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Estimation in the probit normal model for binary outcomes using the SAEM algorithm

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  • Meza, Cristian
  • Jaffrézic, Florence
  • Foulley, Jean-Louis

Abstract

Generalized linear mixed models (GLMM) form a very general class of random effects models for discrete and continuous responses in the exponential family. They are useful in a variety of applications. The traditional likelihood approach for GLMM usually involves high dimensional integrations which are computationally intensive. In this work, we investigate the case of binary outcomes analyzed under a two stage probit normal model with random effects. First, it is shown how ML estimates of the fixed effects and variance components can be computed using a stochastic approximation of the EM algorithm (SAEM). The SAEM algorithm can be applied directly, or in conjunction with a parameter expansion version of EM to speed up the convergence. A procedure is also proposed to obtain REML estimates of variance components and REML-based estimates of fixed effects. Finally an application to a real data set involving a clinical trial is presented, in which these techniques are compared to other procedures (penalized quasi-likelihood, maximum likelihood, Bayesian inference) already available in classical softwares (SAS Glimmix, SAS Nlmixed, WinBUGS), as well as to a Monte Carlo EM (MCEM) algorithm.

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  • Meza, Cristian & Jaffrézic, Florence & Foulley, Jean-Louis, 2009. "Estimation in the probit normal model for binary outcomes using the SAEM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1350-1360, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1350-1360
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    Cited by:

    1. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    2. Naranjo, L. & Martín, J. & Pérez, C.J., 2014. "Bayesian binary regression with exponential power link," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 464-476.

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