On weighting the rates in non-response weights

A basic estimation strategy in sample surveys is to weight units inversely proportional to the probability of selection and response. Response weights in this method are usually estimated by the inverse of the sample-weighted response rate in an adjustment cell, that is, the ratio of the sum of the sampling weights of respondents in a cell to the sum of the sampling weights for respondents and non-respondents in that cell. We show by simulations that weighting the response rates by the sampling weights to adjust for design variables is either incorrect or unnecessary. It is incorrect, in the sense of yielding biased estimates of population quantities, if the design variables are related to survey non-response; it is unnecessary if the design variables are unrelated to survey non-response. The correct approach is to model non-response as a function of the adjustment cell and design variables, and to estimate the response weight as the inverse of the estimated response probability from this model. This approach can be implemented by creating adjustment cells that include design variables in the cross-classification, if the number of cells created in this way is not too large. Otherwise, response propensity weighting can be applied.