Investigating model fit

Factor Analysis in R

Jennifer Brussow

Psychometrician

Default fit statistics

Chi-square test (aka the log likelihood test) is only default

summary(theory_CFA)

 Model Chisquare =  2231.647   Df =  265 Pr(>Chisq) = 1.695873e-307

Often significant due to sample size
Desired outcome is lack of significance

Changing the options

options(fit.indices = c("CFI", "GFI", "RMSEA", "BIC"))

RMSEA < 0.05
GFI (Goodness of Fit Index) > 0.90
CFI (Comparative Fit Index) > 0.90

Absolute model fit

summary(theory_CFA)

 Model Chisquare =  2305.159   Df =  271 Pr(>Chisq) = 0

 Goodness-of-fit index =  0.8527977

 RMSEA index =  0.07815051   90% CI: (NA, NA)

 Bentler CFI =  0.7754574

Relative fit

summary(theory_CFA)

 Model Chisquare =  2305.159   Df =  271 Pr(>Chisq) = 8.422189e-319
 Goodness-of-fit index =  0.8527977
 RMSEA index =  0.07815051   90% CI: (NA, NA)
 Bentler CFI =  0.7754574
 BIC =  377.0563

summary(theory_CFA)$BIC

326.618

Relative fit: comparing models

summary(theory_CFA)$BIC

326.618

# Run a CFA using the EFA syntax you created earlier
EFA_CFA <- sem(EFA_syn, data = bfi_CFA)
summary(EFA_CFA)$BIC

377.0563

Useful for nested models that are fit to the same dataset
Don't use if these conditions are not met!

Let's practice!

Factor Analysis in R