A Bayesian Model for Multivariate Functional Principal Components Analysis

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Mental Health Statistics Section
• Author(s): Kevin Cummins* and Wesley Thompson
• Companies: UC San Diego and UC San Diego
• Keywords: longitudinal ; Bayesian ; multivariate ; FPCA

Abstract

We describe a methodology for performing functional principal components analysis (FPCA) using a reduced-rank model similar to James et al. (Biometrika, 2000). This model is applicable to "sparse" longitudinal data, i.e., data collected with irregular number and timing across subjects. The main methodological innovation is that the FPCA is modeled on multiple sparse longitudinal outcomes simultaneously. While, for identifiability, functional principal components (FPCs) are forced to be independent within a measurement domain, we allow that the FPCs may be correlated among domains, so that modes of variation in one measure can be correlated with modes of variation in another. We describe a mutual information measure as an overall summary of the degree of "connectivity" between two domains. Moreover, if there are three or more domains of measurement, we describe a partial mutual information measure that describes the connectivity between modes of variation in two domains partialling out the effects of a the remaining domains. The inferential methodology is Bayesian, and employs an MCMC algorithm that is described in the talk. We apply the mFPCA methodology to a longitudinal developm