Handling heterogeneity among units in Quantile Regression

Cristina Davino, Domenico Vistocco
(2015) Book of Abstracts - CLADAG 2015, ISBN 978-88-8467-949-9

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In many real data applications statistical units belong to different groups and a statistical model should be tailored to incorporate and exploit this heterogeneity among units. This is also the case of the analysis of the relationship between a response variable and a set of regressors that cannot be carried out by neglecting the membership of the units to the different groups. Several approaches have been proposed in the literature to analyze group effects in a dependence model (the use of dummy variables to denote group membership or multilevel models among the others). All of them share the aim to inspect how the group structure affects the impact of the regressors on the dependent variable, without providing details on the dependence structure inside the groups. Moreover, they are tailored for the estimation of the average effects. To estimate group effects at different points of the response conditional distribution, Davino & Vistocco, 2008 proposed to exploit quantile regression (QR), a method that is able to model the entire conditional distribution of a response variable. This paper discusses strengths and properties of such proposal through a simulation study.