Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.

Fixed effects vector decomposition (FEVD) is simply an instrumental variables (IV) estimator with a particular choice of instruments and a special case of the well-known Hausman-Taylor IV procedure. Plümper and Troeger (PT) now acknowledge this point and disown the three-stage procedure that previously defined FEVD. Their old recipe for SEs, which has regrettably been used in dozens of published research papers, produces dramatic overconfidence in the estimates. Again PT concede the point and now adopt the standard IV formula for SEs. Knowing that FEVD is an application of IV also has the benefit of focusing attention on the choice of instruments. Now it seems PT claim that the FEVD instruments are always the best choice, on the grounds that one cannot know whether any potential instrument is correlated with the unit effect. One could just as readily make the same specious claim about other estimators, such as ordinary least squares, and support it with similar Monte Carlo assumptions and evidence.

The Shapley-Owen value (SOV, Owen and Shapley 1989, Optimal location of candidates in ideological space. International Journal of Game Theory 125–42), a generalization of the Shapley-Shubik value applicable to spatial voting games, is an important concept in that it takes us away from a priori concepts of power to notions of power that are directly tied to the ideological proximity of actors. SOVs can also be used to locate the spatial analogue to the Copeland winner, the strong point, the point with smallest win-set, which is a plausible solution concept for games without cores. However, for spatial voting games with many voters, until recently, it was too computationally difficult to calculate SOVs, and thus, it was impossible to find the strong point analytically. After reviewing the properties of the SOV, such as the result proven by Shapley and Owen that size of win sets increases with the square of distance as we move away from the strong point along any ray, we offer a computer algorithm for computing SOVs that can readily find such values even for legislatures the size of the U.S. House of Representatives or the Russian Duma. We use these values to identify the strong point and show its location with respect to the uncovered set, for several of the U.S. congresses analyzed in Bianco, Jeliazkov, and Sened (2004, The limits of legislative actions: Determining the set of enactable outcomes given legislators preferences. Political Analysis 12:256–76) and for several sessions of the Russian Duma. We then look at many of the experimental committee voting games previously analyzed by Bianco et al. (2006, A theory waiting to be discovered and used: A reanalysis of canonical experiments on majority-rule decision making. Journal of Politics 68:838–51) and show how outcomes in these games tend to be points with small win sets located near to the strong point. We also consider how SOVs can be applied to a lobbying game in a committee of the U.S. Senate.

Measures of constituency preferences are of vital importance for the study of political representation and other research areas. Yet, such measures are often difficult to obtain. Previous survey-based estimates frequently lack precision and coverage due to small samples, rely on questionable assumptions or require detailed auxiliary information about the constituencies' population characteristics. We propose an alternative Bayesian hierarchical approach that exploits minimal geographic information readily available from digitalized constituency maps. If at hand, social background data are easily integrated. To validate the method, we use national polls and district-level results from the 2009 German Bundestag election, an empirical case for which detailed structural information is missing.

Researchers in comparative research are increasingly relying on individual level data to test theories involving unobservable constructs like attitudes and preferences. Estimation is carried out using large-scale cross-national survey data providing responses from individuals living in widely varying contexts. This strategy rests on the assumption of equivalence, that is, no systematic distortion in response behavior of individuals from different countries exists. However, this assumption is frequently violated with rather grave consequences for comparability and interpretation. I present a multilevel mixture ordinal item response model with item bias effects that is able to establish equivalence. It corrects for systematic measurement error induced by unobserved country heterogeneity, and it allows for the simultaneous estimation of structural parameters of interest.

This paper analyzes the use of ideal point estimates for testing pivot theories of lawmaking such as Krehbiel's (1998, Pivotal politics: A theory of U.S. lawmaking. Chicago, IL: University of Chicago) pivotal politics and Cox and McCubbins's (2005, Setting the Agenda: Responsible Party Government in the U.S. House of Representations. New York: Cambridge University Press) party cartel model. Among the prediction of pivot theories is that all pivotal legislators will vote identically on all successful legislation. Clinton (2007, Lawmaking and roll calls. Journal of Politics 69:455–67) argues that the estimated ideal points of the pivotal legislators are therefore predicted to be statistically indistinguishable and false when estimated from the set of successful final passage roll call votes, which implies that ideal point estimates cannot logically be used to test pivot theories. I show using Monte Carlo simulation that when pivot theories are augmented with probabilistic voting, Clinton's prediction only holds in small samples when voting is near perfect. I furthermore show that the predicted bias is unlikely to be consequential with U.S. Congressional voting data. My analysis suggests that the methodology of estimating ideal points to compute theoretically relevant quantities for empirical tests is not inherently flawed in the case of pivot theories.

Efforts to find empirical evidence that campaign money impacts policymaking choices have offered scant support for interest group influence. A possible explanation is that the hypothesis that those receiving campaign monies should adjust their policy choices to favor their donor requires the untenable assumption that interest groups and legislators can implement contracts. We develop a new, alternative, model in which legislators and interest groups cannot engage in any form of contracting, and legislators care about both the policy and fundraising implications of their policy choices. In our model, an interest group gives only to those it believes shares its policy preferences. Nonetheless, we show that the group's giving impacts incumbent policy choices. Importantly, when groups ideologically match, the relationship between actual contributions and bias is not straightforward. As long as a group is uncertain about a member's primitive policy preference, it can influence her policymaking even when it contributes to her challenger or abstains from giving altogether.

