TY - JOUR

T1 - Estimation in nonlinear mixed-effects models using heavy-tailed distributions

AU - Meza, Cristian

AU - Osorio, Felipe

AU - De la Cruz, Rolando

N1 - Funding Information:
Acknowledgements The first author was partially supported by grants PBCT PSD-20, DIPUV 5/2007 and FONDECYT 11090024. The second and third authors were partially supported by Fondo Na-cional de Desarrollo Científico y Tecnológico—FONDECYT grants 11075071 and 11080017, respectively. We would also like to thank the reviewers for their constructive comments, which helped to substantially improve this manuscript.

PY - 2012/1

Y1 - 2012/1

N2 - Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivariate distributions, such as Student-t, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.

AB - Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivariate distributions, such as Student-t, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.

KW - Mixed-effects model

KW - Outliers

KW - Random effects

KW - SAEM algorithm

KW - Scale mixtures of normal distributions

UR - http://www.scopus.com/inward/record.url?scp=81955165471&partnerID=8YFLogxK

U2 - 10.1007/s11222-010-9212-1

DO - 10.1007/s11222-010-9212-1

M3 - Article

AN - SCOPUS:81955165471

VL - 22

SP - 121

EP - 139

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 1

ER -