Open Access
February 1997 Consistency of maximum likelihood estimators in general random effects models for binary data
Steven M. Butler, Thomas A. Louis
Ann. Statist. 25(1): 351-377 (February 1997). DOI: 10.1214/aos/1034276633


We consider a general random effects model for repeated binary measures, assuming a latent linear model with any class of mixing distributions. The latent model is assumed to have the Laird-Ware structure, but the random effects may be from any specified class of multivariate distributions and the error vector may have any specified continuous distribution. Elementwise threshold crossing then gives the observed vector of binary outcomes. Special cases of this model include recently discussed mixed logistic regression and probit models, which have had either parametric (usually Gaussian) or nonparametric mixing distributions. We give sufficient conditions for identifiability of the mixing distribution and fixed effects and for convergence of maximum likelihood estimators for the mixing distribution and fixed effects. As expected, the conditions are much stronger for nonparametric mixing than for Gaussian mixing. We illustrate the conditions by applying them to a practical example.


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Steven M. Butler. Thomas A. Louis. "Consistency of maximum likelihood estimators in general random effects models for binary data." Ann. Statist. 25 (1) 351 - 377, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0897.62032
MathSciNet: MR1429929
Digital Object Identifier: 10.1214/aos/1034276633

Primary: 62G07
Secondary: 62J02 , 62J12

Keywords: Binary , consistency , Identifiability , maximum likelihood , nonparametric , random effect , repeated measures , semiparametric

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 1 • February 1997
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