## Brazilian Journal of Probability and Statistics

### L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications

#### 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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 3 (2019), 455-479.

Dates
Accepted: March 2018
First available in Project Euclid: 10 June 2019

https://projecteuclid.org/euclid.bjps/1560153847

Digital Object Identifier
doi:10.1214/18-BJPS397

Mathematical Reviews number (MathSciNet)
MR3960271

Zentralblatt MATH identifier
07094812

#### Citation

da Paz, Rosineide F.; Balakrishnan, Narayanaswamy; Bazán, Jorge Luis. L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications. Braz. J. Probab. Stat. 33 (2019), no. 3, 455--479. doi:10.1214/18-BJPS397. https://projecteuclid.org/euclid.bjps/1560153847

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#### Supplemental materials

• Supplement to “L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications”. Supplementary information.