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An Application of Linear Programming to Ecological Inference: An Extension of an Old Procedure

William Claggett and John Van Wingen
American Journal of Political Science
Vol. 37, No. 2 (May, 1993), pp. 633-661
DOI: 10.2307/2111387
Stable URL: http://www.jstor.org/stable/2111387
Page Count: 29
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An Application of Linear Programming to Ecological Inference: An Extension of an Old Procedure
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Abstract

Nearly four decades ago, Duncan and Davis (1953) developed a simple ecological inference technique. They noted that, given two dichotomized individual-level variables, the minimum and maximum possible number of individuals having each combination of these variables could be derived, with certainty, from the marginals of the cross-tabulation of their aggregate-level counterparts. Shively (1975, 1991) expanded this technique to allow the use of side information to constrain further the number of individuals having each combination of the individual-level variables. This approach to ecological inference avoided many of the pitfalls of ecological regression. Despite this, the technique has been little used because there has not been any easy, mechanical way to employ this technique and to apply this procedure to larger tables has been difficult. Finally, there was the feeling that the whole approach was ad hoc and without a mathematical foundation. In this paper, we remedy the limitations of this technique. Our remedy is based on a simple observation: both the original Duncan and Davis approach and Shively's extension of it can be seen as an application of linear programming (LP). As such, a large body of mathematical machinery and software exists to solve these problems. Thus, the minimum and maximum possible value for any linear combination of the unobserved internal cells, given any set of linear constraints, for any size table can easily be calculated.

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