less
# Create SEM Model
sem_model <- 'ind60 =~ x1 + x2 + x3
dem60 =~ y1 + y2 + y3 + y4
dem65 =~ y5 + y6 + y7 + y8
dem60 ~ ind60
dem65 ~ ind60 + dem60
y1 ~~ y5
y2 ~~ y4 + y6
y3 ~~ y7
y4 ~~ y8
y6 ~~ y8'
fit_sem <- sem(sem_model, data = sem_data)
summary(fit_sem, standardized = TRUE, fit.measures = TRUE)
semPaths(fit_sem,'std')sem() function
summary() function with the standardized and fit.measures() arguments set to TRUE
semPaths() function with standardized coefficients using the std argument.
lavaan 0.6.15 ended normally after 68 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 31
Number of observations 75
Model Test User Model:
Test statistic 38.125
Degrees of freedom 35
P-value (Chi-square) 0.329
Model Test Baseline Model:
Test statistic 730.654
Degrees of freedom 55
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.995
Tucker-Lewis Index (TLI) 0.993
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1547.791
Loglikelihood unrestricted model (H1) -1528.728
Akaike (AIC) 3157.582
Bayesian (BIC) 3229.424
Sample-size adjusted Bayesian (SABIC) 3131.720
Root Mean Square Error of Approximation:
RMSEA 0.035
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.092
P-value H_0: RMSEA <= 0.050 0.611
P-value H_0: RMSEA >= 0.080 0.114
Standardized Root Mean Square Residual:
SRMR 0.044
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
ind60 =~
x1 1.000 0.670 0.920
x2 2.180 0.139 15.742 0.000 1.460 0.973
x3 1.819 0.152 11.967 0.000 1.218 0.872
dem60 =~
y1 1.000 2.223 0.850
y2 1.257 0.182 6.889 0.000 2.794 0.717
y3 1.058 0.151 6.987 0.000 2.351 0.722
y4 1.265 0.145 8.722 0.000 2.812 0.846
dem65 =~
y5 1.000 2.103 0.808
y6 1.186 0.169 7.024 0.000 2.493 0.746
y7 1.280 0.160 8.002 0.000 2.691 0.824
y8 1.266 0.158 8.007 0.000 2.662 0.828
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
dem60 ~
ind60 1.483 0.399 3.715 0.000 0.447 0.447
dem65 ~
ind60 0.572 0.221 2.586 0.010 0.182 0.182
dem60 0.837 0.098 8.514 0.000 0.885 0.885
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 ~~
.y5 0.624 0.358 1.741 0.082 0.624 0.296
.y2 ~~
.y4 1.313 0.702 1.871 0.061 1.313 0.273
.y6 2.153 0.734 2.934 0.003 2.153 0.356
.y3 ~~
.y7 0.795 0.608 1.308 0.191 0.795 0.191
.y4 ~~
.y8 0.348 0.442 0.787 0.431 0.348 0.109
.y6 ~~
.y8 1.356 0.568 2.386 0.017 1.356 0.338
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.x1 0.082 0.019 4.184 0.000 0.082 0.154
.x2 0.120 0.070 1.718 0.086 0.120 0.053
.x3 0.467 0.090 5.177 0.000 0.467 0.239
.y1 1.891 0.444 4.256 0.000 1.891 0.277
.y2 7.373 1.374 5.366 0.000 7.373 0.486
.y3 5.067 0.952 5.324 0.000 5.067 0.478
.y4 3.148 0.739 4.261 0.000 3.148 0.285
.y5 2.351 0.480 4.895 0.000 2.351 0.347
.y6 4.954 0.914 5.419 0.000 4.954 0.443
.y7 3.431 0.713 4.814 0.000 3.431 0.322
.y8 3.254 0.695 4.685 0.000 3.254 0.315
ind60 0.448 0.087 5.173 0.000 1.000 1.000
.dem60 3.956 0.921 4.295 0.000 0.800 0.800
.dem65 0.172 0.215 0.803 0.422 0.039 0.039As stated above, for SEM models we want the =~ syntax. For reference, a regression syntax is simply ~ while residuals syntax are ~~. Each of these can as with SEM, be interpreted as an “equals” sign.