The tree based linear regression model for hierarchical categorical variables

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Many real-life applications consider nominal categorical predictor variables that have a hierarchical structure, e.g. economic activity data in Official Statistics. In this paper, we focus on linear regression models built in the presence of this type of nominal categorical predictor variables, and study the consolidation of their categories to have a better tradeoff between interpretability and fit of the model to the data. We propose the so-called Tree based Linear Regression (TLR) model that optimizes both the accuracy of the reduced linear regression model and its complexity, measured as a cost function of the level of granularity of the representation of the hierarchical categorical variables. We show that finding non-dominated outcomes for this problem boils down to solving Mixed Integer Convex Quadratic Problems with Linear Constraints, and small to medium size instances can be tackled using off-the-shelf solvers. We illustrate our approach in two real-world datasets, as well as a synthetic one, where our methodology finds a much less complex model with a very mild worsening of the accuracy.

TidsskriftExpert Systems with Applications
Antal sider13
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
This research is partially supported by research grants and projects MTM2015-65915-R ( Ministerio de Economía y Competitividad, Spain ), PID2019-110886RB-I00 ( Ministerio de Ciencia, Innovación y Universidades, Spain ), FQM-329 and P18-FR-2369 ( Junta de Andalucía, Spain ), PR2019-029 ( Universidad de Cádiz, Spain ), Fundación BBVA, EC H2020 MSCA RISE NeEDS Project (Grant agreement ID: 822214 ) and The Insight Centre for Data Analytics (Ireland) . This support is gratefully acknowledged.

Publisher Copyright:
© 2022 The Author(s)

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