BayesTime: Bayesian Functional Principal Components for Sparse Longitudinal Data

TL;DR

BayesTime introduces a Bayesian framework for sparse functional principal components analysis, enhancing model selection and diagnostics for analyzing individual trajectories in sparse longitudinal data.

Contribution

It presents a Bayesian method for SFPCA that improves model selection and diagnostics using LOO, PSIS, and posterior predictive checks.

Findings

Enables efficient model selection with LOO and PSIS.

Provides improved diagnostic tools for Bayesian SFPCA.

Facilitates analysis of individual trajectories in sparse longitudinal data.

Abstract

Modeling non-linear temporal trajectories is of fundamental interest in many application areas, such as in longitudinal microbiome analysis. Many existing methods focus on estimating mean trajectories, but it is also often of value to assess temporal patterns of individual subjects. Sparse principal components analysis (SFPCA) serves as a useful tool for assessing individual variation in non-linear trajectories; however its application to real data often requires careful model selection criteria and diagnostic tools. Here, we propose a Bayesian approach to SFPCA, which allows users to use the efficient leave-one-out cross-validation (LOO) with Pareto-smoothed importance sampling (PSIS) for model selection, and to utilize the estimated shape parameter from PSIS-LOO and also the posterior predictive checks for graphical model diagnostics. This Bayesian implementation thus enables careful application of SFPCA to a wide range of longitudinal data applications.