The tree based linear regression model for hierarchical categorical variables
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...
| Autores: | , , , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/134809 |
| Acceso en línea: | https://hdl.handle.net/11441/134809 https://doi.org/10.1016/j.eswa.2022.117423 |
| Access Level: | acceso abierto |
| Palabra clave: | Hierarchical categorical variables Linear regression models Accuracy vs. model complexity Mixed integer convex quadratic problem with linear constraints |
| Sumario: | 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. |
|---|