Influence diagnostics in beta regression via Hellinger and Wasserstein distances

Abstract Influence diagnostics are essential for evaluating the stability of regression models and detecting data points with disproportionate impact. Classical measures, such as generalized Cook’s distance, are tied to the Fisher information matrix, which can limit their applicability and lead to numerical challenges. We propose novel influence diagnostics for beta regression based on distributional distances, focusing on the Hellinger and Wasserstein metrics. Unlike traditional approaches, these measures do not rely on the information matrix, making them broadly applicable and computationally stable. They also provide complementary perspectives: the Hellinger distance combines analytical tractability with invariance properties, while the Wasserstein distance adds geometric interpretability and flexibility through its p -parameter. The proposed methods are evaluated with real and simulated data, demonstrating their ability to identify influential observations and highlighting their potential as practical and reliable alternatives to existing diagnostics.