zoib: An R Package for Bayesian Inference for Beta Regression and Zero/One Inflated Beta Regression

Abstract The beta distribution is a versatile function that accommodates a broad range of probability distribution shapes. Beta regression based on the beta distribution can be used to model a response variable y that takes values in open unit interval (0, 1). Zero/one inflated beta (ZOIB) regression models can be applied when y takes values from closed unit interval [0, 1]. The ZOIB model is based a piecewise distribution that accounts for the probability mass at 0 and 1, in addition to the probability density within (0, 1). This paper introduces an R package – zoib that provides Bayesian inferences for a class of ZOIB models. The statistical methodology underlying the zoib package is discussed, the functions covered by the package are outlined, and the usage of the package is illustrated with three examples of different data and model types. The package is comprehensive and versatile in that it can model data with or without inflation at 0 or 1, accommodate clustered and correlated data via latent variables, perform penalized regression as needed, and allow for model comparison via the computation of the DIC criterion.