What question did this study set out to answer?

The study aims to develop a performance criterion, $$P^2$$, to improve the robustness of predictions in simplex regression models.

May 8, 2026Open Access

Prediction in the nonlinear simplex model

Key Points

The study aims to develop a performance criterion, $$P^2$$, to improve the robustness of predictions in simplex regression models.
Introduced a new model performance criterion, denoted as $$P^2$$.
Utilized Monte Carlo simulations to test the performance of $$P^2$$ against conventional $$R^2$$-like criteria.
Evaluated influential observations using a modified Cook’s distance.
$$P^2$$ successfully identified link functions for the mean submodel and bias in predicted values.
Demonstrated superior robustness in estimation against influential points compared to standard criteria.
Included three applications, with two using real data and one simulated example.

Abstract

Abstract We propose a model performance criterion focused on prediction and robustness, denoted as P² P 2, applicable to simplex, linear and nonlinear regression models. We also introduce a version of Cook’s distance as a straightforward method to evaluate influential observations within the simplex regression class. Through Monte Carlo simulations, we investigate the performance of P² P 2 relative to conventional R² R 2 -like criteria under various scenarios. The results highlight the ability of P² P 2 to correctly identify link functions for the mean submodel and the bias of predicted values. Finally, we provide three applications, two involving real data and one simulated example. Our findings demonstrate that the proposed criterion effectively identifies the robustness of the estimation process against influential points, a feature that standard criteria fail to provide.

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