Bayesian principal component regression with data-driven component selection

Principal component regression (PCR) has two steps: estimating the principal components and performing the regression using these components. These steps generally are performed sequentially. In PCR, a crucial issue is the selection of the principal components to be included in regression. In this paper, we build a hierarchical probabilistic PCR model with a dynamic component selection procedure. A latent variable is introduced to select promising subsets of components based upon the significance of the relationship between the response variable and principal components in the regression step. We illustrate this model using real and simulated examples. The simulations demonstrate that our approach outperforms some existing methods in terms of root mean squared error of the regression coefficient.