A0907
Title: A monotone single index model for missing-at-random longitudinal proportion data
Authors: Debdeep Pati - Texas A&M University (United States)
Dipankar Bandyopadhyay - Virginia Commonwealth University (United States)
Satwik Acharyya - University of Michigan (United States) [presenting]
Abstract: Beta distributions are commonly used to model proportion valued response variables, commonly encountered in longitudinal studies. We develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using an interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single-index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilizes Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat.
