Recovering a basic space from a set of issue scales

This paper develops a scaling procedure for estimating the latent/unobserva ble dimensions underlying a set of manifest/observable variables. The scali ng procedure performs, in effect, a singular value decomposition of a recta ngular matrix of real elements with missing entries. In contrast to existin g techniques such as factor analysis which work with a correlation or covar iance matrix computed from the data matrix, the scaling procedure shown her e analyzes the data matrix directly. The scaling procedure is a general-purpose tool that can be used not only t o estimate latent/unobservable dimensions but also to estimate an Eckart-Yo ung lower-rank approximation matrix of a matrix with missing entries. Monte Carlo tests show that the procedure reliably estimates the latent dimensio ns and reproduces the missing elements of a matrix even at high levels of e rror and missing data. A number of applications to political data are shown and discussed.