On the use of quantile regression to deal with heterogeneity: the case of multi-block data

Cristina Davino, Rosaria Romano, Domenico Vistocco
(2020) Advances in Data Analysis and Classification, 14, 771-784

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The aim of the paper is to propose a quantile regression based strategy to assess heterogeneity in a multi-block type data structure. Specifically, the paper deals with a particular data structure where several blocks of variables are observed on the same units and a structure of relations is assumed between the different blocks. The idea is that quantile regression complements the results of the least squares regression by evaluating the impact of regressors on the entire distribution of the dependent variable, and not only exclusively on the expected value. By taking advantage of this, the proposed approach analyses the relationship among a dependent variable block and a set of regressors blocks but highlighting possible similarities among the statistical units. An empirical analysis is provided in the consumer analysis framework with the aim to cluster groups of consumers according to the similarities in the dependence structure among their overall liking and the liking for different drivers.