A reduced-size transportation algorithm for maximizing the overlap between surveys

When redesigning a sample with a stratified multi-stage design, it is sometimes considered desirable to maximize the number of primary sampling units retained in the new sample without altering unconditional selection probabilities. For this problem, an optimal solution which uses transportation theory exists for a very general class of designs. However, this procedure has never been used in the redesign of any survey (that the authors are aware of), in part because even for moderately-sized strata, the resulting transportation problem may be too large to solve in practice. In this paper, a modified reduced-size transportation algorithm is presented for maximizing the overlap, which substantially reduces the size of the problem. This reduced-size overlap procedure was used in the recent redesign of the Survey of Income and Program Participation (SIPP). The performance of the reduced-size algorithm is summarized, both for the actual production SIPP overlap and for earlier, artificial simulations of the SIPP overlap. Although the procedure is not optimal and theoretically can produce only negligible improvements in expected overlap compared to independent selection, in practice it gave substantial improvements in overlap over independent selection for SIPP, and generally provided an overlap that is close to optimal.