Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models, discussing several correlation structures for the within group residuals. All the considered group models are parametrized in terms of a single correlation (hyper-)parameter, controlling the shrinkage towards the case of independent residuals (iid). We derive a penalized complexity (PC) prior for the correlation parameter of a generic group model. This prior has desirable properties from a practical point of view: (i) it ensures appropriate shrinkage to the iid case; (ii) it depends on a scaling parameter whose choice only requires a prior guess on the proportion of total variance explained by the grouping factor; (iii) it is defined on a distance scale common to all group models, thus the scaling parameter can be chosen in the same manner regardless the adopted group model. We show the benefit of using these PC priors in a case study in community ecology where different group models are compared.

Ventrucci M., Cocchi D., Burgazzi G., Laini A. (2020). PC priors for residual correlation parameters in one-factor mixed models. STATISTICAL METHODS & APPLICATIONS, 29(4), 745-765 [10.1007/s10260-019-00501-w].

PC priors for residual correlation parameters in one-factor mixed models

Ventrucci M.
;
Cocchi D.;
2020

Abstract

Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models, discussing several correlation structures for the within group residuals. All the considered group models are parametrized in terms of a single correlation (hyper-)parameter, controlling the shrinkage towards the case of independent residuals (iid). We derive a penalized complexity (PC) prior for the correlation parameter of a generic group model. This prior has desirable properties from a practical point of view: (i) it ensures appropriate shrinkage to the iid case; (ii) it depends on a scaling parameter whose choice only requires a prior guess on the proportion of total variance explained by the grouping factor; (iii) it is defined on a distance scale common to all group models, thus the scaling parameter can be chosen in the same manner regardless the adopted group model. We show the benefit of using these PC priors in a case study in community ecology where different group models are compared.
2020
Ventrucci M., Cocchi D., Burgazzi G., Laini A. (2020). PC priors for residual correlation parameters in one-factor mixed models. STATISTICAL METHODS & APPLICATIONS, 29(4), 745-765 [10.1007/s10260-019-00501-w].
Ventrucci M.; Cocchi D.; Burgazzi G.; Laini A.
File in questo prodotto:
File Dimensione Formato  
VentrucciM_SMA_2020_postprint.pdf

Open Access dal 22/11/2020

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 1.67 MB
Formato Adobe PDF
1.67 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/11585/709152
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact