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Conditional Estimation for Generalized Linear Models When Covariates Are Subject‐Specific Parameters in a Mixed Model for Longitudinal Measurements
Author(s) -
Li Erning,
Zhang Daowen,
Davidian Marie
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00170.x
Subject(s) - covariate , random effects model , generalized linear mixed model , mixed model , estimator , mathematics , linear model , statistics , inference , econometrics , marginal model , generalized linear model , normality , conditional probability distribution , asymptotic distribution , linear regression , computer science , regression analysis , artificial intelligence , medicine , meta analysis
Summary. The relationship between a primary endpoint and features of longitudinal profiles of a continuous response is often of interest, and a relevant framework is that of a generalized linear model with covariates that are subject‐specific random effects in a linear mixed model for the longitudinal measurements. Naive implementation by imputing subject‐specific effects from individual regression fits yields biased inference, and several methods for reducing this bias have been proposed. These require a parametric (normality) assumption on the random effects, which may be unrealistic. Adapting a strategy of Stefanski and Carroll (1987, Biometrika 74, 703–716), we propose estimators for the generalized linear model parameters that require no assumptions on the random effects and yield consistent inference regardless of the true distribution. The methods are illustrated via simulation and by application to a study of bone mineral density in women transitioning to menopause.