Bayesian flexible beta regression model with functional covariate

Abstract

Standard parametric regression models are unsuitable when the aim is to predict a bounded continuous response, such as a proportion/percentage or a rate. A possible solution is the flexible beta regression model which is based on a special mixture of betas designed to cope with (though not limited to) bimodality, heavy tails, and outlying observations. This work introduces such a model in the case of a functional covariate, motivated by a spectrometric analysis on milk specimens. Estimation issues are dealt with through a combination of standard basis expansion and Markov chains Monte Carlo techniques. Specifically, the selection of the most significant coefficients of the expansion is done through Bayesian variable selection methods that take advantage of shrinkage priors. The effectiveness of the proposal is illustrated with simulation studies and the application on spectrometric data.