Computationally Stable Estimation Procedure for the Multivariate Linear Mixed-Effect Model and Application to Malaria Public Health Problem

Adjakossa Eric Houngla (), Hounkonnou Norbert Mahouton () and Nuel Grégory ()
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Adjakossa Eric Houngla: International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Université d’Abomey-Calavi, Cotonou, Benin
Hounkonnou Norbert Mahouton: International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Université d’Abomey-Calavi, Cotonou, Benin
Nuel Grégory: Laboratoire de Probabilités, Statistique et Modélisation (UMR 8001), Sorbonne Université, Paris, France

The International Journal of Biostatistics, 2019, vol. 15, issue 2, 19

Abstract: In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. This strategy can be viewed as the generalization of the estimation procedure used by Douglas Bates and his co-authors in the context of the fitting of one-dimensional linear mixed-effects models. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non-consistent. In a simulation study, we compare the estimates obtained from the present method with the EM algorithm-based estimates. We finally apply the method to a study of an immune response to Malaria in Benin.

Keywords: multivariate linear mixed-effects model; profiled deviance; ML and REML criteria; numerical consistency (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1515/ijb-2017-0076

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