Estimation in nonlinear mixed-effects models using heavy-tailed distributions
- 613 Downloads
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.
KeywordsMixed-effects model Outliers Scale mixtures of normal distributions SAEM algorithm Random effects
Unable to display preview. Download preview PDF.
- Beal, S.L., Sheiner, L.B.: NONMEN User’s Guide. Nonlinear Mixed-Effects Models for Repeated Measures Data. University of California, San Francisco (1992) Google Scholar
- Cook, R.D.: Local Influence. In: Kotz, S., Read, C.B., Banks, D.L. (eds.) Encyclopedia of Statistical Sciences, Update, vol. 1, pp. 380–385. Wiley, New York (1997) Google Scholar
- Davidian, M., Giltinan, D.M.: Nonlinear Models for Repeated Measurements Data. Chapman & Hall, New York (1995) Google Scholar
- De la Cruz, R., Branco, M.D.: Bayesian analysis for nonlinear regression model under skewed errors, with application in growth curves. Biometric. J. 51(4), 588609 (2009) Google Scholar
- Jamshidian, M.: Adaptive robust regression by using a nonlinear regression program. J. Stat. Softw. http://www.jstatsoft.org/v04/i06 (1999)
- Lavielle, M.: Monolix User Guide Manual. http://www.monolix.org (2005)
- Lin, T.I.: Longitudinal data analysis using t linear mixed models with autoregressive dependence structures. J. Data Sci. 6, 333–355 (2008) Google Scholar
- Spiegelhalter, D.J., Thomas, A., Best, N.G.: Winbugs version 1.2 user manual. MRC Biostatistics Unit (1999) Google Scholar
- Welsh, A.H., Richardson, A.M.: Approaches to the robust estimation of mixed models. In: Maddala, G.S., Rao, C.R. (eds.) Handbook of Statistics, vol. 15, pp. 343–384. Elsevier Science, Amsterdam (1997) Google Scholar