Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions
Christian E. Galarza,
Panpan Zhang and
Víctor H. Lachos ()
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Christian E. Galarza: Escuela Superior Politécnica del Litoral
Panpan Zhang: University of Pennsylvania
Víctor H. Lachos: University of Connecticut
Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 2, No 6, 325-349
Abstract Mean regression model could be inadequate if the probability distribution of the observed responses is not symmetric. Under such situation, the quantile regression turns to be a more robust alternative for accommodating outliers and misspecification of the error distribution, since it characterizes the entire conditional distribution of the outcome variable. This paper proposes a robust logistic quantile regression model by using a logit link function along the EM-based algorithm for maximum likelihood estimation of the p th quantile regression parameters in Galarza (Stat 6, 1, 2017). The aforementioned quantile regression (QR) model is built on a generalized class of skewed distributions which consists of skewed versions of normal, Student’s t, Laplace, contaminated normal, slash, among other heavy-tailed distributions. We evaluate the performance of our proposal to accommodate bounded responses by investigating a synthetic dataset where we consider a full model including categorical and continuous covariates as well as several of its sub-models. For the full model, we compare our proposal with a non-parametric alternative from the so-called quantreg R package. The algorithm is implemented in the R package lqr, providing full estimation and inference for the parameters, automatic selection of best model, as well as simulation of envelope plots which are useful for assessing the goodness-of-fit.
Keywords: Bounded outcomes; Quantile regression model; EM algorithm; Scale mixtures of Normal distributions; Primary 62M10; Secondary 62E10. (search for similar items in EconPapers)
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