Generalized Linear Latent Variable Modeling for Multi-Group Studies

ABSTRACT

Latent variable modeling is commonly used in behavioral, social, and medical science research. The models used in such analysis relate all observed variables to latent common factors. In many applications, the observations are highly non normal or discrete, e.g., polytomous responses or counts. The existing approaches for non normal observations can be considered lacking in several aspects, especially for multi-group samples situations. We propose a generalized linear model approach for multi-sample latent variable analysis that can handle a broad class of non normal and discrete observations, and that furnishes meaningful interpretation and inference in multi-group studies through maximum likelihood analysis. A Monte Carlo EM algorithm is proposed for parameter estimation. The convergence assessment and standard error estimation is addressed. Simulation studies are reported to show the usefulness of the our approach. An example from a substance abuse prevention study is also presented.

Keywords:

• Exponential family distributions
• Monte Carlo EM algorithm
• Structural equation analysis

Mathematics Subject Classification:

• Primary 62H25
• Secondary 62P15

Acknowledgments

This work was partially supported by National Institute on Drug Abuse Research Grant DA 07029-01A1 and National Institute of Mental Health Grant MH 49217-01A1. We would like to thank the anonymous referee for the constructive comments which helped improve the article.