Linear Models for the Analysis of Longitudinal Studies

TLDR

Longitudinal studies are increasingly important in biomedical research, yet most linear modeling approaches rely on standard multivariate linear models. The article proposes a flexible linear modeling framework that allows the expected response to be an arbitrary linear function of fixed and time‑varying covariates, derived from subject‑matter considerations. The framework incorporates three covariance families—multivariate, autoregressive, and random‑effects—to model serial dependence. Illustrations show the approach’s flexibility and utility for longitudinal analysis. Keywords: repeated measures, multivariate regression, random effects, autoregressive models.

Abstract

Abstract Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis. Key Words: Repeated measuresMultivariate regressionRandom effectsAutoregressive models