Greetings, I am fitting the binary portion of a semincontinuous growth model (as a preliminary step for building the full semicontinuous model) for the first time. I have a few questions regarding the output: (1) I notice that Pearson chi-square and likelihood ratio chi-square values are provided. I had previously thought that a chi-sq test of model fit was not available for analyses requiring numerical integration. The Pearson chi-sq test statistical is highly significant (p<.0001) whereas the likelihood chi-sq test is not (p=1.00). Which one should I use? (1a) Can I use the likelihood ratio chi-sq test for chi-sq difference testing or should I use the Loglikelihood value? How do I incorporate the scaling correction factor when using the LogL for nested model difference testing?
(2) For the residual output - what do you think would be too high of a value for a residual? Basically, I am trying to decide from the output whether the linear model is appropriate or whether I should try other growth forms.
(3) I noticed that the plot of estimated probabilities for being in category 2 was not exactly linear. So is it that the log odds of being in category 2 is constrained to be linear in this model? If I wanted to specify a model of linear growth in propensity, how could I do this?
(4) In a multiple group context, would I use the Known Classes statement?
1. The Pearson and LRT chi-squares are only for the binary part of the model, not a test of the overall fit of the whole model. When the Pearson and the LRT disagree this much, neither is reliable - this is typically due to many empty cells where it is well-known that the chi-square approximation is very poor.
2. It seems easier to try linear vs quadratic and test if the quadratic growth factor parameters are significant.
Thank you for your response. As I am taking the approach of fitting the binary and continuous parts separately to more easily determine the proper growth function prior to looking at the full semicontinuous model.
Regarding the unreliable chi-sq statistics, I do not seem to have any empty cells at the univariate or bivariate level. But I guess at combinations of 3-7 of the variables, there could be missing cells.
How do I use the scale correction factors with the log likelihood for comparing nested models? Can I use the procedures listed at http://www.statmodel.com/chidiff.shtml or do I need to make some adjustment because I am working with log likelihoods and not chi-square values?
I just wanted to check in to make sure that with Mplus 7 fit statistics have not been added for a two-part semicontinuous model. I have reviewers who are asking for them even after I told then mplus does not provide any.
When we do not provide chi-square and related fit statistics, it is because means, variances, and covariances are not sufficient statistics for model estimation. These fit statistics have not been developed for models where means, variances, and covariances are not sufficient statistics for model estimation. This has not changed.