

Multigroup CFA  good fit, but n.s. ... 

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Maja Cambry posted on Tuesday, March 09, 2010  9:57 am



Hi, 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 (nonsign. chisquare, cfi1.0, tli1.020, rmsea  0.0, wrmr  .234), but the twotailed pvalues for the unstandardized estimates (factor loadings) are .140 or greater. Pvalues for the standardized estimates are 0.00. Do the pvalues of the unstandardized estimates mean that those estimates are nonsignificant? If so, why aren't the standardized estimates nonsign also and why might the model have very good overall fit, but n.s. estimates? Thanks 


There are two issues. Standardized and unstandardized estimates can have different pvalues. The other issue is good model fit with nonsignificant 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 followup question. I tested measurement invariance of the 3factor CFA. Invariant model (factor loadings and thresholds constrained) fit stats: chisq sign, cfi.981, tli.980, rmsea.031 and wrmr1.120. 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? 


You should ignore WRMR. It is an experimental fit statistic. 

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