Multinomial logit random effects models

• Published in: Statistical modelling Vol. 1; no. 2; pp. 81 - 102
• Main Authors: Hartzel, Jonathan, Agresti, Alan, Caffo, Brian
• Format: Journal Article
• Language: English
• Published: Thousand Oaks, CA SAGE Publications 01.07.2001
• Subjects: adjacent-categories logit; non-parametric maximum likelihood; quasi symmetry; baseline-category logit; nominal variable; ordinal variable; generalized linear mixed model
• ISSN: 1471-082X; 1477-0342
• DOI: 10.1177/1471082X0100100201

This article presents a general approach for logit random effects modelling of clustered ordinal and nominal responses. We review multinomial logit random effects models in a unified form as multivariate generalized linear mixed models. Maximum likelihood estimation utilizes adaptive Gauss-Hermite quadrature within a quasi-Newton maximization algorithm. For cases in which this is computationally infeasible, we generalize a Monte Carlo EM algorithm. We also generalize a pseudo-likelihood approach that is simpler but provides poorer approximations for the likelihood. Besides the usual normality structure for random effects, we also present a semi-parametric approach treating the random effects in a non-parametric manner. An example comparing reviews of movie critics uses adjacent-categories logit models and a related baseline-category logit model.