Model fit

Factor Analysis in R

Jennifer Brussow

Psychometrician

Absolute vs. relative model fit

Absolute fit statistics have intrinsic meaning and suggested cutoff values.

Chi-square test
Tucker-Lewis Index (TLI)
Root Mean Square Error of Approximation (RMSEA)

Relative fit statistics only have meaning when comparing models.

Bayesian Information Criterion (BIC)

Absolute fit statistics

Commonly used cutoff values:

Chi-square test: Non-significant result
Tucker Lewis Index (TLI): > 0.90
Root Mean Square Error of Approximation (RMSEA): < 0.05

Finding the fit statistics

# Run the EFA with six factors (as indicated by your scree plot)
EFA_model <- fa(bfi_EFA, nfactors = 6)

# View results from the model object
EFA_model

The total number of observations was  1400  
    with Likelihood Chi Square =  618.43  with prob <  1.2e-53

Tucker Lewis Index of factoring reliability =  0.916
RMSEA index =  0.045  and the 90 % confidence intervals are  0.041 0.048

BIC =  -576.87

Relative model fit

# Run each theorized EFA on your dataset
bfi_theory <- fa(bfi_EFA, nfactors = 5)
bfi_eigen <- fa(bfi_EFA, nfactors = 6)

# Compare the BIC values
bfi_theory$BIC
bfi_eigen$BIC

bfi_theory$BIC
bfi_eigen$BIC

-381.5326
-576.8658

In sum: evaluating fit

Make sure your model has good absolute fit (chi-square test, TLI, RMSEA)
If you are comparing multiple models, use relative fit statistics (BIC)

Let's practice!

Factor Analysis in R