Generalized linear latent variable modeling analysis for multi-group studies

Latent variable modeling is commonly used in the behavioral, medical and social sciences. The models used in such analysis relate all observed variables to latent common factors. In many applications, the observed variables are in polytomous form. The existing procedures for models with polytomous outcomes can be considered lacking in several aspects, especially for multi-sample situations. We incorporate a new generalized linear latent variable modeling approach for developing statistically sound procedures that furnish meaningful interpretation and can incorporate many types of outcome variables. In the special case of polytomous outcomes, we also propose a model that incorporates response errors. A rather simple model parameterization used in our approach is appropriate for multi-sample analysis and leads to practically useful inference procedures. A Monte Carlo EM algorithm is developed for computing the full maximum likelihood estimates. Simulation studies are presented to validate the benefits of the new approach and to compare its performance to other methods. The new approach is also applied to analyze data from two substance abuse prevention studies