Shrinkage priors are a popular Bayesian paradigm to handle sparsity in high-dimensional regression. Still limited, however, is a flexible class of shrinkage priors to handle grouped sparsity, where covariates exhibit some natural grouping structure. This paper proposes a novel extension of the \(R^2\) -induced Dirichlet Decomposition (R2D2) prior to accommodate grouped variable selection in linear regression models. The proposed method, called the gR2D2 prior, employs a Dirichlet prior distribution on the coefficient of determination for each group, allowing for a flexible and adaptive shrinkage that operates at both group and individual variable levels. We present several theoretical properties of this proposed prior distribution while also developing a Markov Chain Monte Carlo algorithm. Through simulation studies and real-data analysis, we demonstrate that our method outperforms traditional shrinkage priors in terms of both estimation accuracy, inference, and prediction.
