Prediction Measures in Beta Regression Models

TL;DR

This paper develops and evaluates prediction measures like PRESS statistics for beta regression models, emphasizing predictive power over goodness-of-fit, with simulation studies and a real-world application to natural gas distribution.

Contribution

It introduces and assesses prediction measures for beta regression models, including Monte Carlo simulations and an application to natural gas distribution prediction.

Findings

Monte Carlo simulations show finite sample behavior of prediction measures

Application demonstrates improved prediction limit selection for natural gas data

Prediction measures effectively evaluate model predictive power

Abstract

We consider the issue of constructing PRESS statistics and coefficients of prediction for a class of beta regression models. We aim at displaying measures of predictive power of the model regardless goodness-of-fit. Monte Carlo simulation results on the finite sample behavior of such measures are provided.We also present an application that relates to the distribution of natural gas for home usage in S\~ao Paulo, Brazil. Faced with the economic risk of to overestimate or to underestimate the distribution of gas was necessary to construct prediction limits using beta regression models (Espinheira et al., 2014). Thus, it arises the aim of this work, the selection of best predictive model to construct best prediction limits.