I want to compare the overall if of an MNL model, a fixed effects Bayes model and a random-effects hierarchical Bayes model. The log likelihood measure seems to be most appropirate for that, however how do I calculate the overall log likelihood for the HB model in the PROC BCHOICE procedure?
you could try holding all parameter estimates to the values you estimate using the 3 model frameworks in a framework that can nest all 3 specifications and outputs a true (not psuedo) likelihood. Maybe proc glimmix with method=laplace might work, depending on your original procedures.
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ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.