Dear Linda, Bengt, I fitted several factor mixture models using Mplus and obtained estimated conditional item probabilities for the best fitting model (i.e. estimated probabilities for each class integrated over the factor). My question concerns the standard errors for these conditional item probabilities, that is, the standard errors for the probabilities are missing in the output, because I used numerical integration to estimate the model (On the forum I read that Mplus does not give standard errors in the output when using numerical integration). Based on the conditional item probability plot there seem to be (minor) differences between classes. However, now I am unsure how to interpret differences these differences without standard errors or any other statistic. Can I just assume these probabilities differ between classes based on the plot only? Or do I have to test whether the non-significant thresholds differ between classes significantly using for instance the MODEL TEST option of Mplus? Some more information about the model: thresholds are fixed across classes for categorical indicators, and next to these categorical indicators I included various continuous indicators with class-varying intercepts , residual variances , factor means fixed at zero and factor variance at one. The model has two classes, and one factor within each class. I am using Mplus version 6.1. Thank you in advance!
Thank you for your prompt reply. I think I did not make myself clear; I did use BIC (and BLRT) to decide on the number of classes. But now, for the best fitting model (that has 2 classes and 1 factor) I would like to compare conditional item probabilities between classes. That is, the conditional item probability plot suggests there are minor differences between classes for certain items. So my first question was whether it is possible to obtain standard errors for these conditional item probabilities (considering that I used numerical integration). And if not, whether I can assume that these probabilities differ between classes based on the plot only?
SEs for cond'l item probabilities are not given in Mplus and cannot be computed in Model Constraint due to numerical integration. Testing differences in thresholds would be akin to testing differences conditional on a zero factor value. The plot just gives the visual description for the unconditional probabilities. But if you are interested in whether the overall profiles are different, I would report the BIC difference for the 1- and 2-class models.