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A sparse factor analytic probit model for congressional voting patterns
Author(s) -
Richard Hahn P.,
Carvalho Carlos M.,
Scott James G.
Publication year - 2012
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2012.01044.x
Subject(s) - factor analysis , multivariate probit model , probit model , covariance , multivariate statistics , factor (programming language) , econometrics , voting , computer science , exploratory factor analysis , gaussian , binary number , variance (accounting) , latent variable , covariance matrix , statistics , artificial intelligence , mathematics , machine learning , algorithm , structural equation modeling , economics , physics , arithmetic , quantum mechanics , politics , political science , law , programming language , accounting
Summary. The paper adapts sparse factor models for exploring covariation in multivariate binary data, with an application to measuring latent factors in US Congressional roll‐call voting patterns. This straightforward modification provides two advantages over traditional factor analysis of binary data. First, a sparsity prior can be used to assess the evidence that a given factor loading may be exactly 0, realizing a principled unification of exploratory and confirmatory factory analysis. Second, incorporating sparsity into existing factor analytic probit models effects a favourable bias–variance trade‐off in estimating the covariance matrix of the multivariate Gaussian latent variables. Posterior summaries from this model applied to the roll‐call data provide novel metrics of partisanship of a given Senate.