A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression:

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization al...