Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
20/10/2012
20/10/2012
2009
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Resumo |
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 measurements 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. |
Identificador |
BIOMETRICAL JOURNAL, v.51, n.4, p.588-609, 2009 0323-3847 http://producao.usp.br/handle/BDPI/30489 10.1002/bimj.200800154 |
Idioma(s) |
eng |
Publicador |
WILEY-V C H VERLAG GMBH |
Relação |
Biometrical Journal |
Direitos |
restrictedAccess Copyright WILEY-V C H VERLAG GMBH |
Palavras-Chave | #Bayesian nonlinear regression #Continuous ranked probability score #Gibbs sampling #Repeated measurements #Skew-normal and skew-t distributions #HUMAN CHORIONIC-GONADOTROPIN #T-DISTRIBUTION #LONGITUDINAL DATA #DISTRIBUTIONS #PREGNANCY #Mathematical & Computational Biology #Statistics & Probability |
Tipo |
article original article publishedVersion |