PLreg: An R Package for Modeling Bounded Continuous Data

The power logit class of distributions is useful for modeling continuous data on the unit interval, such as fractions and proportions. It is very flexible and the parameters represent the median, dispersion and skewness of the distribution. Based on the power logit class, Queiroz and Ferrari (2023b, Statistical Modelling) proposed the power logit regression models. The dependent variable is assumed to have a distribution in the power logit class, with its median and dispersion linked to regressors through linear predictors with unknown coefficients. We present the R package PLreg which implements a suite of functions for working with power logit class of distributions and the associated regression models. This paper describes and illustrates the methods and algorithms implemented in the package, including tools for parameter estimation, diagnosis of fitted models, and various helper functions for working with power logit distributions, including density, cumulative distribution, quantile, and random number generating functions. Additional examples are presented to show the ability of the PLreg package to fit generalized Johnson SB, log-log, and inflated power logit regression models.

Francisco F. Queiroz (Department of Statistics, University of São Paulo) , Silvia L.P. Ferrari (Department of Statistics, University of São Paulo)

0.1 Supplementary materials

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O. E. Barndorff-Nielsen and B. Jørgensen. Some parametric models on the simplex. Journal of Multivariate Analysis, 39(1): 106–116, 1991. DOI 10.1016/0047-259X(91)90008-P.
C. L. Bayes, J. L. Bazán and C. García. A new robust regression model for proportions. Bayesian Analysis, 7(4): 841–866, 2012. DOI 10.1214/12-BA728.
J. M. Chambers and T. J. Hastie, eds. Statistical models in s. London: Chapman & Hall, 1992.
T. L. Cheng, A. Gerson, M. S. Moore, J. D. Reichard, J. DeSimone, C. K. R. Willis, W. F. Frick and A. M. Kilpatrick. Higher fat stores contribute to persistence of little brown bat populations with white-nose syndrome. Journal of Animal Ecology, 88(4): 591–600, 2019. DOI 10.1111/1365-2656.12954.
P. K. Dunn and G. K. Smyth. Randomized quantile residuals. Journal of Computational and Graphical Statistics, 5(3): 236–244, 1996. DOI 10.1080/10618600.1996.10474708.
S. L. P. Ferrari and F. Cribari-Neto. Beta regression for modelling rates and proportions. Journal of Applied Statistics, 31(7): 799–815, 2004. DOI 1010.1080/0266476042000214501.
E. Gómez-Déniz, M. A. Sordo and E. Calderín-Ojeda. The log–lindley distribution as an alternative to the beta regression model with applications in insurance. Insurance: Mathematics and Economics, 54: 49–57, 2014. DOI 10.1016/j.insmatheco.2013.10.017.
N. L. Johnson. Systems of frequency curves generated by methods of translation. Biometrika, 36(1/2): 149–176, 1949. DOI 10.2307/2332539.
M. Korkmaz. A new heavy-tailed distribution defined on the bounded interval: The logit slash distribution and its application. Journal of Applied Statistics, 47(12): 2097–2119, 2020. DOI 10.1080/02664763.2019.1704701.
A. J. Lemonte and J. L. Bazán. New class of johnson distributions and its associated regression model for rates and proportions. Biometrical Journal, 58(4): 727–746, 2016. DOI 10.1002/bimj.201500030.
R. F. da Paz, N. Balakrishnan and J. L. Bazán. L-logistic regression models: Prior sensitivity analysis, robustness to outliers and applications. Brazilian Journal of Probability and Statistics, 33(3): 455–479, 2019. DOI 10.1214/18-BJPS397.
F. F. Queiroz and S. L. P. Ferrari. PLreg: Power logit regression for modeling bounded data. 2023a. URL R package version 0.4.1.
F. F. Queiroz and S. L. P. Ferrari. Power logit regression for modeling bounded data. Statistical Modelling, 2023b. DOI 10.1177/1471082X221140157.
F. F. Queiroz and A. J. Lemonte. A broad class of zero-or-one inflated regression models for rates and proportions. Canadian Journal of Statistics, 49(2): 566–590, 2021. DOI 10.1002/cjs.11576.
J. T. Schmit and K. Roth. Cost effectiveness of risk management practices. The Journal of Risk and Insurance, 57(3): 455–470, 1990.
Y. Shou and M. Smithson. Cdfquantreg: Quantile regression for random variables on the unit interval. 2022. URL R package version 1.3.1-1.
M. Smithson and Y. Shou. CDF-quantile distributions for modelling random variables on the unit interval. British Journal of Mathematical and Statistical Psychology, 70(3): 412–438, 2017. DOI 10.1111/bmsp.12091.
D. M. Stasinopoulos and R. A. Rigby. Generalized additive models for location scale and shape (GAMLSS) in r. Journal of Statistical Software, 23(7): 1–46, 2007. DOI 10.18637/jss.v023.i07.
A. Zeileis, F. Cribari-Neto, B. Gruen and I. Kosmidis. Betareg: Beta regression. 2021. URL R package version 3.1-4.
A. Zeileis and Y. Croissant. Extended model formulas in r: Multiple parts and multiple responses. Journal of Statistical Software, 34(1): 1–13, 2010. DOI 10.18637/jss.v034.i01.
P. Zhang and Z. Qiu. Regression analysis of proportional data using simplex distribution. Science China Mathematics (Chinese Version), 44(1): 89–104, 2014. DOI 10.1360/012013-200.
P. Zhang, Z. Qiu and C. Shi. Simplexreg: Regression analysis of proportional data using simplex distribution. 2016. URL R package version 1.3.



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For attribution, please cite this work as

Queiroz & Ferrari, "PLreg: An R Package for Modeling Bounded Continuous Data", The R Journal, 2024

BibTeX citation

  author = {Queiroz, Francisco F. and Ferrari, Silvia L.P.},
  title = {PLreg: An R Package for Modeling Bounded Continuous Data},
  journal = {The R Journal},
  year = {2024},
  note = {},
  doi = {10.32614/RJ-2023-093},
  volume = {15},
  issue = {4},
  issn = {2073-4859},
  pages = {236-254}