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Multinomial logit random effects models

Merck Research Labs, West Point, USA

Alan Agresti

Department of Statistics, University of Florida, Gainesville, USA, aa{at}stat.ufl.edu

Brian Caffo

Department of Statistics, University of Florida, Gainesville, USA

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.

Key Words: adjacent-categories logit • baseline-category logit • generalized linear mixed model • nominal variable • non-parametric maximum likelihood • ordinal variable • quasi symmetry

Statistical Modelling, Vol. 1, No. 2, 81-102 (2001)
DOI: 10.1177/1471082X0100100201


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