Mixed Effects Envelope Models

TL;DR

This paper extends the envelope method to mixed effects models for longitudinal data, improving estimation efficiency and accuracy over standard methods, demonstrated through simulations and real data analysis.

Contribution

It introduces a novel mixed effects envelope model that enhances efficiency in longitudinal data analysis with unbalanced designs and time-varying predictors.

Findings

More efficient estimators than standard mixed effects models.

Improved accuracy demonstrated in simulations.

Enhanced performance shown in the ACCORD study.

Abstract

When multiple measures are collected repeatedly over time, redundancy typically exists among responses. The envelope method was recently proposed to reduce the dimension of responses without loss of information in regression with multivariate responses. It can gain substantial efficiency over the standard least squares estimator. In this paper, we generalize the envelope method to mixed effects models for longitudinal data with possibly unbalanced design and time-varying predictors. We show that our model provides more efficient estimators than the standard estimators in mixed effects models. Improved accuracy and efficiency of the proposed method over the standard mixed effects model estimator are observed in both the simulations and the Action to Control Cardiovascular Risk in Diabetes (ACCORD) study.