TY - JOUR

T1 - A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models

AU - Couri, Lucas

AU - Ospina, Raydonal

AU - da Silva, Geiza

AU - Leiva, Víctor

AU - Figueroa-Zúñiga, Jorge

N1 - Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/2/1

Y1 - 2022/2/1

N2 - 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.

AB - 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.

KW - Computational statistics

KW - Heuristic

KW - Likelihood function

KW - Monte Carlo method

KW - R software

UR - http://www.scopus.com/inward/record.url?scp=85123126735&partnerID=8YFLogxK

U2 - 10.3390/math10030299

DO - 10.3390/math10030299

M3 - Article

AN - SCOPUS:85123126735

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 3

M1 - 299

ER -