Parametric mode regression for bounded responses

TL;DR

This paper introduces new parametric regression models focusing on the conditional mode for bounded responses, with methods for estimation, diagnostics, and practical application demonstrated through simulations and Alzheimer's data.

Contribution

It presents novel parametric frameworks for mode regression with bounded responses, including estimation, diagnostics, and real data application.

Findings

Effective mode estimation for bounded responses.

Diagnostic tools for model misspecification.

Successful application to Alzheimer's data.

Abstract

We propose new parametric frameworks of regression analysis with the conditional mode of a bounded response as the focal point of interest. Covariate effects estimation and prediction based on the maximum likelihood method under two new classes of regression models are demonstrated. We also develop graphical and numerical diagnostic tools to detect various sources of model misspecification. Predictions based on different central tendency measures inferred using various regression models are compared using synthetic data in simulations. Finally, we conduct regression analysis for data from the Alzheimer's Disease Neuroimaging Initiative to demonstrate practical implementation of the proposed methods. Supplementary materials that contain technical details, and additional simulation and data analysis results are available online.