# Simultaneous Variable Selection, Clustering, and Smoothing in Function on Scalar Regression

## TL;DR

This paper introduces a Bayesian approach for function-on-scalar regression that simultaneously performs variable selection, clustering of correlated effects, and smoothing, effectively addressing multicollinearity and reducing dimensionality.

## Contribution

It proposes a novel prior that groups correlated predictors, enabling dimension reduction without losing relevant variables, validated through simulations and real data application.

## Key findings

- Outperforms existing dimension reduction methods in simulations
- Effectively clusters correlated predictors in real data
- Reduces multicollinearity issues in functional regression

## Abstract

We address the problem of multicollinearity in a function-on-scalar regression model by using a prior which simultaneously selects, clusters, and smooths functional effects. Our methodology groups 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 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.