Fitting exponential family mixed models
نویسندگان
چکیده
The seminal papers by Nelder and Wedderburn (Generalized Linear Models, JRSS A 1972) and Cox (Regression models and life tables, JRSS B 1972) both rely on the assumption that conditionally on covariate information (including time) the observations are independent. The difficulty in identifying and measuring all relevant covariates has pushed for methods that can handle both mean and covariance structures jointly. There has been a parallel development of (i) marginal models and (ii) random effects models as multivariate extensions of the generalized linear model and the multiplicative hazard model, respectively. After a brief review of this development we focus on estimation and computational aspects of fitting random effects models. We discuss the use of penalized likelihood, Monte Carlo EM and MCMC methods using examples involving censored survival time responses and Poisson responses.
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