Finite mixture-based Bayesian analysis of linear-circular models

In many environmental and agricultural studies data on both linear and circular measurements are collected, with possible dependence between the variables. An example of linear-circular data, taken from the literature, consists of observations on some index of air quality, associated temperature, wind speed, and wind direction. The latter is a circular variable, while the others are linear variables. Classically, analysis of such data has been carried out by assuming a classical regression framework, where one variable, the prediction of which is of interest, is assumed to be the response variable, while others are considered fixed covariates. It is not clear, however, other than reasons of simplicity, why except one variable all others must be treated as fixed. It is certainly more appropriate to assume a joint multivariate model of all the variables, consisting of both linear and circular components. In our linear-circular model, marginally, the circular component is assumed to be a mixture of von Mises (or, circular normal) distributions. We propose a Bayesian framework for this model, and use Markov chain Monte Carlo techniques for inference. We also describe model comparison using pseudo Bayes factor. Illustrations of our methodologies with simulated and real data sets are also provided.