Brazilian Journal of Probability and Statistics

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

Rosineide F. da Paz, Narayanaswamy Balakrishnan, and Jorge Luis Bazán

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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
Received: May 2017
Accepted: March 2018
First available in Project Euclid: 10 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1560153847

Digital Object Identifier
doi:10.1214/18-BJPS397

Mathematical Reviews number (MathSciNet)
MR3960271

Zentralblatt MATH identifier
07094812

Keywords
Bayesian analysis L-Logistic distribution regression analysis beta distribution sensibility analysis

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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References

  • Albert, I., Donnet, S., Guihenneuc-Jouyaux, C., Low-Choy, S., Mengersen, K. and Rousseau, J. (2012). Combining expert opinions in prior elicitation. Bayesian Analysis 7, 503–532.
  • Arnold, B. C. and Groeneveld, R. A. (1995). Measuring skewness with respect to the mode. American Statistician 49, 34–38.
  • Bayes, C., Bazán, J. L. and García, C. (2012). A new robust regression model for proportions. Bayesian Analysis 7, 841–866.
  • Bayes, L. C., Bazán, J. L. and Castro, M. (2017). A quantile parametric mixed regression model for bounded response variables. Statistics & Its Interface 10, 483–493.
  • Brys, G., Hubert, M. and Struyf, A. (2003). A comparison of some new measures of skewness. In Developments in Robust Statistics (R. Dutter, P. Filzmoser, U. Gather and P. J. Rousseeuw, eds.) 98–113. Springer.
  • Buckley, J. (2003). Estimation of models with beta-distributed dependent variables: A replication and extension of Paolino’s study. Political Analysis 11, 204–205.
  • Cai, Y. and Jiang, T. (2015). Estimation of non-crossing quantile regression curves. Australian & New Zealand Journal of Statistics 57, 139–162.
  • da Paz, R. F., Balakrishnan, N. and Bazán, J. L. (2018). Supplement to “L-Logistic regression models: Prior sensitivity analysis, robustness to outliers and applications.” DOI:10.1214/18-BJPS397SUPP.
  • Ferrari, S. and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics 31, 799–815.
  • Figueroa-Zúñiga, J. I., Arellano-Valle, R. B. and Ferrari, S. L. P. (2013). Mixed beta regression: A Bayesian perspective. Computational Statistics & Data Analysis 61, 137–147.
  • Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A. and Rubin, D. B. (2013). Bayesian Data Analysis. Philadelphia, PA.: Third Edition, Taylor & Francis.
  • Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2014). Bayesian Data Analysis, Vol. 2. Boca Raton, FL, USA: Chapman & Hall/CRC Press.
  • Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In Bayesian Statistics (J. M. Bernardo, J. Berger, A. P. Dawid and J. F. M. Smith, eds.) 169–193. London, England: Oxford University Press.
  • Gómez-Déniz, E., Sordo, M. A. and Calderín-Ojeda, E. (2014). The Log-Lindley distribution as an alternative to the beta regression model with applications in insurance. Insurance Mathematics & Economics 54, 49–57.
  • Gupta, A. K. and Nadarajah, S. (2004). Handbook of Beta Distribution and Its Applications. Philadelphia: Taylor & Francis.
  • Hao, L. and Naiman, D. Q. (2007). Quantile Regression. New Jersey: SAGE Publications.
  • Hinkley, D. V. (1975). On power transformations to symmetry. Biometrika 62, 101–111.
  • Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika 36, 149–176.
  • Johnson, N. L. and Tadikamalla, P. R. (1991). Translated family of distribution. In Handbook of the Logistic Distribution (N. Balakrishnan, ed.), 189–208. New York: Marcel Derrer.
  • Koenker, R. and Bassett, G. Jr. (1978). Regression quantiles. Econometrica 46, 33–50.
  • Lemonte, A. J. and Bazán, J. L. (2016). New class of Johnson SB distributions and its associated regression model for rates and proportions. Biometrical Journal 58, 727–746. ISSN 1521-4036.
  • Martin, A. D., Quinn, K. M. and Park, J. H. (2011). MCMCpack: Markov Chain Monte Carlo in R. Journal of Statistical Software 42, 1–22.
  • Moors, J. J. A. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society, Series B 37, 25–32.
  • Paz, R. F., Bazán, J. L. and Milan, L. A. (2015). Bayesian estimation for a mixture of simplex distributions with an unknown number of components: HDI analysis in Brazil. Journal of Applied Statistics 44, 1–14.
  • PNUD, IPEA and FJP (2013). Atlas do Desenvolvimento Humano No Brasil. Brasilia, Brazil: PNUD. Disponible in: http://www.atlasbrasil.org.br/2013/pt/.
  • R Development Core Team (2015) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. Available at http://www.r-project.org/.
  • Smithson, M. and Verkuilen, J. (2006). A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. Psychological Methods 11, 1–54.
  • Tadikamalla, P. R. and Johnson, N. L. (1982). Systems of frequency curves generated by transformations of logistic variables. Biometrika 69, 461–465.
  • Tadikamalla, P. R. and Johnson, N. L. (1990). Tables to facilitate fitting Tadikamalla and Johnson’s LB distributions. Communications in Statistics Simulation and Computation 19(4), 1201–1229.
  • Wang, M. and Rennolls, K. (2005). Tree diameter distribution modelling: Introducing the logit–logistic distribution. Canadian Journal of Forest Research 35, 1305–1313.

Supplemental materials

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