Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 96, Issue 455, Pages 1102-1112Publisher
AMER STATISTICAL ASSOC
DOI: 10.1198/016214501753208762
Keywords
generalized linear mixed model; latent variable; Monte Carlo EM algorithm; random effect; teratology
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A difficulty in joint modeling of continuous and discrete response variables is the lack of a natural multivariate distribution. For joint modeling of clustered observations on binary and continuous responses, we study a correlated probit model that has an underlying normal latent variable for the binary responses. Catalano and Ryan have factored the model into a marginal and a conditional component and used generalized estimating equations methodology to estimate the effects. We propose a Monte Carlo expectation-conditional maximization algorithm for finding maximum likelihood estimates of the mixed model itself, extending and accelerating an algorithm for models with binary responses. We demonstrate the methodology with a developmental toxicity study measuring fetal weight and a binary malformation status for several litters of mice. A simulation study suggests that efficiency gains of joint fittings over separate fittings of the response variables occur mainly for small datasets with strong correlations between the responses within cluster.
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