Prediction Measures in Nonlinear Beta Regression Models

TL;DR

This paper introduces PRESS statistics and prediction coefficients, including P^2, for nonlinear beta regression models, enhancing model selection by combining prediction accuracy and goodness-of-fit measures, with validation through simulations and real data applications.

Contribution

It proposes new prediction-based and goodness-of-fit criteria for nonlinear beta regression models, integrating them into a comprehensive model selection framework.

Findings

Monte Carlo simulations demonstrate the effectiveness of P^2 and pseudo-R^2 criteria.

Applications to natural gas distribution data show the practical utility of the proposed methods.

Combining prediction and fit measures improves model selection accuracy.

Abstract

Nonlinear models are frequently applied to determine the optimal supply natural gas to a given residential unit based on economical and technical factors, or used to fit biochemical and pharmaceutical assay nonlinear data. In this article we propose PRESS statistics and prediction coefficients for a class of nonlinear beta regression models, namely $P^2$ statistics. We aim at using both prediction coefficients and goodness-of-fit measures as a scheme of model select criteria. In this sense, we introduce for beta regression models under nonlinearity the use of the model selection criteria based on robust pseudo-$R^2$ statistics. Monte Carlo simulation results on the finite sample behavior of both prediction-based model selection criteria $P^2$ and the pseudo-$R^2$ statistics are provided. Three applications for real data are presented. The linear application relates to the distribution of natural gas for home usage in S\~ao Paulo, Brazil. Faced with the economic risk of too overestimate or to underestimate the distribution of gas has been necessary to construct prediction limits and to select the best predicted and fitted model to construct best prediction limits it is the aim of the first application. Additionally, the two nonlinear applications presented also highlight the importance of considering both goodness-of-predictive and goodness-of-fit of the competitive models.