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Entropy 2015, 17(8), 5353-5381; doi:10.3390/e17085353

Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models

Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung 40724, Taiwan
Academic Editors: Carlos Alberto De Bragança Pereira and Adriano Polpo
Received: 21 April 2015 / Revised: 17 July 2015 / Accepted: 21 July 2015 / Published: 29 July 2015
(This article belongs to the Special Issue Inductive Statistical Methods)
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Abstract

Multivariate nonlinear mixed-effects models (MNLMM) have received increasing use due to their flexibility for analyzing multi-outcome longitudinal data following possibly nonlinear profiles. This paper presents and compares five different iterative algorithms for maximum likelihood estimation of the MNLMM. These algorithmic schemes include the penalized nonlinear least squares coupled to the multivariate linear mixed-effects (PNLS-MLME) procedure, Laplacian approximation, the pseudo-data expectation conditional maximization (ECM) algorithm, the Monte Carlo EM algorithm and the importance sampling EM algorithm. When fitting the MNLMM, it is rather difficult to exactly evaluate the observed log-likelihood function in a closed-form expression, because it involves complicated multiple integrals. To address this issue, the corresponding approximations of the observed log-likelihood function under the five algorithms are presented. An expected information matrix of parameters is also provided to calculate the standard errors of model parameters. A comparison of computational performances is investigated through simulation and a real data example from an AIDS clinical study. View Full-Text
Keywords: importance sampling; Laplacian approximation; Monte Carlo EM; penalized nonlinear least squares; pseudo expectation conditional maximization importance sampling; Laplacian approximation; Monte Carlo EM; penalized nonlinear least squares; pseudo expectation conditional maximization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, W.-L. Approximate Methods for Maximum Likelihood Estimation of Multivariate Nonlinear Mixed-Effects Models. Entropy 2015, 17, 5353-5381.

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