Removing loadings to improve fit

Factor Analysis in R

Jennifer Brussow

Psychometrician

What does it mean to remove a loading?

summary(theory_CFA)

 Parameter Estimates
            Estimate Std Error z value Pr(>|z|)              
lam[A1:AGE] -0.501   0.0449    -11.17   5.79e-29 A1 <--- AGE 

...

lam[O1:OPE]  0.636   0.0379     16.79   2.88e-63 O1 <--- OPE 
lam[O2:OPE] -0.731   0.0532    -13.75   5.39e-43 O2 <--- OPE 
lam[O3:OPE]  0.809   0.0399     20.25   3.24e-91 O3 <--- OPE 
lam[O4:OPE]  0.287   0.0413      6.95   3.69e-12 O4 <--- OPE 
lam[O5:OPE] -0.624   0.0444    -14.06   7.07e-45 O5 <--- OPE

delloadings

Removing a loading in the syntax

# The original syntax
theory_syn_eq <- "
AGE: A1, A2, A3, A4, A5
CON: C1, C2, C3, C4, C5
EXT: E1, E2, E3, E4, E5
NEU: N1, N2, N3, N4, N5
OPE: O1, O2, O3, O4, O5 "

# Remove the worst item/factor loadings from the syntax
theory_syn_del <- "
AGE: A1, A2, A3, A4, A5
CON: C1, C2, C3, C4, C5
EXT: E1, E2, E3, E4, E5
NEU: N1, N2, N3, N4, N5
OPE: O1, O2, O3, O5 "

# As before, convert your equations to sem-compatible syntax
theory_syn3 <- cfa(text = theory_syn_del, reference.indicators = FALSE)

Running the revised CFA

# Run a CFA with the revised syntax
theory_CFA_del <- sem(model = theory_syn3, data = bfi_CFA)

Warning messages:
1: In sem.semmod(model = theory_syn3, data = bfi_CFA) :
  -170 observations removed due to missingness
2: In sem.semmod(model = theory_syn3, data = bfi_CFA) :
  The following observed variables are in the input covariance 
  or raw-moment matrix but do not appear in the model:
O4

Comparing the original and revised models

anova(theory_CFA, theory_CFA_del)

Error in anova.objectiveML(theory_CFA, theory_CFA_del) : 
  the models are fit to different moment matrices

# Compare the comparative fit indices - higher is better!
summary(theory_CFA)$CFI

0.785075

summary(theory_CFA_del)$CFI

0.7995587

Comparing the original and revised models

# Compare the RMSEA values - lower is better!
summary(theory_CFA)$RMSEA

0.07731925         NA         NA 0.90000000

summary(theory_CFA_del)$RMSEA

0.07718057         NA         NA 0.90000000

More information about fit indices: http://davidakenny.net/cm/fit.htm

Let's practice!

Factor Analysis in R