Abstract
In this paper, we propose a new method for finding similarity of effects based on quantile regression models. Clustering of effects curves (CEC) techniques are applied to quantile regression coefficients, which are one-to-one functions of the order of the quantile. We adopt the quantile regression coefficients modeling (QRCM) framework to describe the functional form of the coefficient functions by means of parametric models. The proposed method can be utilized to cluster the effect of covariates with a univariate response variable, or to cluster a multivariate outcome. We report simulation results, comparing our approach with the existing techniques. The idea of combining CEC with QRCM permits simplifying computation and interpretation of the results, and may improve the ability to identify clusters. We illustrate a variety of applications, highlighting the advantages and the usefulness of the described method.
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Acknowledgements
We would like to thank the two anonymous reviewers for their suggestions and comments, that allowed us to considerably improve the manuscript.
Funding This paper has been partially supported by the national grant of the Italian Ministry of Education University and Research (MIUR) for the PRIN-2015 program (Progetti di ricerca di Rilevante Interesse Nazionale), “Prot. 20157PRZC4 - Research Project Title Complex space-time modelling and functional analysis for probabilistic forecast of seismic events. PI: Giada Adelfio”.
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Sottile, G., Adelfio, G. Clusters of effects curves in quantile regression models. Comput Stat 34, 551–569 (2019). https://doi.org/10.1007/s00180-018-0817-8
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DOI: https://doi.org/10.1007/s00180-018-0817-8