cdfquantreg: An R Package for CDF-Quantile Regression

Yiyun Shou, Michael Smithson

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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.

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