The empirical study of spatial issue voting has experienced a resurgence in recent years due to advances in data collection and research design. Grynaviski and Corrigan make several important contributions to this literature. In this note, we comment on one of Grynaviski and Corrigan's recommendations—to not include a main effect for issue importance when estimating models assessing the interactive relationship between importance and policy proximity. According to the authors, including the main importance term is incorrect because it is not necessary in representing a scale-invariant functional form under some assumptions and is insufficient under others. In deriving their reduced-form expression, the authors produce a model that is unintuitive and inappropriate for most data. Moreover, the restrictions Grynaviski and Corrigan impose on their model can produce perverse empirical predictions. We show that a model including main effect terms for importance is indeed scale invariant and that inclusion of the main importance term is necessary for scale invariance with respect to partial utility functions.

Spatial statistical methods in political science provide a tool to deal with spatial and other forms of interdependence in observational data. In this article, I derive a statistical model from a game of impure public goods provision. The resulting strategic autoregressive model (StratAM) allows the researcher to systematically explore the sources of free-riding behavior in the provision of public goods. The StratAM model is tightly related to the well-known spatial autoregressive (SAR) model and can be estimated in a maximum likelihood framework. I demonstrate the use of the StratAM model by analyzing free riding in the provision of foreign aid. Indicators of developmental needs and good governance strongly increase free-riding during the 1990s. Free-riding patterns in the 2000s are more similar to Cold War patterns.

Political scientists have increasingly focused on causal processes that operate not solely on mean differences but on other stochastic characteristics of the distribution of a dependent variable. This paper surveys important statistical tools used to assess data in situations where the entire distribution of values is of interest. We first outline three broad conditions under which stochastic process methods are applicable and show that these conditions cover many domains of social inquiry. We discuss a variety of visual and analytical techniques, including distributional analysis, direct parameter estimates of probability density functions, and quantile regression. We illustrate the utility of these statistical tools with an application to budgetary data because strong theoretical expectations at the micro- and macrolevel exist about the distributional characteristics for such data. The expository analysis concentrates on three budget series (total, domestic, and defense outlays) of the U.S. government for 1800–2004.

Contingency tables are among the most basic and useful techniques available for analyzing categorical data, but they produce highly imprecise estimates in small samples or for population subgroups that arise following repeated stratification. I demonstrate that preprocessing an observed set of categorical variables using a latent class model can greatly improve the quality of table-based inferences. As a density estimator, the latent class model closely approximates the underlying joint distribution of the variables of interest, which enables reliable estimation of conditional probabilities and marginal effects, even among subgroups containing fewer than 40 observations. Though here focused on applications to public opinion, the procedure has a wide range of potential uses. I illustrate the benefits of the latent class model—based approach for greatly improved accuracy in estimating and forecasting vote preferences within small demographic subgroups using survey data from the 2004 and 2008 U.S. presidential election campaigns.

In this paper, I introduce changepoint models for binary and ordered time series data based on Chib's hidden Markov model. The extension of the changepoint model to a binary probit model is straightforward in a Bayesian setting. However, detecting parameter breaks from ordered regression models is difficult because ordered time series data often have clustering along the break points. To address this issue, I propose an estimation method that uses the linear regression likelihood function for the sampling of hidden states of the ordinal probit changepoint model. The marginal likelihood method is used to detect the number of hidden regimes. I evaluate the performance of the introduced methods using simulated data and apply the ordinal probit changepoint model to the study of Eichengreen, Watson, and Grossman on violations of the “rules of the game” of the gold standard by the Bank of England during the interwar period.

This paper extends models of micro- and macropartisanship in two ways. It first develops a model of individual partisanship that accommodates changes in partisan utilities. Achen's Bayesian partisan updating is a special case of our model. This more general micromodel is then aggregated to create a model of macropartisanship. This macromodel is a more general version of the models of macropartisanship estimated by various authors. The less restricted version incorporates possible individual and temporal heterogeneity. We present an example using real data that offers a possible way to estimate the parameters in the full aggregate model.

Lewis and Schultz (2003) develop a statistical signaling model to deal with international conflicts or bargaining situations in which states have private information about their payoffs. They claim that they can confirm that there always exists a unique equilibrium in their model. In this paper, I show that Lewis and Schultz's claim is not true and their model admits multiple equilibria under some parameter settings. Monte Carlo analysis shows that when there are multiple equilibria, the parameter estimates may not converge to their true values even if the number of observations increases.

If ignored, noncompliance with a treatment or nonresponse on outcome measures can bias estimates of treatment effects in a randomized experiment. To identify and estimate causal treatment effects in the case where compliance and response depend on unobservables, we propose the parametric generalized endogenous treatment (GET) model. GET incorporates behavioral responses within an experiment to measure each subject's latent compliance type and identifies causal effects via principal stratification. Using simulation methods and an application to field experimental data, we show GET has a dramatically lower mean squared error for treatment effect estimates than existing approaches to principal stratification that impute, rather than measure, compliance type. In addition, we show that GET allows one to relax and test the instrumental variable exclusion restriction assumption, to test for the presence of treatment effect heterogeneity across a range of compliance types, and to test for treatment ignorability when treatment and control samples are balanced on observable covariates.

Although methodologists have provided us ample notice of both the problem of nonproportional hazards (NPHs) and the means of correcting for them, less attention has been paid to the postestimation interpretation. The suggested inclusion of time interactions in our models is more than a statistical fix: These corrections alter the substantive meaning and interpretation of results. Framing the issue as a specific case of multiplicative-interaction modeling, I provide detailed discussion of the problem of NPHs and present several appropriate means of interpreting both the substantive impact and the significance of variables whose effects may change over time.