Multi-group CFA - good fit, but n.s. ... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Maja Cambry posted on Tuesday, March 09, 2010 - 9:57 am
I'm testing a CFA with 3 latent factors that have 2 indicators each (all categorical except one indicator) across two groups. Model has adequate fit on full sample (cfi - .991, tli-.981, rmsea - .030, wrmr - .689). When I run the model for each group individually, one group has very good model fit (non-sign. chi-square, cfi-1.0, tli-1.020, rmsea - 0.0, wrmr - .234), but the two-tailed p-values for the unstandardized estimates (factor loadings) are .140 or greater. P-values for the standardized estimates are 0.00.

Do the p-values of the unstandardized estimates mean that those estimates are non-significant? If so, why aren't the standardized estimates non-sign also and why might the model have very good overall fit, but n.s. estimates?
 Linda K. Muthen posted on Tuesday, March 09, 2010 - 2:22 pm
There are two issues. Standardized and unstandardized estimates can have different p-values.

The other issue is good model fit with non-significant results. This can occur. Model fit depends on how well the H0 model reproduces the sample statistics used for model estimation. The significance of estimates depends on variance of the dependent variable explained by an independent variable.
 Maja Cambry posted on Wednesday, March 10, 2010 - 3:32 am
Thanks. I have a follow-up question. I tested measurement invariance of the 3-factor CFA. Invariant model (factor loadings and thresholds constrained) fit stats: chi-sq sign, cfi-.981, tli-.980, rmsea-.031 and wrmr-1.120. Parameter estimates were significant in the constrained model as well. Although cfi and tli are acceptable, wrmr is not good. How should I interpret the model?
 Linda K. Muthen posted on Wednesday, March 10, 2010 - 9:58 am
You should ignore WRMR. It is an experimental fit statistic.
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