Optimizing Solution Sets in Two-Way Controlled Selection Problems

• Activity Number: 75
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods*
• Author(s): Sun-Woong Kim*+ and Steven Heeringa and Peter Solenberger
• Affiliation(s): Dongguk University and University of Michigan and University of Michigan
• Keywords: Controlled selection ; Optimal samples ; Linear programming

Abstract

The probability sampling technique of controlled selection, described by Goodman and Kish (1950) identifies possible, although not necessarily optimal, solution sets for deep stratification and other highly constrained sample selection problems. Sitter and Skinner (1994), following Rao and Nigam(1990, 1992), applied linear programming methods to optimize the solution set for multi-dimensional controlled selection problems under simple marginal constraints. Tiwari and Nigam(1998) also used linear programming for controlled selection, applying basic controls to increase the selection probabilities of preferred combinations of units. In this paper, we introduce a new linear programming problem specification that uses a distance metric to minimize the distortion to each cell in two-dimensional controlled selection problems with integer or non-integer expectations for marginal and cell sample sizes. We describe new public-use SAS-based software that incorporates our linear programming approach to solve controlled selection problems. Further, we demonstrate the simplicity and utility of the method through comparisons based on example problems from the literature.