Bayesian model selection for a linear model with grouped covariates

Abstract

Model selection for normal linear regression models with grouped covariates is considered under a class of Zellner's g-priors. The marginal likelihood function is derived under the proposed priors, and a simplified closed-form expression is given assuming the commutativity of the projection matrices from the design matrices. As illustration, the marginal likelihood functions of the balanced q-way ANOVA models, either solely with main effects or with all interaction effects, are calculated using the closed-form expression. The performance of the proposed priors in model comparison problems is demonstrated by simulation studies on two-way ANOVA models and by two real data studies. Electronic supplementary materialThe online version of this article (

Model Averaging and its Use in Economics

“…Their motivation is to avoid certain paradoxes, related to different asymptotic behaviour for different subsets of predictors. Min and Sun (2016) consider the situation of grouped covariates (occurring, for example, in ANOVA models where each factor has various levels) and propose separate gpriors for the associated groups of regression coefficients. This also circumvents the fact that in ANOVA models the full design matrix is often not of full rank.…”

Bayesian cusp regression and linear mixed model

“…In Chapter 3, model selection for linear mixed models with grouped covariates is considered under a class of Zellner's g-priors (Zellner, 1986). We will extend the work by Min and Sun (2016) on linear models with only fixed effects and proposed 7 Options of the priors for random components of linear mixed model. The marginal likelihood functions are derived under the proposed priors and the approach for computing the corresponding Bayes factors is given.…”

“…, it is natural to assign independent prior for all parameters, We adopt the priors in Min and Sun (2016) for σ 2 and (β 0 , Min and Sun (2016) assigned a Right…”

“…Liang et al (2008) summarized multiple choices of g in the Zellner's g-prior, reviewed the paradoxes of fixing the value g and compared among different choice of hyper priors of g in the mixture of g-prior. Min and Sun (2016) considered grouping the covariates of the Zellner's g-prior and propose separate g-priors for the associated groups of regression coefficients since grouping structure occurred in the various situations (e.g., in analysis-of-variance, or ANOVA, models where each factor has multiple levels).…”

“…The motivation of this chapter is to extend the work of Min and Sun (2016) to linear mixed model to incorporate more complicated situations and unify the fixed and random effects model. We consider linear mixed models where both fixed and random effect have a grouped structure and try to propose suitable priors for the random components that can be used in model selection.…”