Influence diagnostics for generalized CP tensor regression models

Tensor regression models are widely used in diverse fields, but influence diagnostics for these models remain underdeveloped. This study extends local influence analysis and the case-deletion method to generalized CP tensor regression. We derive one-step approximations of generalized Cook's distance using the Hessian and Fisher information matrices. Three perturbation schemes–case-weighted, single-explanatory-variable, and group-explanatory-variable–are analyzed via the likelihood displacement's largest curvature. Simulations and empirical results confirm that our diagnostic methods accurately identify influential observations, even under higher-than-true rank assumptions.