Generally high within cluster correlations yield higher residuals than generally low within cluster correlations (abslute values). Consequenlty, the fit seems better with high unique variance and low reliabilty, and vice versa.
This is a suggestion I make in my article, but not being a statistician I am far from certain of this.
(There are a few imperfections in the article: you can ask me for the most recent copy.)
Yes, the chi-squared test of model fit, as well as related indices such as estimated RMSEA, tend to be lower powered / show better fit if the correlations in the data are weak. Essentially, it's easier to reproduce the results of a weak signal with a lot of noise around it than it is a strong signal.
Null-model-based indices, such as the CFI, tend to have the opposite behavior. If the saturated model simply isn't that much better than the null, then it's harder to get a high index.
Thanks. However, in that case, why not introduce a correction for average level of within-cluster inter-correlations in the formulas with which chi-square and the indices are calculated?
Heh. More mathematically-oriented researchers than I have spent decades seeking the "perfect" means to assess fit. Many will argue that the chi-squared test is it. I'm honestly not equipped to help further.
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