Multivariate Skew Normal Independent Nonlinear Mixed Model for Longitudinal Data

Maha  E. Qura; Ahmed  M. Gad; Zohdi  Nofal

Authors

Maha E. Qura Department of Statistics, Mathematics & Insurance, Faculty of Commerce, Banha University, Egypt
Ahmed M. Gad Business Administration Department, Faculty of Business Administration, Economics and Political Science, British University in Egypt (BUE), Egypt
Zohdi Nofal Department of Statistics, Mathematics & Insurance, Faculty of Commerce, Banha University, Egypt

Keywords:

AR(1) correlation, multivariate longitudinal data, nonlinear mixed effects, damped exponential correlation, unstructured correlation

Abstract

The multivariate nonlinear mixed effects models (MNLMM) have received increasing attention due to their flexibility in analyzing and modeling multivariate longitudinal data. In the framework of MNLMM, the random effects and within-subject errors are assumed to be normally distributed for mathematical tractability and computational simplicity. However, such assumption might not offer robust inference if the data, even after being transformed, exhibit skewness. In this paper, we propose a multivariate skew normal independent nonlinear mixed model (MSNI-NLMM) constructed by assuming a multivariate skew normal independent distribution for the random effects and a multivariate normal independent distribution for the random errors. We develop a new model which can flexibly handle asymmetric, unbalanced, and irregularly observed multivariate longitudinal data. Also, we present two different iterative algorithms for maximum likelihood estimation of the MSNI-NLMM. They are the penalized nonlinear least squares coupled to the multivariate linear mixed effects (PNLS-MLME) procedure and the pseudo-data expectation conditional maximization (ECM) algorithm. The proposed approaches are illustrated through an application to ACTG 315 data and a simulation study.

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