Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

de la Cruz R.; Branco, MD

Abstract

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated mea- surements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Más información

Título según WOS: Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves
Título según SCOPUS: Bayesian analysis for nonlinear regression model under Skewed errors, with application in growth curves
Título de la Revista: BIOMETRICAL JOURNAL
Volumen: 51
Número: 4
Editorial: Wiley
Fecha de publicación: 2009
Página de inicio: 588
Página final: 609
Idioma: English
URL: http://doi.wiley.com/10.1002/bimj.200800154
DOI:

10.1002/bimj.200800154

Notas: ISI, SCOPUS