Module 10: Intro to Confirmatory Factor Analysis (CFA)
Dr. Broda
Load in packages - lavaan is our “go-to” package for CFA and SEM!
library(tidyverse) #all things data managementRegistered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ──────────────────────────────────────────────── tidyverse 1.3.0 ──
✓ ggplot2 3.3.3 ✓ purrr 0.3.4
✓ tibble 3.0.6 ✓ dplyr 1.0.4
✓ tidyr 1.1.2 ✓ stringr 1.4.0
✓ readr 1.4.0 ✓ forcats 0.5.1
── Conflicts ─────────────────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()library(haven) # importing data from other packages
library(lavaan) # all things SEMThis is lavaan 0.6-7
lavaan is BETA software! Please report any bugs.library(semPlot) # cool path diagrams for SEM modelsReturn to SPSS Anxiety Questionnaire, from Field, Ch. 17
saq <- read_dta("saq.dta")
glimpse(saq)Rows: 2,571
Columns: 23
$ Q01 <dbl+lbl> 2, 1, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 1,…
$ Q02 <dbl+lbl> 1, 1, 3, 1, 1, 1, 3, 2, 3, 4, 1, 1, 1, 2, 2, 1, 2, 2, 3, 1, 2, 2, 1, 1,…
$ Q03 <dbl+lbl> 4, 4, 2, 1, 3, 3, 3, 3, 1, 4, 5, 3, 3, 1, 3, 2, 5, 3, 4, 1, 3, 2, 4, 2,…
$ Q04 <dbl+lbl> 2, 3, 2, 4, 2, 2, 2, 2, 4, 3, 2, 3, 4, 2, 4, 2, 2, 3, 2, 2, 2, 4, 4, 2,…
$ Q05 <dbl+lbl> 2, 2, 4, 3, 2, 4, 2, 2, 5, 2, 2, 4, 3, 2, 2, 2, 1, 3, 3, 3, 4, 4, 2, 2,…
$ Q06 <dbl+lbl> 2, 2, 1, 3, 3, 4, 2, 2, 3, 1, 1, 3, 2, 2, 2, 2, 1, 4, 1, 4, 1, 5, 2, 1,…
$ Q07 <dbl+lbl> 3, 2, 2, 4, 3, 4, 2, 2, 5, 2, 2, 3, 3, 3, 3, 2, 1, 3, 1, 4, 2, 5, 4, 1,…
$ Q08 <dbl+lbl> 1, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 1, 3, 2, 2, 2, 1, 2, 1, 1, 1, 2, 3, 2,…
$ Q09 <dbl+lbl> 1, 5, 2, 2, 4, 4, 3, 4, 3, 3, 5, 3, 2, 2, 2, 2, 4, 5, 5, 5, 1, 3, 4, 2,…
$ Q10 <dbl+lbl> 2, 2, 2, 4, 2, 3, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 1, 2, 2, 1, 1, 3, 2, 1,…
$ Q11 <dbl+lbl> 1, 2, 3, 2, 2, 2, 2, 2, 5, 2, 1, 2, 3, 2, 2, 2, 1, 3, 1, 2, 1, 3, 3, 2,…
$ Q12 <dbl+lbl> 2, 3, 3, 2, 3, 4, 2, 3, 5, 3, 3, 3, 4, 4, 3, 3, 2, 3, 3, 5, 4, 3, 3, 4,…
$ Q13 <dbl+lbl> 2, 1, 2, 2, 3, 3, 2, 2, 5, 2, 1, 2, 4, 2, 2, 2, 1, 3, 1, 2, 1, 4, 2, 3,…
$ Q14 <dbl+lbl> 2, 3, 4, 3, 2, 3, 2, 2, 5, 1, 2, 2, 4, 4, 3, 3, 1, 3, 2, 5, 1, 3, 4, 2,…
$ Q15 <dbl+lbl> 2, 4, 2, 3, 2, 5, 2, 3, 5, 2, 1, 3, 4, 4, 3, 2, 1, 4, 2, 5, 1, 2, 4, 4,…
$ Q16 <dbl+lbl> 3, 3, 3, 3, 2, 2, 2, 2, 5, 3, 2, 3, 4, 4, 4, 3, 2, 3, 3, 5, 2, 3, 4, 2,…
$ Q17 <dbl+lbl> 1, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 1, 2, 1, 4, 3, 2,…
$ Q18 <dbl+lbl> 2, 2, 3, 4, 3, 5, 2, 2, 5, 2, 2, 2, 3, 4, 3, 3, 1, 2, 1, 5, 1, 4, 3, 1,…
