Social scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. Using this technique requires some expertise,

We propose a remedy for the discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. Methodologists and statisticians agree that "multiple imputation" is a superior approach to the problem of missing data scattered through one's explanatory and dependent variables than the methods currently used in applied data analysis. The reason for this discrepancy lies with the fact that the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise. In this paper, we adapt an existing algorithm, and use it to implement a generalpurpose, multiple imputation model for missing data. This algorithm is considerably faster and easier to use than the leading method recommended in the statistics literature. We also quantify the risks of current missing data practices, ...

We propose a remedy to the substantial discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. With a few notable exceptions, statisticians and methodologists have agreed on a widely applicable approach to many missing data problems based on the concept of \multiple imputation, " but most researchers in our eld and other social sciences still use far inferior methods. Indeed, we demonstrate that the threats to validity from current missing data practices rival the biases from the much better known omitted variable problem. As it turns out, this discrepancy is not entirely our fault, as the computational algorithms used to apply the best multiple imputation models have been slow, di cult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise on the part of the user (even experts disagree on how to use them). In this paper, we adapt an existing algorithm, and use it to implement a generalpurpose, multiple imputation model for missing data. This algorithm is between 65 and

1The authors thank Greg Huber and seminar participants at Dartmouth College and the University of Chicago for comments on an earlier draft of this paper and thank election officials in Charlotte, Collier, DeSoto, Hardee, Hillsborough, Lee, Manatee, Pinellas, and Sarasota Counties for providing data and assistance. The most recent version of this paper can be found

We develop a robust estimator -- the hyperbolic tangent (tanh) estimator --for overdispersed multinomial regression models of count data. The tanh estimator provides accurate estimates and reliable inferences even when the specified model is not good for as much as half of the data. Seriously ill-fitted counts -- outliers -- are identified as part of the estimation. A Monte Carlo sampling experiment shows that the tanh estimator produces good results at practical sample sizes even when ten percent of the data are generated by a significantly dierent process. The experiment shows that, with contaminated data, estimation fails using four other estimators: the nonrobust maximum likelihood estimator, the additive logistic model and two SUR models. Using the tanh estimator to analyze data from Florida for the 2000 presidential election matches well-known features of the election that the other four estimators fail to capture. In an analysis of data from the 1993 Polish parliamentary election, the tanh estimator gives sharper inferences than does a previously proposed heteroscedastic SUR model.

The enormous Nazi voting literature rarely builds on modern statistical or economic research. By adding these approaches, we find that the most widely accepted existing theories of this era cannot distinguish the Weimar elections from almost any others in any country. Via a retrospective voting account, we show that voters most hurt by the depression, and most likely to oppose the government, fall into separate groups with divergent interests. This explains why some turned to the Nazis and others turned away. The consequences of Hitler’s election were extraordinary, but the voting behavior that led to it was not.

Bayesian simulation is increasingly exploited in the social sciences for estimation and inference of model parameters. But an especially useful (if often overlooked) feature of Bayesian simulation is that it can be used to estimate any function of model parameters, including “auxiliary ” quantities such as goodness-of-fit statistics, predicted values, and residuals. Bayesian simulation treats these quantities as if they were missing data, sampling from their implied posterior densities. Exploiting this principle also lets researchers estimate models via Bayesian simulation where maximum-likelihood estimation would be intractable. Bayesian simulation thus provides a unified solution for quantitative social science. I elaborate these ideas in a variety of contexts: these include generalized linear models for binary responses using data on bill cosponsorship recently reanalyzed in Political Analysis, item–response models for the measurement of respondent’s levels of political information in public opinion surveys, the estimation and analysis of legislators’ ideal points from roll-call data, and outlier-resistant regression estimates of incumbency advantage in U.S. Congressional elections. 1 Bayesian Simulation: Estimation, Inference, and Communication

Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. Their model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. KK applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here for improves on KK's (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that i...

Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. Their model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied their model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we o#er here improves on Katz and King's (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also o#...

This paper explores one contributing causal explanation to this phenomenon. In a simple model of parties as collections of incumbents, it is shown that the distribution of Median voters across districts can help or harm parties in equilibrium. In equilibrium in asymmetric distributions the members of one party will rationally choose a policy position which in expectation gives their party a strict minority of seats.