A multivariate regression estimator for rotating sampling surveys

Longitudinal surveys collect information on several occasions , or time points. Consider that we have two occasions or waves labelled 1 and 2. The samples selected on occasions 1 and 2 are rarely completely overlapping samples, as not all the units are selected on both occasions. It is common practice to have a large fraction of units sampled at both occasions. Surveys which have this feature are called rotating sampling surveys. The customary point estimators are the Horvitz Thompson and generalised regression estimators of a total or a mean. We propose a new regression estimator for cross-sectional totals and change between totals. This estimator uses the information from both occasions simultaneously instead of each occasion separately. This estimator incorporates the auxiliary variables similar to the general regression estimator and the sample design variables specifying the rotating sampling design. The proposed estimator is multivariate because it combines the auxiliary information from the first and second occasion. Longitudinal surveys are used to monitor change between population target parameters. For social policy makers, the estimation of change over time of social indicators as such youth employment rate, literacy rate and social deprivation indicators may be as important as cross-sectional indicators. The variance of change, for rotating sampling surveys, is a challenging subject since it requires to estimate correlations. Several authors proposed different estimators for correlations. A variance of change is proposed by extending the estimator proposed Berger & Priam (2015) where besides the design variables, the auxiliary variables are included. In the simulation study, the proposed estimator is compared with the Horvitz Thompson (HT) and generalised regression estimators. The relative bias and ratio of relative mean square errors are computed for the estimator of totals. We consider different correlations between the response variables and the auxiliary variable