Are Survey Weights Necessary: The Maximum Likelihood Approach to Sample Survey Inference

摘要

In survey sample inference, there are two fundamental positions that can be taken with respect to randomized designs and the use of design weights (inverses of selection probabilities): (1) both are necessary; (2) neither is necessary. Indeed, neither is necessary, and there are occasions when insistence on their use undermines inference. There are other occasions when, the analyst being at a remove from the sampling process, the selection probabilities are helpful information, which it makes sense to incorporate into the method of inference. Strict maximum likelihood inference (as distinguished from the pseudo-likelihood or weighted distribution likelihood approaches) can suitably incorporate the sample weights. The theory of this is not simple, but the practice usually is. We illustrate these points.