Prediction in the nonlinear simplex model

Abstract We propose a model performance criterion focused on prediction and robustness, denoted as $$P^2$$ 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 $$P^2$$ P 2 relative to conventional $$R^2$$ R 2 -like criteria under various scenarios. The results highlight the ability of $$P^2$$ 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.