A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models

Abstract

Beta regressions describe the relationship between a response that assumes values in the zero-one range and covariates. These regressions are used for modeling rates, ratios, and proportions. We study computational aspects related to parameter estimation of a class of beta regressions for the mean with fixed precision by maximizing the log-likelihood function with heuristics and other optimization methods. Through Monte Carlo simulations, we analyze the behavior of ten algorithms, where four of them present satisfactory results. These are the differential evolutionary, simulated annealing, stochastic ranking evolutionary, and controlled random search algorithms, with the latter one having the best performance. Using the four algorithms and the optim function of R, we study sets of parameters that are hard to be estimated. We detect that this function fails in most cases, but when it is successful, it is more accurate and faster than the others. The annealing algorithm obtains satisfactory estimates in viable time with few failures so that we recommend its use when the optim function fails.