$ Q19 <dbl+lbl> 3, 3, 1, 2, 3, 1, 3, 4, 2, 3, 5, 3, 2, 1, 3, 2, 4, 2, 4, 1, 2, 2, 2, 1,…
$ Q20 <dbl+lbl> 2, 4, 4, 4, 4, 5, 2, 3, 5, 3, 3, 4, 4, 5, 4, 3, 2, 3, 2, 5, 4, 5, 3, 5,…
$ Q21 <dbl+lbl> 2, 4, 3, 4, 2, 3, 2, 2, 5, 2, 2, 3, 4, 5, 4, 2, 1, 3, 2, 5, 3, 5, 4, 2,…
$ Q22 <dbl+lbl> 2, 4, 2, 4, 4, 1, 4, 4, 3, 4, 5, 4, 3, 3, 4, 3, 4, 3, 4, 5, 2, 2, 3, 4,…
$ Q23 <dbl+lbl> 5, 2, 2, 3, 4, 4, 4, 4, 3, 4, 5, 4, 4, 1, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5,…Reverse Code Item 3, Like Last Time
saq.clean <-saq %>%
mutate(.,
Q03R = 6- Q03) %>%
select(.,
-Q03)Double check that the reverse coding worked:
glimpse(saq.clean$Q03R) num [1:2571] 2 2 4 5 3 3 3 3 5 2 ...Specifying, running, and interpreting a CFA for the “Computers” subscale
Note the single quotation mark at the start and end of the CFA model below. This is required for lavaan to correctly interpret and estimate your CFA model.
computers_cfa1 <- 'computers =~ Q06 + Q07 + Q10 + Q12 + Q13 + Q14 + Q15 + Q18'
computers_cfa1_model <- cfa(computers_cfa1, data=saq.clean)
summary(computers_cfa1_model)lavaan 0.6-7 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 16
Number of observations 2571
Model Test User Model:
Test statistic 253.847
Degrees of freedom 20
P-value (Chi-square) 0.000
Parameter Estimates:
Standard errors Standard
Information Expected
Information saturated (h1) model Structured
Latent Variables:
Estimate Std.Err z-value P(>|z|)
computers =~
Q06 1.000
Q07 1.017 0.035 29.399 0.000
Q10 0.503 0.026 19.289 0.000
Q12 0.772 0.028 27.243 0.000
Q13 0.892 0.030 29.853 0.000
Q14 0.878 0.031 28.235 0.000
Q15 0.718 0.031 23.486 0.000
Q18 1.061 0.034 31.504 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.Q06 0.706 0.023 31.044 0.000
.Q07 0.643 0.021 30.381 0.000
.Q10 0.629 0.018 34.501 0.000
.Q12 0.511 0.016 31.897 0.000
.Q13 0.460 0.015 29.963 0.000
.Q14 0.572 0.018 31.280 0.000
.Q15 0.734 0.022 33.485 0.000
.Q18 0.487 0.017 27.960 0.000
computers 0.552 0.031 17.693 0.000By default, lavaan gives the latent variables its scale by fixing the loading of the first item to 1 (also known as the marker method). Other options are possible (for example, fixing the variance of the latent variable to 1). In order to free a parameter, put NA* in front of the parameter to be freed, to fix a parameter to 1, put 1* in front of the parameter to be fixed. For example, the syntax NA*q03 would free the loading of the first item because by default marker method fixes it to one, and f ~~ 1*f would fix the variance of the latent factor to one.
