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August 2019 L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications
Rosineide F. da Paz, Narayanaswamy Balakrishnan, Jorge Luis Bazán
Braz. J. Probab. Stat. 33(3): 455-479 (August 2019). DOI: 10.1214/18-BJPS397

Abstract

Tadikamalla and Johnson [Biometrika 69 (1982) 461–465] developed the $L_{B}$ distribution to variables with bounded support by considering a transformation of the standard Logistic distribution. In this manuscript, a convenient parametrization of this distribution is proposed in order to develop regression models. This distribution, referred to here as L-Logistic distribution, provides great flexibility and includes the uniform distribution as a particular case. Several properties of this distribution are studied, and a Bayesian approach is adopted for the parameter estimation. Simulation studies, considering prior sensitivity analysis, recovery of parameters and comparison of algorithms, and robustness to outliers are all discussed showing that the results are insensitive to the choice of priors, efficiency of the algorithm MCMC adopted, and robustness of the model when compared with the beta distribution. Applications to estimate the vulnerability to poverty and to explain the anxiety are performed. The results to applications show that the L-Logistic regression models provide a better fit than the corresponding beta regression models.

Citation

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Rosineide F. da Paz. Narayanaswamy Balakrishnan. Jorge Luis Bazán. "L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications." Braz. J. Probab. Stat. 33 (3) 455 - 479, August 2019. https://doi.org/10.1214/18-BJPS397

Information

Received: 1 May 2017; Accepted: 1 March 2018; Published: August 2019
First available in Project Euclid: 10 June 2019

zbMATH: 07094812
MathSciNet: MR3960271
Digital Object Identifier: 10.1214/18-BJPS397

Rights: Copyright © 2019 Brazilian Statistical Association

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Vol.33 • No. 3 • August 2019
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