Variance estimation of imputed estimators of change for repeated rotating surveys

A common problem in survey sampling is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions. These cross-sectional estimates often include imputed values to compensate for item non-response. The estimation of the sampling variance of the estimator of change is useful to judge whether the observed change is statistically significant. Estimating the variance of a change is not straightforward due to rotation in repeated surveys. We propose using a multivariate linear regression approach and show how it can be used to accommodate the effect of imputation. The regression approach gives design-consistent estimation of the variance of change when the sampling fraction is small. We illustrate the proposed approach using random hot-deck imputation, although the proposed estimator can be implemented with other imputation techniques