Visualize it with the semPaths function from the semPlot package
semPlot::semPaths(computers_cfa1_model, whatLabels = "est")
Same thing, but with standardized estimates…just re-run the summary function
summary(computers_cfa1_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 16
Number of observations 2571
Model Test User Model:
Test statistic 253.847
Degrees of freedom 20
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 6309.869
Degrees of freedom 28
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.963
Tucker-Lewis Index (TLI) 0.948
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -26155.590
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 52343.180
Bayesian (BIC) 52436.812
Sample-size adjusted Bayesian (BIC) 52385.976
Root Mean Square Error of Approximation:
RMSEA 0.067
90 Percent confidence interval - lower 0.060
90 Percent confidence interval - upper 0.075
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.031
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
computers =~
Q06 1.000 0.743 0.662
Q07 1.017 0.035 29.399 0.000 0.756 0.686
Q10 0.503 0.026 19.289 0.000 0.374 0.426
Q12 0.772 0.028 27.243 0.000 0.574 0.626
Q13 0.892 0.030 29.853 0.000 0.663 0.699
Q14 0.878 0.031 28.235 0.000 0.652 0.653
Q15 0.718 0.031 23.486 0.000 0.533 0.528
Q18 1.061 0.034 31.504 0.000 0.789 0.749
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q06 0.706 0.023 31.044 0.000 0.706 0.561
.Q07 0.643 0.021 30.381 0.000 0.643 0.530
.Q10 0.629 0.018 34.501 0.000 0.629 0.818
.Q12 0.511 0.016 31.897 0.000 0.511 0.608
.Q13 0.460 0.015 29.963 0.000 0.460 0.512
.Q14 0.572 0.018 31.280 0.000 0.572 0.574
.Q15 0.734 0.022 33.485 0.000 0.734 0.721
.Q18 0.487 0.017 27.960 0.000 0.487 0.439
computers 0.552 0.031 17.693 0.000 1.000 1.000Visualize the standardized estimates
semPlot::semPaths(computers_cfa1_model, whatLabels = "stand")
Should we add another item? We can test this!
computers_cfa2 <- ' computers =~ Q06 + Q07 + Q10 + Q12 + Q13 + Q14 + Q15 + Q18 + Q23'
computers_cfa2_model <- cfa(computers_cfa2, data=saq.clean)
summary(computers_cfa2_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 18
Number of observations 2571
Model Test User Model:
Test statistic 258.748
Degrees of freedom 27
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 6334.827
Degrees of freedom 36
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.963
Tucker-Lewis Index (TLI) 0.951
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -29903.202
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 59842.405
Bayesian (BIC) 59947.741
Sample-size adjusted Bayesian (BIC) 59890.550
Root Mean Square Error of Approximation:
RMSEA 0.058
90 Percent confidence interval - lower 0.051
90 Percent confidence interval - upper 0.064
P-value RMSEA <= 0.05 0.022
Standardized Root Mean Square Residual:
SRMR 0.028
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
computers =~
Q06 1.000 0.743 0.662
Q07 1.017 0.035 29.418 0.000 0.756 0.686
Q10 0.503 0.026 19.310 0.000 0.374 0.426
Q12 0.771 0.028 27.242 0.000 0.573 0.626
Q13 0.891 0.030 29.855 0.000 0.662 0.699
Q14 0.877 0.031 28.236 0.000 0.652 0.653
Q15 0.718 0.031 23.502 0.000 0.533 0.529
Q18 1.061 0.034 31.528 0.000 0.789 0.749
Q23 -0.134 0.030 -4.463 0.000 -0.099 -0.095
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q06 0.706 0.023 31.047 0.000 0.706 0.561
.Q07 0.643 0.021 30.385 0.000 0.643 0.530
.Q10 0.629 0.018 34.500 0.000 0.629 0.818
.Q12 0.511 0.016 31.910 0.000 0.511 0.609
.Q13 0.460 0.015 29.984 0.000 0.460 0.512
.Q14 0.572 0.018 31.295 0.000 0.572 0.574
.Q15 0.734 0.022 33.486 0.000 0.734 0.721
.Q18 0.487 0.017 27.962 0.000 0.487 0.439
.Q23 1.079 0.030 35.798 0.000 1.079 0.991
computers 0.552 0.031 17.702 0.000 1.000 1.000Now, try a CFA for the “friends” subscale (with standardized estimates)
friends_cfa <- ' friends =~ Q02 + Q09 + Q19 + Q22 + Q23'
friends_cfa_model <- cfa(friends_cfa, data=saq.clean)
summary(friends_cfa_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 10
Number of observations 2571
Model Test User Model:
Test statistic 44.608
Degrees of freedom 5
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 978.759
Degrees of freedom 10
