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Global and local distance-based generalized linear models

Author

Listed:
  • Eva Boj
  • Adrià Caballé
  • Pedro Delicado
  • Anna Esteve
  • Josep Fortiana

Abstract

This paper introduces local distance-based generalized linear models. These models extend (weighted) distance-based linear models first to the generalized linear model framework. Then, a nonparametric version of these models is proposed by means of local fitting. Distances between individuals are the only predictor information needed to fit these models. Therefore, they are applicable, among others, to mixed (qualitative and quantitative) explanatory variables or when the regressor is of functional type. An implementation is provided by the R package dbstats, which also implements other distance-based prediction methods. Supplementary material for this article is available online, which reproduces all the results of this article. Copyright Sociedad de Estadística e Investigación Operativa 2016

Suggested Citation

  • Eva Boj & Adrià Caballé & Pedro Delicado & Anna Esteve & Josep Fortiana, 2016. "Global and local distance-based generalized linear models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 170-195, March.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:1:p:170-195
    DOI: 10.1007/s11749-015-0447-1
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    Cited by:

    1. Beibei Yuan & Willem Heiser & Mark Rooij, 2019. "The δ-Machine: Classification Based on Distances Towards Prototypes," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 442-470, October.
    2. S. Barahona & P. Centella & X. Gual-Arnau & M. V. Ibáñez & A. Simó, 2020. "Supervised classification of geometrical objects by integrating currents and functional data analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 637-660, September.
    3. Amparo Baíllo & Aurea Grané, 2021. "Subsampling and Aggregation: A Solution to the Scalability Problem in Distance-Based Prediction for Mixed-Type Data," Mathematics, MDPI, vol. 9(18), pages 1-17, September.

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