As pointed out by the reviewers, these are the strengths and weaknesses of the paper: STRENGTHS The reviewers agree that the paper makes a contribution towards understanding the theoretical and empirical limitations of influence functions when samples are not missing at random. The empirical results show that influence functions are correlated with true influence even when the estimate error is high but they can also underestimate the true influence. The paper is well written and structured. FOR IMPROVEMENT The main reviewers’ concerns that need to be addressed in the revision are the ones discussed in the authors’ response: discussion on applicability to non-convex functions and different labeling functions, and contrasting with methods that specify groups as features.