Could you please these two questions- 1. I am running a linear growth model with categorical data, using ML estimator ( I do not have the same number of categories for each wave and hence am unable to use the default WLS estimator). How should I interpret the Pearson Chi-square and the Likelihood Ratio Chi-Square? Are there any other fit indices I should examine?
2. I also ran a Latent Class Growth analysis with the same categorical data. I understand that the mean intercept and slope values are expressed as logits. I want to graph the average level of my categorical variable at each time point for each trajectory, along with 95% confidence interval (95% CI). This would only be for illustrative purposes, as it involves the interpretation of my ordered categorical data as if it was continuous. How do I do such a graph? Would you recommend some other graphic visualization that would ease interpretation?
To add to my previous post, I used Example 6.4 to run the first analysis. My categorical variable has three ordered categories - 0,1,2 and is measured weekly for 9 weeks.
I also have one more question - When I ran the Latent Class Growth Analysis, I had negative values for intercepts in 2 of my three classes. The fit indices (BIC, LRT, Posterior Probabilities, Entropy) all support a 3-class model. I know these are expressed on the logit scale and can be converted to odds ratios. I was wondering if the negative sign has any specific meaning.
1. The Pearson and LR chi-squares consider the fit to the multiway frequency table of the categorical outcomes at all the time points. These tests are often problematic when there are many time points because then there are many zero cells in the multiway table - in this case, the two chi-squares disagree and you cannot trust either one. I would suggest using chi-square testing via -2*loglikelihood differences among nested models to find the best model.
2. I would use the Mplus graphics facility to plot the estimated mean probability curve.
Regarding your follow-up question, the intercept means must be understood in conjunction with the thresholds of the outcomes. For example, with a binary outcome and a logit model, the probability for the time point at the centering point (first time point in ex 6.4) is computed via