Mixture models provide a useful tool to account for unobserved heterogeneity and are at the basis of many model-based clustering methods. To gain additional flexibility, some model parameters can be expressed as functions of concomitant covariates. In this Paper, a semiparametric finite mixture of regression models is defined, with concomitant information assumed to influence both the component weights and the conditional means. In particular, linear predictors are replaced with smooth functions of the covariate considered by resorting to cubic splines. An estimation procedure within the Bayesian paradigm is suggested, where smoothness of the covariate effects is controlled by suitable choices for the prior distributions of the spline coefficients. A data augmentation scheme based on difference random utility models is exploited to describe the mixture weights as functions of the covariate. The performance of the proposed methodology is investigated via simulation experiments and two real-world datasets, one about baseball salaries and the other concerning nitrogen oxide in engine exhaust.

Berrettini, M., Galimberti, G., Ranciati, S. (2023). Semiparametric finite mixture of regression models with Bayesian P-splines. ADVANCES IN DATA ANALYSIS AND CLASSIFICATION, 17(3), 745-775 [10.1007/s11634-022-00523-5].

Semiparametric finite mixture of regression models with Bayesian P-splines

Berrettini, M
;
Galimberti, G;Ranciati, S
2023

Abstract

Mixture models provide a useful tool to account for unobserved heterogeneity and are at the basis of many model-based clustering methods. To gain additional flexibility, some model parameters can be expressed as functions of concomitant covariates. In this Paper, a semiparametric finite mixture of regression models is defined, with concomitant information assumed to influence both the component weights and the conditional means. In particular, linear predictors are replaced with smooth functions of the covariate considered by resorting to cubic splines. An estimation procedure within the Bayesian paradigm is suggested, where smoothness of the covariate effects is controlled by suitable choices for the prior distributions of the spline coefficients. A data augmentation scheme based on difference random utility models is exploited to describe the mixture weights as functions of the covariate. The performance of the proposed methodology is investigated via simulation experiments and two real-world datasets, one about baseball salaries and the other concerning nitrogen oxide in engine exhaust.
2023
Berrettini, M., Galimberti, G., Ranciati, S. (2023). Semiparametric finite mixture of regression models with Bayesian P-splines. ADVANCES IN DATA ANALYSIS AND CLASSIFICATION, 17(3), 745-775 [10.1007/s11634-022-00523-5].
Berrettini, M; Galimberti, G; Ranciati, S
File in questo prodotto:
File Dimensione Formato  
s11634-022-00523-5.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
Dimensione 2.2 MB
Formato Adobe PDF
2.2 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/940698
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 1
social impact