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Recovering a Basic Space From a Set of Issue Scales

Keith T. Poole
American Journal of Political Science
Vol. 42, No. 3 (Jul., 1998), pp. 954-993
DOI: 10.2307/2991737
Stable URL: http://www.jstor.org/stable/2991737
Page Count: 40
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Recovering a Basic Space From a Set of Issue Scales
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Abstract

This paper develops a scaling procedure for estimating the latent/unobservable dimensions underlying a set of manifest/observable variables. The scaling procedure performs, in effect, a singular value decomposition of a rectangular matrix of real elements with missing entries. In contrast to existing techniques such as factor analysis which work with a correlation or covariance matrix computed from the data matrix, the scaling procedure shown here analyzes the data matrix directly. The scaling procedure is a general-purpose tool that can be used not only to estimate latent/unobservable dimensions but also to estimate an Eckart-Young lower-rank approximation matrix of a matrix with missing entries. Monte Carlo tests show that the procedure reliably estimates the latent dimensions and reproduces the missing elements of a matrix even at high levels of error and missing data. A number of applications to political data are shown and discussed.

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