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

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  • Cristina Davino

    (University of Naples Federico II)

  • Rosaria Romano

    (University of Naples Federico II)

  • Domenico Vistocco

    (University of Naples Federico II)

Abstract

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.

Suggested Citation

  • Cristina Davino & Rosaria Romano & Domenico Vistocco, 2020. "On the use of quantile regression to deal with heterogeneity: the case of multi-block data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(4), pages 771-784, December.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:4:d:10.1007_s11634-020-00410-x
    DOI: 10.1007/s11634-020-00410-x
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    References listed on IDEAS

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    1. Dario Bruzzese & Domenico Vistocco, 2015. "DESPOTA: DEndrogram Slicing through a PemutatiOn Test Approach," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 285-304, July.
    2. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    3. Martens, Harald & Anderssen, Endre & Flatberg, Arnar & Gidskehaug, Lars Halvor & Hoy, Martin & Westad, Frank & Thybo, Anette & Martens, Magni, 2005. "Regression of a data matrix on descriptors of both its rows and of its columns via latent variables: L-PLSR," Computational Statistics & Data Analysis, Elsevier, vol. 48(1), pages 103-123, January.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Cristina Davino & Rosaria Romano, 2014. "Assessment of Composite Indicators Using the ANOVA Model Combined with Multivariate Methods," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 119(2), pages 627-646, November.
    6. Hanafi, Mohamed & Kiers, Henk A.L., 2006. "Analysis of K sets of data, with differential emphasis on agreement between and within sets," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1491-1508, December.
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    Cited by:

    1. Maria Iannario & Rosaria Romano & Domenico Vistocco, 2023. "Dyadic analysis for multi-block data in sport surveys analytics," Annals of Operations Research, Springer, vol. 325(1), pages 701-714, June.
    2. Cristina Davino & Tormod Næs & Rosaria Romano & Domenico Vistocco, 2022. "A quantile regression perspective on external preference mapping," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 545-571, December.

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