TY - JOUR
T1 - Cdfquantreg
T2 - An R package for CDF-quantile regression
AU - Shou, Yiyun
AU - Smithson, Michael
N1 - Publisher Copyright:
© 2019, American Statistical Association. All rights reserved.
PY - 2019
Y1 - 2019
N2 - The CDF-quantile family of two-parameter distributions with support (0, 1) described in Smithson and Merkle (2014) and recently elaborated by Smithson and Shou (2017), considerably expands the variety of distributions available for modeling random variables on the unit interval. This family is especially useful for modeling quantiles, and also sometimes out-performs the other distributions. The distributions are very tractable, with a location and dispersion parameter, explicit probability distribution functions, cumulative distribution functions, and quantiles. They enable a wide variety of quantile regression models with predictors for the location and dispersion parameters, and simple interpretations of those parameters. The R package cdfquantreg (Shou and Smithson 2019) (at least R 3.2.0) presented in this paper includes 36 distributions from the CDF-quantile family. Separate submodels may be specified for the location and for the dispersion parameters, with different or overlapping sets of predictors in each. The package offers maximum likelihood, Bayesian MCMC, and bootstrap estimation methods. Model diagnostics, including the gradient, three types of residuals, and the dfbeta influence measures, are available for evaluating models. The package also provides pseudo-random generators for all of its distributions. Many of its functions and their usage have forms familiar to R users, and the documentation is extensive. We also present a SAS macro for general linear models using the CDF-quantile family that includes many of the same capabilities as the cdfquantreg package. The paper provides examples of applications to real data-sets.
AB - The CDF-quantile family of two-parameter distributions with support (0, 1) described in Smithson and Merkle (2014) and recently elaborated by Smithson and Shou (2017), considerably expands the variety of distributions available for modeling random variables on the unit interval. This family is especially useful for modeling quantiles, and also sometimes out-performs the other distributions. The distributions are very tractable, with a location and dispersion parameter, explicit probability distribution functions, cumulative distribution functions, and quantiles. They enable a wide variety of quantile regression models with predictors for the location and dispersion parameters, and simple interpretations of those parameters. The R package cdfquantreg (Shou and Smithson 2019) (at least R 3.2.0) presented in this paper includes 36 distributions from the CDF-quantile family. Separate submodels may be specified for the location and for the dispersion parameters, with different or overlapping sets of predictors in each. The package offers maximum likelihood, Bayesian MCMC, and bootstrap estimation methods. Model diagnostics, including the gradient, three types of residuals, and the dfbeta influence measures, are available for evaluating models. The package also provides pseudo-random generators for all of its distributions. Many of its functions and their usage have forms familiar to R users, and the documentation is extensive. We also present a SAS macro for general linear models using the CDF-quantile family that includes many of the same capabilities as the cdfquantreg package. The paper provides examples of applications to real data-sets.
KW - Distribution
KW - Quantile regression
KW - R
KW - Unit interval
UR - http://www.scopus.com/inward/record.url?scp=85061397766&partnerID=8YFLogxK
U2 - 10.18637/jss.v088.i01
DO - 10.18637/jss.v088.i01
M3 - Article
SN - 1548-7660
VL - 88
JO - Journal of Statistical Software
JF - Journal of Statistical Software
IS - 1
ER -