The Design of a General and Flexible System for Handling Nonresponse in Sample Surveys

The general approach to nonresponse (missingness) in sur veys that I will take here will be to impute values for missing data (really, several values for each missing datum). The ap proach that imputes one value for each missing datum is stan dard in practice, although often criticized by more mathematical statisticians who prefer to think about estimating parameters un der some model. I am very sympathetic with the imputation position. There do not exist parameters except under hypothetical models; there do, however, exist actual observed values and values that would have been observed. Focusing on the estimation of parameters is often not what we want to do since a hypothetical model is simply a structure that guides us to do sensible things with observed values. Of course (1) imputing one value for missing datum can't be correct in general, and (2) in order to insert sensible values for a missing datum we must rely more or less on some model relating unobserved values to observed values. Hence, I see the best approach to be one where we can (1) insert more than one value for a missing datum, and (2) the inserted values reflect a variety of models for the dataset. This position focusing on values to impute rather than param eters to be estimated is actually very Bayesian, and the Bayesian perspective guides us in our design of a general system for nonre sponse. What we really want to impute is the distribu tion of the missing values given then observed values (having integrated?averaged?over all model parameters). The theo retical Bayesian position tells us that (1) the missing data has a distribution given the observed data (the predictive distribution) and (2) this distribution depends on assumptions that have been made about the model. Notice that the (l)'s and (2)'s in the above paragraphs are meant to refer to the same two points. The related practical questions are (1) how do we represent in a dataset a distribution of values to impute for each missing datum? And (2) what models should we use to tie observed and unobserved values to each other in order to produce the predictive distribution needed in (1). Section 2 addresses the first question and Section 3 addresses the second question.