Recovering a Basic Space From a Set of Issue Scales

This paper develops a procedure for estimating the basic dimensions underlying a set of issue or attribute scales. A simple Hinich-Ordeshook spatial theory of voting is used to model Converses fundamental insight that individuals positions on issues are bundled together, and the knowledge of one or two issue positions makes the remaining positions very predictable. The model assumes that individuals positions on a set issue or attribute dimensions are determined by the individuals positions on a small number of underlying evaluative or basic dimensions. The procedure developed in this paper for estimating these basic dimensions is, in effect, a method of performing singular value decomposition of a matrix with missing elements. Monte Carlo testing shows that the procedure reliably reproduces the missing elements. Because of this reliability, the estimation procedure can be used to produce Eckart-Young matrix lower rank approximations. A number of applications to political data are...