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

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Estadística, CIMFAV, Universidad de Valparaíso, Gran Bretaña 1091, Valparaíso, Chile

    Cristian Meza & Felipe Osorio

  2. Departamento de Salud Pública, Escuela de Medicina, and Departamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Marcoleta 434, Casilla 114D, Santiago, Chile

    Rolando De la Cruz

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  1. Cristian Meza
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  2. Felipe Osorio
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  3. Rolando De la Cruz
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Correspondence to Cristian Meza.

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Meza, C., Osorio, F. & De la Cruz, R. Estimation in nonlinear mixed-effects models using heavy-tailed distributions. Stat Comput 22, 121–139 (2012). https://doi.org/10.1007/s11222-010-9212-1

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