B1782
Title: A comprehensive R package for regression models with bounded continuous and discrete responses
Authors: Agnese Maria Di Brisco - University of Piemonte Orientale (Italy) [presenting]
Roberto Ascari - University of Milano-Bicocca (Italy)
Sonia Migliorati - University of Milano Bicocca (Italy)
Andrea Ongaro - University of Milano-Bicocca (Italy)
Abstract: The development of regression models for bounded responses has grown considerably in recent years. When the response is bounded continuous, for example, rates and proportions, some widespread choices are the beta regression model and its more flexible alternatives such as the flexible beta and the variance inflated beta. Interestingly, the latter two models can address outlying observations, latent structures, and heavy tails. In addition, the augmented alternatives of these models can be formulated to deal with the presence of values at the boundary of the support. When the response is bounded discrete, for example, the number of successes in n Bernoulli trials, a widespread approach is to use the binomial regression model. Nonetheless, to cope with overdispersion problems, interesting alternative models are the beta-binomial and the flexible beta-binomial. Apart from a comprehensive review, this contribution shows, through simulation studies and applications to real data, how to implement all these models in R thanks to the FlexReg package. Indeed, the package includes two main functions for fitting the above-mentioned regression models with a Bayesian approach to inference through the Hamiltonian Monte Carlo algorithm. Besides, it provides numerous functions to summarize the results of the regression models, to provide graphical representations, to check for convergence of the Markov chains, and to compute residuals, posterior predictive, and goodness-of-fit measures.
