Nonlinear Simplex Regression Models

TL;DR

This paper introduces a nonlinear simplex regression model with new diagnostic tools, demonstrating its robustness to influential data points compared to beta regression models, and provides practical estimation and influence assessment methods.

Contribution

It develops a nonlinear simplex regression framework with closed-form expressions, diagnostic measures, and influence analysis, enhancing modeling robustness and estimation procedures.

Findings

Simplex models are more robust to influential cases than beta regression models.

Diagnostic measures effectively identify influential data points.

Proposed estimation scheme improves parameter estimation in nonlinear models.

Abstract

In this paper, we propose a simplex regression model in which both the mean and the dispersion parameters are related to covariates by nonlinear predictors. We provide closed-form expressions for the score function, for Fisher's information matrix and its inverse. Some diagnostic measures are introduced. We propose a residual, obtained using Fisher's scoring iterative scheme for the estimation of the parameters that index the regression nonlinear predictor to the mean response and numerically evaluate its behaviour. We also derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We also proposed a scheme for the choice of starting values for the Fisher's iterative scheme for nonlinear simplex models. The diagnostic techniques were applied on actual data. The local influence analyses reveal that the simplex models can be a modeling alternative more robust to influential cases than the beta regression models, both to linear and nonlinear models.