A Markov Chain Monte Carlo Approach to the Nonlinear Mixed Model for Repeated Measures Data
Monte Carlo Markov process methods based on the Gibbs sampler and the Metropolis algorithm are employed to estimate the posterior distributions of parameters in the nonlinear mixed model. A hierarchical Bayes approach is used to specify the nonlinear mixed model, enabling estimation of the posterior distributions of the variance components as well as the fixed and random effects.
The Gibbs sampler requires iterative sampling from conditional distributions, which frequently cannot be directly computed in the nonlinear mixed model. To sample from such unavailable conditional distributions, approximate Gibbs sampler schemes based on the Metropolis algorithm are employed. These techniques, first suggested by Hastings (1970), retain much of the simplicity of the Gibbs sampler (moving one coordinate at a time, based on one-step conditional distributions) while requiring considerably less computing time than other methods (e.g., rejection sampling and ratio of uniforms) proposed for applying the Gibbs sampler when conditional distributions are not directly computable
Two applications to repeated measures data are presented.
Longitudinal Data Analysis and Time Series | Numerical Analysis and Computation | Statistical Models
Gerson, Jack; Brand, Richard J.; and Raz, Jonathan, "A Markov Chain Monte Carlo Approach to the Nonlinear Mixed Model for Repeated Measures Data" (March 1993). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 39.