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In unitquantreg: Parametric Quantile Regression Models for Bounded Data

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

The goal of unitquantreg is to provide tools for estimation and inference on parametric quantile regression models for bounded data.

The package was written following the same interface as stats::glm function, containing several S3 methods for inference, residual analysis, prediction, plotting, and model comparison.

For more computation efficient the [dpqr]'s, likelihood, score and hessian functions are vectorized and written in C++.

The parameter estimation and inference are performed under the frequentist paradigm, and the optimx package is used to perform the numerical optimization. Besides that, the analytical score function are provided in the optimization process and the standard errors are computed from the analytical hessian matrix, both function are implemented in efficient away using C++.

The distribution families available are:

lt_families <- list("unit-Weibull" = "uweibull",
                    "Kumaraswamy" = "kum",
                    "unit-Logistic" = "ulogistic",
                    "unit-Birnbaum-Saunders" = "ubs",
                    "log-extended Exponential-Geometric" = "leeg",
                    "unit-Chen" = "uchen",
                    "unit-Generalized Half-Normal-E" = "ughne",
                    "unit-Generalized Half-Normal-X" = "ughnx",
                    "unit-Gompertz" = "ugompertz",
                    "Johnson-SB" = "johnsonsb",
                    "unit-Burr-XII" = "uburrxii",
                    "arc-secant hyperbolic Weibull" = "ashw",
                    "unit-Gumbel" = "ugumbel")

The workhorse function is unitquantreg, which follows the same interface as stats::glm.

library(unitquantreg)
data(water)
lt_fits <- lapply(lt_families, function(fam) {
  unitquantreg(
    formula = phpws ~ mhdi + incpc + region + log(pop), data = water, tau = 0.5,
    family = fam, link = "logit", link.theta = "log")
})
t(sapply(lt_fits, coef))

You can use the likelihood_stats to get likelihood-base statistics:

likelihood_stats(lt = lt_fits)

It is also possible to perform pairwise Vuong test to model selection of nonnested models.

# Select just a few model to not mess the output
lt_chosen <- lt_fits[c("unit-Logistic", "Johnson-SB", "unit-Burr-XII", "unit-Weibull")]
pairwise.vuong.test(lt = lt_chosen)

The currently methods implemented for unitquantreg objects are:

methods(class = "unitquantreg")

Another feature of unitquantreg package is to fit different models for several quantiles values.

fits <- unitquantreg(formula = phpws ~ mhdi + incpc + region + log(pop),
                     data = water, tau = 1:49/50, family = "uweibull",
                     link = "logit", link.theta = "log")
class(fits)