Estimation in nonlinear mixed-effects models using heavy-tailed distributions |
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Authors: | Cristian Meza Felipe Osorio Rolando De?la?Cruz |
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Institution: | (1) Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7420, USA;(2) Department of Psychiatry, Columbia University and New York State Psychiatric Institute, 1051 Riverside Drive, Unit 74, New York, New York 10032, USA;(3) Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China |
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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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Keywords: | |
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