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

Entropy

Wan-Lun Wang¹  Carlos Alberto De Bragan๺ Pereira¹ 

[1] Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung 40724, Taiwan; E-Mail

关键词: importance sampling;    Laplacian approximation;    Monte Carlo EM;    penalized nonlinear least squares;    pseudo expectation conditional maximization;   

DOI  :  10.3390/e17085353

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the author; licensee MDPI, Basel, Switzerland.