Chi-Square Values for Nominal LCA/LTA...
Message/Author
 Anonymous posted on Tuesday, November 02, 2004 - 10:17 am
I am trying to determine the goodness-of-fit of some LCA and LTA models where my variables are nominal. I would really like to get the Pearson chi-square and likelihood ratio chi-square values for these nominal models, but apparently I can only get these chi-square values for categorical models. What should I do?
 bmuthen posted on Tuesday, November 02, 2004 - 11:09 am
The current version does not yet have these chi-squares for nominal outcomes. But you can obtain this test by specifying the variables as categorical instead of nominal since that gives the same model fit (same number of parameters and loglikelihood value) when you don't have covariates.
 Boliang Guo posted on Thursday, November 17, 2005 - 1:57 am
Dr. Muthen,
here is a general issue on model identificant which need your help to shed light me on.

Professor Velicer in University of Rhode Island, published a paper on LTA for smoker. he used winLTA for his study (result from WinLTA is almost same with the result from Mplus, G2 in winlta is same as the likelihood chi sq in Mplus).

Briefly say, he tested 3 LTA models to see which one is the best. He concluded that the Model3, with the least G2 value are the best model for his study.

I check his paper and find all his G2 value are significant, even the G2 in his best model are also 284.35, 703.979, 457.343 and 564.485, all with 7 df, respectively for different measurement occassion. For pure model comparison, model 3 with the least G2 is accepted but G2 in all his models are statistically significant, generally speaking, nonsignificant G2 is a indicator for an accepted model, if I am not wrong, I will say all his model are not accepted following the nonsignificant G2 rule, am I right?
some one say Chi sq is a badness of fit, less chi sq like the less badness for model comparsion, but could we say a less bad model is accpeted although it is really BAD!!!?

thanks for your attention on my novice question.
Prof.Velicer's paper: Addictive behaviors, 21, 67-80, 1996
 bmuthen posted on Thursday, November 17, 2005 - 5:20 am
The LRT chi square testing against an unrestricted frequency table is only useful with a small number of variables, say < 10. Otherwise, small cell frequencies make the test statistic deviate from chi square. Another consideration is if the sample size is very big in which case you may have more power than you need to reject the model. If the number of items is small and the sample size not huge, I think a significant LRT should lead to model rejection. Other statistics are also useful for deciding on the number of classes such as BIC and bootstrapped LRT for testing k-1 vs k classes.