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.959
Tucker-Lewis Index (TLI) 0.918
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -18417.898
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 36855.796
Bayesian (BIC) 36914.317
Sample-size adjusted Bayesian (BIC) 36882.544
Root Mean Square Error of Approximation:
RMSEA 0.056
90 Percent confidence interval - lower 0.041
90 Percent confidence interval - upper 0.071
P-value RMSEA <= 0.05 0.247
Standardized Root Mean Square Residual:
SRMR 0.027
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
friends =~
Q02 1.000 0.413 0.486
Q09 1.749 0.124 14.094 0.000 0.723 0.572
Q19 1.161 0.090 12.873 0.000 0.480 0.436
Q22 1.263 0.092 13.700 0.000 0.522 0.501
Q23 0.793 0.076 10.483 0.000 0.328 0.314
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q02 0.553 0.020 28.043 0.000 0.553 0.764
.Q09 1.072 0.046 23.496 0.000 1.072 0.672
.Q19 0.982 0.033 29.979 0.000 0.982 0.810
.Q22 0.810 0.030 27.319 0.000 0.810 0.749
.Q23 0.982 0.030 33.159 0.000 0.982 0.901
friends 0.171 0.018 9.530 0.000 1.000 1.000Visualize the friends CFA model
semPlot::semPaths(friends_cfa_model, whatLabels = "stand")
What about models with more than one factor? Combining computers, friends, and math
cfa_3factor <- ' computers =~ Q06 + Q07 + Q10 + Q12 + Q13 + Q14 + Q15 + Q18
friends =~ Q02 + Q09 + Q19 + Q22 + Q23
math =~ Q08 + Q11 + Q17'
cfa_3factor_model <- cfa(cfa_3factor, data=saq.clean)
summary(cfa_3factor_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 46 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 35
Number of observations 2571
Model Test User Model:
Test statistic 843.108
Degrees of freedom 101
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 11775.153
Degrees of freedom 120
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.936
Tucker-Lewis Index (TLI) 0.924
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -52550.485
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 105170.970
Bayesian (BIC) 105375.792
Sample-size adjusted Bayesian (BIC) 105264.587
Root Mean Square Error of Approximation:
RMSEA 0.053
90 Percent confidence interval - lower 0.050
90 Percent confidence interval - upper 0.057
P-value RMSEA <= 0.05 0.043
Standardized Root Mean Square Residual:
SRMR 0.041
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
computers =~
Q06 1.000 0.724 0.646
Q07 1.043 0.036 29.112 0.000 0.755 0.685
Q10 0.520 0.027 19.410 0.000 0.376 0.429
Q12 0.798 0.029 27.218 0.000 0.578 0.631
Q13 0.925 0.031 29.815 0.000 0.670 0.706
Q14 0.900 0.032 27.991 0.000 0.652 0.653
Q15 0.766 0.032 24.221 0.000 0.555 0.550
Q18 1.073 0.035 30.836 0.000 0.777 0.738
friends =~
Q02 1.000 0.401 0.471
Q09 1.663 0.113 14.762 0.000 0.666 0.527
Q19 1.385 0.096 14.486 0.000 0.555 0.504
Q22 1.313 0.091 14.509 0.000 0.526 0.505
Q23 0.758 0.074 10.292 0.000 0.304 0.291
math =~
Q08 1.000 0.662 0.758
Q11 1.073 0.029 36.459 0.000 0.710 0.806
Q17 1.018 0.029 35.256 0.000 0.673 0.762
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
computers ~~
friends -0.149 0.011 -12.970 0.000 -0.513 -0.513
math 0.309 0.016 19.667 0.000 0.646 0.646
friends ~~
math -0.077 0.009 -9.020 0.000 -0.290 -0.290
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q06 0.734 0.023 31.931 0.000 0.734 0.583
.Q07 0.644 0.021 30.982 0.000 0.644 0.530
.Q10 0.627 0.018 34.622 0.000 0.627 0.816
.Q12 0.505 0.016 32.227 0.000 0.505 0.602
.Q13 0.450 0.015 30.369 0.000 0.450 0.501
.Q14 0.572 0.018 31.777 0.000 0.572 0.574
.Q15 0.711 0.021 33.484 0.000 0.711 0.698
.Q18 0.505 0.017 29.255 0.000 0.505 0.455
.Q02 0.564 0.019 29.854 0.000 0.564 0.778
.Q09 1.151 0.042 27.695 0.000 1.151 0.722
.Q19 0.905 0.032 28.670 0.000 0.905 0.746
.Q22 0.806 0.028 28.598 0.000 0.806 0.745
.Q23 0.997 0.029 33.929 0.000 0.997 0.915
.Q08 0.323 0.013 25.763 0.000 0.323 0.425
.Q11 0.272 0.012 22.036 0.000 0.272 0.350
.Q17 0.327 0.013 25.510 0.000 0.327 0.419
computers 0.525 0.030 17.272 0.000 1.000 1.000
friends 0.160 0.016 9.763 0.000 1.000 1.000
math 0.438 0.021 20.734 0.000 1.000 1.000Visualize the three-factor CFA model
semPlot::semPaths(cfa_3factor_model, whatLabels = "stand")
What about combining the whole scale all together? Do all 23 items fit together?
