The classical Poisson, geometric and negative binomial regression models for count data belong to the family of generalized linear models and are available at the core of the statistics toolbox in the R system for statistical computing. After reviewing the conceptual and computational features of these methods, a new implementation of hurdle and zero-inflated regression models in the functions hurdle() and zeroinfl() from the package pscl is introduced. It re-uses design and functionality of the basic R functions just as the underlying conceptual tools extend the classical models. Both hurdle and zeroinflated model, are able to incorporate over-dispersion and excess zeros-two problems that typically occur in count data sets in economics and the social sciences-better than their classical counterparts. Using cross-section data on the demand for medical care, it is illustrated how the classical as well as the zero-augmented models can be fitted, inspected and tested in practice.

Modern studies of legislative behavior focus upon the relationship among the policy preferences of legislators, institutional arrangements, and legislative outcomes. In spatial models of legislatures, policies are represented geometrically, as points in a low-dimensional Euclidean space. Each legislator has a most preferred policy or ideal point in this space and his or her utility for a policy declines with the distance of the policy from his or her ideal point; see Davis, Hinich, and Ordeshook (1970) for an early survey.The primary use of roll call data-the recorded votes of deliberative bodies 1 -is the estimation of ideal points. The appeal and importance of ideal point estimation arises in two ways. First, ideal point estimates let us describe legislators and legislatures. The distribution of ideal points estimates reveals how cleavages between legislators reflect partisan affiliation or region or become more polarized over time (e.g., McCarty, Poole, and Rosenthal 2001). Roll call data serve similar purposes for interest groups, such as Americans for Democratic Action, the National Taxpayers Union, and the Sierra Club, to produce "ratings" of legislators along different policy dimensions. Second, estimates from roll call analysis can be used to test theories of legislative behavior. For instance, roll call analysis has been used Joshua Clinton is Assistant Professor, Department of Politics, Princeton University, Princeton, NJ 08540 (clinton@princeton.edu).Simon Jackman is Associate Professor (Voeten 2000). In short, roll call analysis make conjectures about legislative behavior amenable to quantitative analysis, helping make the study of legislative politics an empirically grounded, cumulative body of scientific knowledge.Current methods of estimating ideal points in political science suffer from both statistical and theoretical deficiencies. First, any method of ideal point estimation embodies an explicit or implicit model of legislative behavior. Generally, it is inappropriate to use ideal points estimated under one set of assumptions (such as sincere voting over a unidimensional policy space) to test a different behavioral model (such as log-rolling). Second, the computations required for estimating even the simplest roll call model are very difficult and extending these models to incorporate more realistic behavioral assumptions is nearly impossible with extant methods. Finally, the statistical basis of current methods for ideal point estimation is, to be polite, questionable. Roll call analysis involves very large numbers of parameters, 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 methods for ideal point estimation and the analysis of...

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We apply formal, statistical measurement models to the Polity indicators, used widely in studies of international relations to measure democracy. In so doing, we make explicit the hitherto implicit assumptions underlying scales built using the Polity indicators. Modeling democracy as a latent variable allows us to assess the "noise" (measurement error) in the resulting measure. We show that this measurement error is considerable and has substantive consequences when using a measure of democracy as an independent variable in cross-national statistical analyses. Our analysis suggests that skepticism as to the precision of the Polity democracy scale is well founded and that many researchers have been overly sanguine about the properties of the Polity democracy scale in applied statistical work.

Vote-specific parameters are often by-products of roll call analysis, the primary goal being the measurement of legislators' ideal points. But these vote-specific parameters are more important in higher-dimensional settings: prior restrictions on vote parameters help identify the model, and researchers often have prior beliefs about the nature of the dimensions underlying the proposal space. Bayesian methods provide a straightforward and rigorous way for incorporating these prior beliefs into roll call analysis. I demonstrate this by exploiting the close connections among roll call analysis, item-response models, and “full-information” factor analysis. Vote-specific discrimination parameters are equivalent to factor loadings, and as in factor analysis, they (1) enable researchers to discern the substantive content of the recovered dimensions, (2) can be used for assessing dimensionality and model checking, and (3) are an obvious vehicle for introducing and testing researchers' prior beliefs about the dimensions. Bayesian simulation facilitates these uses of discrimination parameters, by simplifying estimation and inference for the massive number of parameters generated by roll call analysis.