Generalized Conditional Functional Principal Component Analysis

TL;DR

This paper introduces GC-FPCA, a scalable method for joint modeling of non-Gaussian functional data that combines local GLMMs, FPCA, and joint mixed effects modeling, demonstrated on large NHANES activity data.

Contribution

The paper presents a novel scalable approach for non-Gaussian functional data analysis combining local GLMMs, FPCA, and joint modeling, suitable for very large datasets.

Findings

GC-FPCA handles large-scale NHANES data efficiently.

State-of-the-art methods cannot scale to this data size.

GC-FPCA accurately models minute-level activity profiles.

Abstract

We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by estimating the principal components of the covariance matrix on the linear predictor scale conditional on the fixed effects. This is achieved by combining three modeling innovations: (1) fit local generalized linear mixed models (GLMMs) conditional on covariates in windows along the functional domain; (2) conduct a functional principal component analysis (FPCA) on the person-specific functional effects obtained by assembling the estimated random effects from the local GLMMs; and (3) fit a joint functional mixed effects model conditional on covariates and the estimated principal components from the previous step. GC-FPCA was motivated by modeling the minute-level active/inactive profiles over the day ($1{,}440$ 0/1 measurements per person) for $8{,}700$ study participants in the National Health and Nutrition Examination Survey (NHANES) 2011-2014. We show that state-of-the-art approaches cannot handle data of this size and complexity, while GC-FPCA can.