Multi-level composite estimators and the evaluation of the three-way balanced multi-level rotation designs

The general concept of the three-way balanced multi-level rotation design has been discussed. It has four elements expressing the number of reports in a interview, the number of months for a unit to be in sample and out of sample, and the number of interview waves. However, the role of each element in the three-way balanced multi-level rotation design remains unevaluated, since past research for rotation designs only focused on the balancing conditions and effects and making efficient estimators under the correlation structure from the rotation designs. In this paper, we evaluate effects of the elements in the three-way balanced multi-level rotation designs using numerical studies. We propose multi-level composite estimators (MCEs) and introduce old and new designs from the US Monthly Retail Trade Survey, as criteria in comparative studies with some alternative designs. We also derive variances and mean squared errors of the MCEs, assuming the correlation from the measurements of the same sample unit and the three types of biases in the monthly sample. MCEs are used in numerical studies as main tools to measure the design efficiency of the three-way balanced multi-level rotation designs with three types of biases and revisions between preliminary estimators and final estimator.