Modeling Multivariate Mixed-Response Functional Data

TL;DR

This paper introduces a Bayesian framework for jointly modeling multiple types of functional data using a multivariate latent Gaussian process, enabling flexible dependence modeling and covariate inclusion.

Contribution

The paper presents a novel Bayesian approach for multivariate mixed-response functional data analysis using latent Gaussian processes, with methods for covariance estimation and FPCA.

Findings

Effective in simulation studies

Successfully applied to periodontal data

Provides a flexible modeling framework

Abstract

We propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence among the functional responses through the dependence of the latent process. Our framework easily accommodates additional covariates. We offer a way to estimate the multivariate latent covariance, allowing for implementation of multivariate functional principal components analysis (FPCA) to specify basis expansions and simplify computation. We demonstrate our method through both simulation studies and an application to real data from a periodontal study.