This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main families of algorithms discussed are a variational approximation, Gibbs sampling, and Rao-Blackwellised Gibbs sampling. Applications are presented for voting records from the United States Senate for 2003, and for the Reuters-21578 newswire collection.

We develop a Bayesian procedure for estimation and inference for spatial models of roll call voting. This approach is extremely flexible, applicable to any legislative setting, irrespective of size, the extremism of the legislators ’ voting histories, or the number of roll calls available for analysis. The model is easily extended to let other sources of information inform the analysis of roll call data, such as the number and nature of the underlying dimensions, the presence of party whipping, the determinants of legislator preferences, and the evolution of the legislative agenda; this is especially helpful since generally it is inappropriate to use estimates of extant methods (usually generated under assumptions of sincere voting) to test models embodying alternate assumptions (e.g., log-rolling, party discipline). A Bayesian approach also provides a coherent framework for estimation and inference with roll call data that eludes extant methods; moreover, via Bayesian simulation methods, it is straightforward to generate uncertainty assessments or hypothesis tests concerning any auxiliary quantity of interest or to formally compare models. In a series of examples we show how our method is easily extended to accommodate theoretically interesting models of legislative behavior. Our goal is to provide a statistical framework for combining the measurement of legislative preferences with tests of models of legislative behavior. Modern studies of legislative behavior focus

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Abstract. This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis (ICA), non-negative matrix factorisation (NMF) and latent Dirichlet allocation (LDA). The main families of algorithms discussed are mean field, Gibbs sampling, and Rao-Blackwellised Gibbs sampling. Applications are presented for voting records from the United States Senate for 2003, and the use of components in subsequent classification.

Multidimensional scaling (MDS) is a class of methods used to find a low-dimensional representation of a set of points given a matrix of pairwise distances between them. Problems of this kind arise in various applications, from dimensionality reduction of image manifolds to psychology and statistics. In many of these applications, efficient and accurate solution of an MDS problem is required. In this paper, we propose using vector extrapolation techniques to accelerate the numerical solution of MDS problems. Vector extrapolation is used to accelerate the convergence of fixed-point iterative algorithms. We review the problem of multidimensional scaling and vector extrapolation techniques, and show several examples of our accelerated solver for multidimensional scaling problems in various applications. 1

Language universals are usually thought of as properties holding of all languages. But very few, if any, such universals exist, due to the extreme structural diversity of languages. Instead, there are many typological universals, which allow for variation but constrain it or at least limit its distribution. This is true even of linguistic categories. Formal (grammatical or lexical categories) are not universal, but are constrained by the structure of conceptual space, as demonstrated by a multidimensional scaling analysis of adpositional semantic data from Levinson et al. (2003). Even so, broad conceptual categories are not universal either. Instead, what is universal is the holistic conceptualization of highly particular situation types, and the conceptual relationships that hold among them. This conclusion is confirmed by the analysis of data on within-language variation in verbalization from Croft (2010).

A difficult yet prevalent problem in legislative politics is how to assess explanations when observable actions may not represent true (and unobserved) legislator preferences. We present a method for analyzing the validity of theoretical/historical accounts that unifies theory, history, and measurement. We argue that approaches to testing accounts of legislative behavior which are theoretically and historically agnostic are not always best and present an approach which: (1) forms an explicit explanation of behavior (here a simple dynamic voting game) that yields estimable parameter constraints, and (2) tests these constraints using a customized empirical model that is as consistent as possible with the explanation. We demonstrate the method using legislative voting data from the first Congress (1789–1791). Using the idea of sophisticated equivalents from voting theory we subject the traditional account of the “Compromise of 1790 ” to a statistical test and find that there is reason to doubt the claim that legislators of the time believed the specified log roll was taking place. The results suggest that the capital location and assumption issues were resolved independently. Great progress has been made advancing our theoretical understanding of strategic voting (e.g.,

We develop a Bayesian procedure for estimation and inference for spatial models of roll call voting. Our approach is extremely flexible, applicable to any legislative setting, irrespective of size, the extremism of the legislative voting histories, or the number of roll calls available for analysis. Our model is easily extended to let other sources of information inform the analysis of roll call data, such as the number and nature of the underlying dimensions, the presence of party whipping, the determinants of legislator preferences, or the evolution of the legislative agenda; this is especially helpful since generally it is inappropriate to use estimates of extant methods (usually generated under assumptions of sincere voting) to test models embodying alternate assumptions (e.g., logrolling) . A Bayesian approach also provides a coherent framework for estimation and inference with roll call data that eludes extant methods; moreover, via Bayesian simulation methods, it is straightforward to generate uncertainty assessments or hypothesis tests concerning any auxiliary quantity of interest or to formally compare models. In a series of examples we show how our method is easily extended to accommodate theoretically interesting models of legislative behavior. Our goal is to move roll call analysis away from pure measurement or description towards a tool for testing substantive theories of legislative behavior. 1.

This package estimates Poole’s Optimal Classification scores from roll call votes supplied though a rollcall object from package pscl. 1 Optimal Classification fits a Euclidean spatial model that places legislators in a specified number of dimensions (usually one or two). It maximizes the correct classification

This package estimates Poole’s Optimal Classification scores from roll call votes supplied though a rollcall object from package pscl. 1 Optimal Classification fits a Euclidean spatial model that places legislators in a specified number of dimensions (usually one or two). It maximizes the correct classification