Model-Based Recursive Partitioning of Extended Redundancy Analysis with Applications to Nicotine Dependence and Obesity Data among US adults

Sunmee Kim
B204 Academic Building

Extended redundancy analysis (ERA) is used to reduce multiple sets of predictor variables to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioral studies, auxiliary covariates (e.g., gender, ethnicity, etc.) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the effects of predictor components on a response variable vary across subgroups differentiated by covariates. To address this issue, we propose to combine ERA with model-based recursive partitioning in a single framework. This method aims to partition observations into heterogeneous subgroups recursively based on a set of covariates and to apply ERA to each subgroup simultaneously. It can show how the parameter estimates of ERA differ across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of covariates, as well as interpreting their interactions. In the analyses of two publicly available data concerning nicotine dependence and obesity among US adults, the method uncovered heterogeneous subgroups characterized by several covariates, each of which yielded different ERA solutions.