Bayesian beta regression: Applications to household expenditure data and genetic distance between foot-and-mouth disease viruses

Summary There is considerable interest in understanding how factors such as time and geographic distance between isolates might influence the evolutionary direction of foot-and-mouth disease. Genetic differences between viruses can be measured as the proportion of nucleotides that differ for a given sequence or gene. We present a Bayesian hierarchical regression model for the statistical analysis of continuous data with sample space restricted to the interval (0, 1). The data are modelled using beta distributions with means that depend on covariates through a link function. We discuss methodology for: (i) the incorporation of informative prior information into an analysis; (ii) fitting the model using Markov chain Monte Carlo sampling; (iii) model selection using Bayes factors; and (iv) semiparametric beta regression using penalized splines. The model was applied to two different datasets.