Spherical radial approximation for nested mixed effects models

摘要: We consider a likelihood approximation in generalized linear mixed-effects models (GLMM) with multilevel nested random effects. Likelihood evaluation such is difficult, hindered by the need for high dimensional integration, where dimension proportional to number of units per level and effects unit. Various integration approaches have been proposed, including penalized quasi-likelihood method, Laplace approximation, quadrature simulation, MCMC algorithms. propose new which based on spherical radial approach Monahan Genz (J Am Stat Assoc 92:664---674 1997), at same time takes advantage hierarchical structure integration. Our method has complexity that unit, contrast exponential adaptive Gaussian Pinheiro Chao Comput Graph 15:58---81 2006) problem. Using spline additive mixed (GAMM) are GLMMs two levels apply our estimation GAMMs. compare it competing methods through simulations analyze virologic immunologic responses an AIDS clinical trial. An R package written available http://users.wpi.edu/~jgagnon/software.html.