Bayesian latent factor regression for multivariate functional data with variable selection

Abstract

In biomedical research, multivariate functional data (MFD) are frequently encountered. Majority of the existing approaches for functional data analysis focus on univariate functional data (UFD) and the methodology for MFD is far less studied. Particularly, the problem of investigating covariate effects on MFD has received little attention. In this dissertation, we propose a fully Bayesian latent factor regression for studying covariate effects on MFD. The proposed model obtains a low-dimensional representation of MFD through basis expansions for splines and factor analysis for the basis coefficients. Then, the latent factors specific to each functional outcome are regressed onto covariates accounting for residual correlations among multiple outcomes. The assessment of covariate effects is conducted based on the marginal inclusion probability for each covariate, which is calculated a posteriori by assigning a stochastic search variable selection (SSVS) prior to the regression coefficients. To better control for the false discovery rate, we propose a multivariate SSVS prior that allows for a set of coefficients to be zero simultaneously. We illustrate the proposed method through a simulation study and an application to the Japan weather data.