

Why do fit indices change? 

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I conducted mixture modeling on 5 subscale scores 2 ways: 1. Using raw subscale scores. 2. rescaling the scores by dividing them by the number of items on the subscale, because there was a different number of items on each subscale. This rescaling made the means within class comparable. Fit indices (e.g., loglikelihood, BIC)weren’t the same across the two ways. Why? When will fit indices be the same and when will they differ? 


LogL and BIC will be the same only when you use the same set of dependent variables and when the metric of those variables is the same. 


For many of the mixture models we've created, the BIC, SSABIC, CAIC, and BLRT never settle on a class solution. They continue getting smaller (or, in the case of the BLRT, remain significant) as more classes are attempted, even when the smallest class contains as few as two subjects. The LMRLRT is the only index that picks a solution. Do you know why this might be? Thank you! 


I often use BIC where this is a common occurrence. It probably implies that either the model type is wrong (perhaps a factor model is better), or model details are wrong (e.g. withinclass correlations between some items), or there just isn't a simple model to be found for the data at hand. 


Thank you very much for your help! 

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