Hilbert principal component regression for bimodal bounded responses

The flexible beta regression model is an effective approach to deal with bounded and bimodal responses. The aim of this work is to generalized this regression model to cope with a generic Hilbert covariate, either high-dimensional or functional. The dimensionality reduction procedure is based on principal components and the selection of the significant ones in the regression framework is carried out within a Bayesian rationale. The effectiveness of the proposal is illustrated both on simulated and real data.