Statistical Modelling 11 (2011), 185–201
A Bayesian regression model for circular data based on the projected
normal distribution
Gabriel Nuñez-Antonio
Department of Mathematics,
Universidad Autónoma Metropolitana, Iztapalapa,
Av. Golondrinas 25, Col. Benito Juárez
Cd. Nezahualcoyotl, Edo. de Méx., C.P. 57000
México
and
Department of Statistics,
Universidad Carlos III de Madrid
España
eMail: gab.nunezantonio@gmail.com
Eduardo Gutiérrez-Peña
Department of Probability and Statistics,
IIMAS-Universidad Nacional Autónoma de México
México
Gabriel Escarela
Department of Mathematics,
Universidad Autónoma Metropolitana, Iztapalapa
México
Abstract:
Inferences based on regression models for a directional response are
usually problematic. This paper presents a Bayesian analysis of a
regression model for circular data using the projected normal
distribution. Inferences about the model are based on samples from the
posterior densities which are obtained using the Gibbs sampler after the
introduction of suitable latent variables. The problem of missing data
in the response variable is also addressed in this context as is the use
of a predictive criterion for model selection. The procedures are
illustrated using two simulated datasets a dataset previously analysed
in the literature and a real dataset concerning wind directions.
Keywords:
circular-linear regression; Gibbs sampler; latent variables;
missing data; model selection
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