Comment: A Bayesian Approach to the Nonresponse Problem, Using Covariates à la Freedman

Abstract

David Freedman has presented an ingenious and deceptively simple argument that should prove to be of value in many nonrespondent problems. I would like to discuss both the general form of the argument and the specific details from a subjective Bayesian viewpoint, as I believe the argument implicitly involves some delicate questions that are best understood from this viewpoint. The basic structure of Freedman's argument is that although he concedes in general that there may be substantial nonrespondent bias, in the present situation this can be largely ignored because of additional data, in the form of covariates representing the distributions of orders by size and by geographical residence. He does not take a formal inferential point of view, but it seems clear that his argument must be to the effect that the additional information he supplies regarding the covariates must somehow change one's initial opinions about the magnitude of the nonrespondent bias, making it in some sense more probable, given this additional data, that the nonrespondent bias is negligible or at least can be ignored. This is sufficiently close to the subjective Bayesian scenario that it may be worth examining the argument from this point of view. I shall present an informal Bayesian analysis, but one that can easily be made formal.