Clustering Profiles in Generalized Linear Mixed Models Settings Using Bayesian Nonparametric Statistics
Predrag Mizdrak · 2018
Generalized linear mixed models are used to model clustered and longitudinal data in which the distribution of the response variable is a member of the exponential family.This thesis introduces a novel method for simultaneous clustering of such data and estimation of parameters of the underlying generalized linear mixed models.Clustering has been extensively studied for both cross-sectional and longitudinal data.In longitudinal data, one has to take into account the association between observations taken on the same individual.This has found applications in epidemiology, genetics, biology, market research, economics, and many other areas.Generalized linear mixed models consist of two sets of parameters: fixed effects parameters that associate covariates to the response at the population level, and random effects parameters that associate covariates to the response at the individual level.We introduce a method that identifies homogeneous groups in the data based on similarities among random effects parameters that are obtained when homogeneous groups are modeled using generalized linear mixed models.We achieve this by placing a Dirichlet Process prior on random effects parameters, which induces clustering of random effects and subsequently the clustering of profiles.As a result, our method simultaneously groups profiles into clusters and estimates model