Some Improvements on an Algorithm for Controlled Selection
Ting Kwong Lin · Singapore Management University Institutional Knowledge (InK) (Singapore Management University) · 1992
The sampling technique called controlled selection was f'u'st described by Goodman and Kish (1950). It was found to be a very useful sampling technique among practicing survey samplers, especially in selecting first-stage units in multi-stage sampling. Hess, Riedel and Fitzpatrick (1961, 1975) have given a simple illustration on how it can be implemented in the sampling of hospitals in the state of Michigan. Causey, Cox and Ernst (1985), using transportation theory, have shown for two-dimensional controlled selection problems complete solutions do always exist. They have given an algorithm on how the twodimensional controlled selection problems can be solved. Computer programs are available to solve the transportation problems. Groves and Hess (1975) gave a formal algorithm for obtaining solutions to the two-dimensional and the much more complex three-dimensional problems. A computer program written by Groves for the mainframe is available. However, this algorithm may not always yield a solution. There are simple examples that can be solved by hand but which the algorithm fails to solve, even in the two-dimensional situation. In this paper, we show how the Groves-Hess algorithm can be improved and how further controls which are useful to survey practitioners can be built into the algorithm. Problems the old algorithm could not solve can now be solved by the new algorithm. The computer program written by Groves for the