1. I am trying to running example 10.5 monte carlo study. But I want this data include a covariate variable. (for example a gender variable: 600 females in latent class 1, 400 males in latent class 2; 400 females in latent class 2 and 600 males in latent class 1=2000 observations totaly gender splşt is 50% and . How can I add such a variable in this study?
2. Another question is: Which prior paramter used for this simulation study? Can we generate response patterns in this example based on item response model? Because I want to item diffuculties differ between latent classes.
I try to fit my data to the multilevel mixture item response model. For this reason I used example 10.5. I guess the syntax is for 1-PL model or Rasch model. I have now class spesicific item diffuculties.
I want to use these parameter for differential item functioning detection. But I wonder that these item diffuculties directly comparable? Should I bring the parameters the same scale?