## The statistical analysis of roll call data (2004)

Venue: | Am. Political Sc. Review |

Citations: | 20 - 0 self |

### BibTeX

@ARTICLE{Clinton04thestatistical,

author = {Joshua Clinton and Simon Jackman and Douglas Rivers},

title = {The statistical analysis of roll call data},

journal = {Am. Political Sc. Review},

year = {2004}

}

### OpenURL

### Abstract

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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Citation Context ...remendous increases in computing power available to social scientists over the last decade or so: Estimation and inference via simulation—long known to be an attractive statistical methodology (e.g., =-=Metropolis and Ulam 1949-=-)—is now a reality. Consequently, our model works in any legislative setting, irrespective of the size of the legislature or its agenda. Thus Bayesian methods can make roll call analysis less a mechan... |

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Citation Context ...meters, since each legislator has an ideal point and each bill has a policy location that must be estimated. Popular methods of roll call analysis compute standard errors that are admittedly invalid (=-=Poole and Rosenthal 1997-=-, 246) and one cannot appeal to standard statistical theory to ensure the consistency and other properties of estimators (we revisit this point below). In this paper we develop and illustrate Bayesian... |

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Citation Context ...roll call context the latent trait or “ability” parameter xi is the ideal point of the ith legislator. There is a large literature in psychometrics on estimation of these models (e.g., Baker 1992 and =-=Bock and Aitken 1981-=-), but the focus is usually on estimation of the βj (the item parameters), which are used for test equating. In roll call analysis, however, primary interest almost always centers on the xi (the ideal... |

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Citation Context ...er, but in the roll call context the latent trait or “ability” parameter xi is the ideal point of the ith legislator. There is a large literature in psychometrics on estimation of these models (e.g., =-=Baker 1992-=- and Bock and Aitken 1981), but the focus is usually on estimation of the βj (the item parameters), which are used for test equating. In roll call analysis, however, primary interest almost always cen... |

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Citation Context ... legislators. Estimation becomes progressively more difficult in higher dimensions. In addition to the necessary identifying restrictions, it is also beneficial to add other a priori information (see =-=Jackman 2001-=- for an example). ESTIMATION AND INFERENCE The classical or frequentist approach treats ideal points as fixed but unknown parameters. An estimation technique, such as maximum likelihood, is evaluated ... |

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Citation Context ...role of identification in Bayesian estimation is more controversial. Bayesian procedures can be applied to unidentified models, though the data are only informative about identified parameters (e.g., =-=Neath and Samaniego 1997-=-). However, in many cases it is difficult to formulate a reasonable prior for problems involving 2 This equivalence has been noted by several authors, including Bailey and Rivers (1997), Londregan (20... |

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Citation Context ...tter computed assuming that the joint posterior densities can be approximated with bivariate normal densities. Computing For small roll call data sets, the free, general-purpose MCMC package WinBUGS (=-=Spiegelhalter et al. 1997-=-) can be used to implement our approach: only a few lines of WinBUGS commands are needed. For instance, the WinBUGS code for a simple unidimensional model fitted via logit and the Kennedy–Helms identi... |

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