Journal ArticleDOI
Recovering a basic space from a set of issue scales
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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.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.read more
Citations
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Polarized America: The Dance of Ideology and Unequal Riches
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Enhancing the Validity and Cross-Cultural Comparability of Measurement in Survey Research
TL;DR: This paper measured response category incomparability via respondents' assessments, on the same scale as the self-assessments to be corrected, of hypothetical individuals described in short vignettes.
Journal ArticleDOI
Enhancing the Validity and Cross-cultural Comparability of Measurement in Survey Research
TL;DR: This article measured response category incomparability via respondents' assessments, on the same scale as the self-assessments to be corrected, of hypothetical individuals described in short vignettes.
Journal ArticleDOI
Resurgent Mass Partisanship: The Role of Elite Polarization
TL;DR: This paper found that parties in the electorate have experienced a noteworthy resurgence over the last two decades, and that greater partisan polarization in Congress has clarified the parties' ideological positions for ordinary Americans, which in turn has increased party importance and saliency on the mass level.
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The American Voter Revisited
TL;DR: The American Voter Revisited as discussed by the authors examines how contemporary voters decide, using the lens of the 1960 text, which was based on the presidential elections of 1952 and 1956, and tests the ideas and methods of "The American voter" are tested against presidential election surveys from 2000 and 2004.
References
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Book
Solving least squares problems
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
Journal ArticleDOI
Analysis of individual differences in multidimensional scaling via an n-way generalization of 'eckart-young' decomposition
J. Douglas Carroll,Jih-Jie Chang +1 more
TL;DR: In this paper, an individual differences model for multidimensional scaling is outlined in which individuals are assumed differentially to weight the several dimensions of a common "psychological space" and a corresponding method of analyzing similarities data is proposed, involving a generalization of Eckart-Young analysis to decomposition of three-way (or higher-way) tables.
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The approximation of one matrix by another of lower rank
Carl Eckart,Gale Young +1 more
TL;DR: In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.
Book
Congress: A Political-Economic History of Roll Call Voting
Keith T. Poole,Howard Rosenthal +1 more
TL;DR: Poole and Rosenthal as mentioned in this paper used 200 years of congressional roll call voting as a framework for an interpretation of important episodes in American political and economic history, finding that over 80 percent of a legislator's voting decisions can be attributed to a consistent ideological position ranging from ultraconservatism to ultraliberalism.
Journal ArticleDOI
A generalized solution of the orthogonal procrustes problem
TL;DR: In this paper, a solution for the least square problem with respect to matrices of less than full column rank is presented. But this solution is applicable to only matrices A and B and is not applicable to all matrices.