ℓ1-based Bayesian Ideal Point Model for Multidimensional Politics
Conference
64th ISI World Statistics Congress
Format: IPS Abstract
Keywords: ideal point estimation, l1-norm, multidimensional ideal points, multivariate slice sampling, us congress
Session: IPS 202 - Advances in Bayesian Hierarchical Modeling and Variable Selection for Complex Data
Tuesday 18 July 2 p.m. - 3:40 p.m. (Canada/Eastern)
Abstract
We present a novel method for estimating multidimensional ideal points based on $\ell_1$ distance. Existing ideal point estimation methods in social sciences lack a principled approach for identifying multidimensional ideal points. In the Bayesian framework, the use of $\ell_1$ distance transforms the invariance problem of infinite rotational turns into the signed perpendicular problem, yielding posterior estimates that contract around a small area. Our simulation shows that the proposed method successfully recovers planted multidimensional ideal points in a variety of settings. The proposed method is applied to the analysis of roll call data from the United States House of Representatives during the late Gilded Age (1891-1899), when legislative coalitions were distinguished not only by partisan divisions but also by sectional divisions that ran across party lines.