cfa_all_1factor <- 'anx =~ Q01 + Q02 + Q03R + Q04 + Q05 + Q06 + Q07 + Q08 + Q09 + Q10 + Q11 + Q12 + Q13 + Q14 + Q15 + Q16 + Q17 + Q18 + Q19 + Q21 + Q22 + Q23'
cfa_all_1factor_model <- cfa(cfa_all_1factor, data=saq.clean)
summary(cfa_all_1factor_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 34 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 44
Number of observations 2571
Model Test User Model:
Test statistic 4075.552
Degrees of freedom 209
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 18596.355
Degrees of freedom 231
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.789
Tucker-Lewis Index (TLI) 0.767
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -71849.166
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 143786.333
Bayesian (BIC) 144043.823
Sample-size adjusted Bayesian (BIC) 143904.023
Root Mean Square Error of Approximation:
RMSEA 0.085
90 Percent confidence interval - lower 0.083
90 Percent confidence interval - upper 0.087
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.062
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
anx =~
Q01 1.000 0.463 0.559
Q02 -0.481 0.040 -12.152 0.000 -0.222 -0.261
Q03R 1.361 0.057 23.768 0.000 0.630 0.586
Q04 1.248 0.051 24.410 0.000 0.578 0.609
Q05 1.093 0.050 21.942 0.000 0.506 0.525
Q06 1.327 0.059 22.645 0.000 0.614 0.548
Q07 1.590 0.061 25.952 0.000 0.736 0.668
Q08 0.989 0.045 21.941 0.000 0.458 0.525
Q09 -0.663 0.058 -11.356 0.000 -0.307 -0.243
Q10 0.779 0.043 18.097 0.000 0.360 0.411
Q11 1.182 0.048 24.754 0.000 0.547 0.622
Q12 1.277 0.050 25.366 0.000 0.591 0.645
Q13 1.347 0.052 25.686 0.000 0.623 0.657
Q14 1.373 0.055 25.143 0.000 0.635 0.636
Q15 1.226 0.053 23.083 0.000 0.568 0.562
Q16 1.288 0.050 25.521 0.000 0.596 0.651
Q17 1.187 0.048 24.751 0.000 0.549 0.622
Q18 1.567 0.059 26.463 0.000 0.725 0.689
Q19 -0.911 0.053 -17.056 0.000 -0.422 -0.383
Q21 1.318 0.053 24.702 0.000 0.610 0.620
Q22 -0.597 0.048 -12.327 0.000 -0.276 -0.265
Q23 -0.276 0.047 -5.877 0.000 -0.128 -0.123
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q01 0.471 0.014 34.269 0.000 0.471 0.687
.Q02 0.675 0.019 35.599 0.000 0.675 0.932
.Q03R 0.758 0.022 34.030 0.000 0.758 0.657
.Q04 0.566 0.017 33.798 0.000 0.566 0.629
.Q05 0.674 0.020 34.529 0.000 0.674 0.725
.Q06 0.881 0.026 34.360 0.000 0.881 0.700
.Q07 0.673 0.020 33.044 0.000 0.673 0.554
.Q08 0.552 0.016 34.530 0.000 0.552 0.725
.Q09 1.501 0.042 35.635 0.000 1.501 0.941
.Q10 0.639 0.018 35.146 0.000 0.639 0.831
.Q11 0.475 0.014 33.657 0.000 0.475 0.614
.Q12 0.490 0.015 33.370 0.000 0.490 0.584
.Q13 0.511 0.015 33.199 0.000 0.511 0.568
.Q14 0.593 0.018 33.480 0.000 0.593 0.595
.Q15 0.696 0.020 34.241 0.000 0.696 0.684
.Q16 0.483 0.015 33.290 0.000 0.483 0.576
.Q17 0.479 0.014 33.658 0.000 0.479 0.614
.Q18 0.583 0.018 32.704 0.000 0.583 0.526
.Q19 1.035 0.029 35.255 0.000 1.035 0.853
.Q21 0.597 0.018 33.679 0.000 0.597 0.616
.Q22 1.006 0.028 35.590 0.000 1.006 0.930
.Q23 1.073 0.030 35.801 0.000 1.073 0.985
anx 0.214 0.014 14.817 0.000 1.000 1.000Visualize the one-factor CFA model
semPlot::semPaths(cfa_all_1factor_model, whatLabels = "stand")
