Statistical Modelling 1 (2001), 81–102
Multinomial Logit Random Effects Models
Jonathan Hartzel
Merck Research Labs, West Point,
PA 19486, USA
Alan Agresti
Dept of Statistics, Univ of Florida, Gainesville,
FL 32611-8545, USA
eMail: aa@stat.ufl.edu
Brian Caffo
Dept of Statistics, Univ of Florida, Gainesville,
FL 32611-8545, USA
Abstract:
This article presents
a general approach for logit random effects
modeling 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 pseudo likelihood approaches that are simpler but
provide 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
nonparametric manner. An example comparing reviews of movie critics
uses adjacent-categories logit models and a related
baseline-category logit model.
Keywords:
Adjacent-categories logit;
Baseline-category logit;
Generalized linear mixed model;
Nominal variable;
Nonparametric maximum likelihood;
Ordinal variable;
Quasi symmetry.
Downloads:
SAS code
for fitting multinomial random effects models
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