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

Author

Listed:
  • Lucas Couri

    (Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

  • Raydonal Ospina

    (Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

  • Geiza da Silva

    (Department of Statistics, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Jorge Figueroa-Zúñiga

    (Department of Statistics, Universidad de Concepción, Concepción 4070386, Chile)

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.

Suggested Citation

  • Lucas Couri & Raydonal Ospina & Geiza da Silva & Víctor Leiva & Jorge Figueroa-Zúñiga, 2022. "A Study on Computational Algorithms in the Estimation of Parameters for a Class of Beta Regression Models," Mathematics, MDPI, vol. 10(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:299-:d:728062
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    References listed on IDEAS

    as
    1. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
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