Opening Pandora’s Box!?! - using modification indices
Modification indices tell you how model fit would change if you added new parameters to the model. This is not the same as adding new items - rather, it usually means covarying items, or including items from one latent factor that also fit with a second factor. Since your CFA model should in most cases not be exploratory (i.e. you should know what parameters you want to include in the model before you begin), modification indices can be dangerous. Hence the Pandora’s Box reference! If you make the changes they suggest, you often run the risk of over-fitting this specific model to your data and reducing the generalizability of your results in other samples.
modificationIndices(computers_cfa1_model, sort.=TRUE, minimum.value = 3)I recommend using modification indices mostly as another description of the places where your model is not fitting well, a bit like examining the residuals.
Same Model- with error covariance for q12 and q06
computers_cfa3 <- ' computers =~ Q06 + Q07 + Q10 + Q12 + Q13 + Q14 + Q15 + Q18
Q06 ~~ Q12'
computers_cfa3_model <- cfa(computers_cfa3, data=saq.clean)
summary(computers_cfa3_model, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 20 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 17
Number of observations 2571
Model Test User Model:
Test statistic 136.693
Degrees of freedom 19
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 6309.869
Degrees of freedom 28
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.981
Tucker-Lewis Index (TLI) 0.972
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -26097.013
Loglikelihood unrestricted model (H1) NA
Akaike (AIC) 52228.025
Bayesian (BIC) 52327.510
Sample-size adjusted Bayesian (BIC) 52273.496
Root Mean Square Error of Approximation:
RMSEA 0.049
90 Percent confidence interval - lower 0.042
90 Percent confidence interval - upper 0.057
P-value RMSEA <= 0.05 0.560
Standardized Root Mean Square Residual:
SRMR 0.024
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
computers =~
Q06 1.000 0.776 0.691
Q07 0.970 0.032 30.255 0.000 0.753 0.683
Q10 0.479 0.025 19.533 0.000 0.371 0.423
Q12 0.777 0.030 26.272 0.000 0.603 0.658
Q13 0.850 0.028 30.736 0.000 0.660 0.696
Q14 0.828 0.029 28.741 0.000 0.643 0.644
Q15 0.681 0.029 23.840 0.000 0.528 0.523
Q18 1.008 0.031 32.431 0.000 0.782 0.742
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q06 ~~
.Q12 -0.146 0.013 -11.031 0.000 -0.146 -0.262
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.Q06 0.657 0.022 29.485 0.000 0.657 0.522
.Q07 0.648 0.021 31.004 0.000 0.648 0.534
.Q10 0.631 0.018 34.663 0.000 0.631 0.821
.Q12 0.476 0.016 30.402 0.000 0.476 0.567
.Q13 0.464 0.015 30.638 0.000 0.464 0.516
.Q14 0.584 0.018 31.947 0.000 0.584 0.586
.Q15 0.739 0.022 33.788 0.000 0.739 0.726
.Q18 0.498 0.017 28.962 0.000 0.498 0.449
computers 0.602 0.033 18.508 0.000 1.000 1.000Visualize the model with the extra covariance between q12 and q06
semPlot::semPaths(computers_cfa3_model, whatLabels = "stand")
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