Generalized additive mixed models.

A new class of models, generalized additive mixed models (GAMMs), are proposed for analyzing correlated continuous and discrete data. GAMMs use random effects to account for the correlation and use additive nonparametric functions to allow for flexible dependence of the outcome variable on the covariates. Smoothing splines are used to estimate the nonparametric functions and marginal quasi-likelihood is used to estimate the smoothing parameters and the variance components simultaneously. Due to the intractable integration, the double penalized quasi-likelihood approach is proposed to draw approximate inference for the model components. A bias-corrected double penalized quasi-likelihood is used to improve the performance of the double penalized quasi-likelihood estimates. A linearity test and a variance component test are developed. Extensive simulation studies were conducted to evaluate the performance of the proposed inference procedure. Our simulation results show that the proposed procedure performs reasonably well in estimating the nonparametric functions, and the bias-corrected double penalized quasi-likelihood yields practically satisfactory variance component estimates. The proposed models are illustrated through application to several data sets from biomedical research.Ph.D.Biological SciencesBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/130828/2/9811187.pd