Simultaneous variable selection, clustering, and smoothing in function-on-scalar regression

We address the problem of multicollinearity in a function-on-scalar regression model by using a prior that simultaneously selects, clusters, and smooths functional effects. Our methodology groups the effects of highly correlated predictors, performing dimension reduction without dropping relevant predictors from the model. We validate our approach via a simulation study, showing superior performance relative to existing dimension-reduction approaches described in the function-on-scalar literature. We also demonstrate the use of our model on a data set of age-specific fertility rates from the United Nations Gender Information database.