# Profiled deviance for the multivariate linear mixed-effects model fitting

## TL;DR

This paper introduces a novel approach for estimating the covariance matrix of random effects in multivariate linear mixed-effects models, improving accuracy over traditional methods like EM, demonstrated through simulations and real-world data analysis.

## Contribution

It proposes a new profiling deviance method for better covariance estimation in multivariate mixed-effects models, addressing limitations of existing estimation techniques.

## Key findings

- The new method provides more accurate covariance estimates than EM.
- Simulation studies show improved estimation performance.
- Application to real data demonstrates practical utility.

## Abstract

This paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the marginal residual terms are assumed uncorrelated and homoscedastic with possibly different standard deviations. The random effects covariance matrix is Cholesky factorized to directly estimate the variance components of these random effects. This strategy enables a consistent estimate of the random effects covariance matrix which, generally, has a poor estimate when it is grossly (or directly) estimated, using the estimating methods such as the EM algorithm. By using simulated data sets, we compare the estimates based on the present method with the EM algorithm-based estimates. We provide an illustration by using the real-life data concerning the study of the child's immune against malaria in Benin (West Africa).