This paper shows a general nonparametric unfolding technique for maximizing the correct classification of binary choice or two-category data. The motivation for and the primary focus of the unfolding technique are parliamentary roll call voting data. However, the procedures that implement the unfolding also can be applied to the problem of unfolding rank order data as well as analyzing a data set that would normally be the subject of a probit, logit, or linear probability analysis. One aspect of the scaling method greatly improves Manski's “maximum score estimator” technique for estimating limited dependent variable models. To unfold binary choice data two subproblems must be solved. First, given a set of chooser or legislator points, a cutting plane must be found such that it divides the legislators/choosers into two sets that reproduce the actual choices as closely as possible. Second, given a set of cutting planes for the binary choices, a point for each chooser or legislator must be found which reproduces the actual choices as closely as possible. Solutions for these two problems are shown in this paper. Monte Carlo tests of the procedure show it to be highly accurate in the presence of voting error and missing data.

Measures of change in pairs of attitudinal variables can provide important insights into the structure of the political belief systems of mass publics. Panel data reveal evidence of the greater centrality of some idea elements rather than others in the context of short-term dynamic constraint. Specification of the theoretically relevant voter attributes makes it possible to test for expected structural differences connecting policy related predispositions and policy preferences; specification also makes it possible to test propositions involving the reciprocal effects of attitudes and emerging vote preferences. Some of the more helpful specifications disclose the extent to which population heterogeneity produces a blurred image of relationships when analysis is based on the total electorate rather than limited to voters or subsets of voters specified by theoretical criteria.

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

There has been much discussion about how members of Congress desire money early in the campaign season. However, theoretical models of how contributions are allocated during the electoral cycle have been lacking. Our analysis attempts to remedy this gap by providing and testing a model which specifies how the process of bargaining between members of Congress and organized interests produces the pattern of donations observed over the course of the electoral cycle. Most notably, our results suggest that strategic incumbents can receive money early in the campaign if they desire but that they are generally unwilling to pay the price of lower aggregate fundraising and greater provision of access. These findings buttress earlier empirical findings that question the instrumental value of early money. In addition, our results highlight that contribution choices are fundamentally influenced by short-term factors, especially electoral conditions, that do not lend themselves to the routinized behavior necessary for contributors to invest in incumbents for long-run payoffs.

Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multiequation models with reciprocal causation has focused on models with continuous dependent variables (e.g., Markus and Converse 1979; Page and Jones 1979). Yet, many models of political behavior involve discrete or dichotomous dependent variables; this paper describes two techniques which can consistently estimate reciprocal relationships between dichotomous and continuous dependent variables. The first, two-stage probit least squares (2SPLS), is very similar to two-stage instrumental variable techniques. The second, two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. We demonstrate the potential pitfalls of ignoring the problems of reciprocal causation in nonrecursive choice models and examine the properties of both techniques using Monte Carlo simulations: we find that 2SPLS slightly outperforms 2SCML in terms of bias but that 2SCML produces more accurate standard errors. However, the 2SCML model offers an explicit statistical test for endogeneity. The results from our simulations, and the statistical test for exogeneity, lead us to advocate the use of 2SCML for estimation of this class of causal models. We then apply both of these techniques to an empirical example focusing on the relationship between voter preferences in a presidential election and the voter's uncertainty about the policy positions taken by the candidates. This example demonstrates the importance of these techniques for political science research.

Parallel panel and fresh cross-section samples in recent National Election Study surveys provide valuable leverage for assessing the magnitude of biases in statistical analyses of survey data due to panel attrition and panel conditioning. My analyses employing a variety of typical regression models suggest that substantial panel biases are likely to be fairly rare in these data, even when panel and cross-section respondents have markedly different characteristics. However, two of the dependent variables considered here—campaign interest and turnout—do appear to be sufficiently sensitive to panel effects to warrant significant discounting or adjustment of panel data. I propose adjustments for panel effects in both cross-sectional and dynamic analyses, based upon variants of the “fractional pooling” (Bartels 1996) and “two-stage auxiliary instrumental variables” (Franklin 1990) methods.

Publication of King's A Solution to the Ecological Inference Problem has rekindled interest in the estimation of unknown cell values in two- and three-dimensional matrices from knowledge of the marginal sums. This paper outlines an entropy-maximizing (EM) procedure which employs more constraints than King's EI method and produces mathematical rather than statistical procedures: the estimates are maximum-likelihood values. The mathematics are outlined, and the procedure's use illustrated with a study of ticket-splitting at New Zealand's first (1996) general election using the mixed-member proportional representation system, for which official figures provide a check against the EM estimate of the number voting a straight party ticket in each constituency.

While it is very common for Congressional researchers to use interest group ratings as measures of legislator policy preferences, this paper argues that the manner in which such ratings are calculated implies that they may poorly approximate the underlying legislator preferences on which they are based. In light of this, the paper develops a technique designed to adjust interest group ratings so that they more closely correlate with legislator preferences. It argues based on Monte Carlo simulations that the technique produces adjusted ratings that improve on unadjusted ratings, and it applies the adjustment technique to historical ratings published by the Americans for Democratic Action.

Political scientists are making increasing use of the Tobit and Heckit models. This paper addresses some common problems in the application and interpretation of these models. Through numerical experiments and reanalysis of data from a study by Romer and Snyder (1994), we illustrate the consequences of using the standard Tobit model, which assumes a censoring point at zero, when the zeros are not due to censoring mechanisms or when actual censoring is not at zero. In the latter case, we also show that Greene's (1981) well-known results on the direction and size of the bias of the OLS estimator in the standard Tobit model do not necessarily hold. Because the Heckit model is often used as an alternative to Tobit, we examine its assumptions and discuss the proper interpretation of the Heckit/Tobit estimation results using Grier and co-workers' (1994) Heckit model of campaign contribution data. Sensitivity analyses of the Heckit estimation results suggest some conclusions rather different from those reached by Grier et al.

The directional and proximity models offer dramatically different theories for how voters make decisions and fundamentally divergent views of the supposed microfoundations on which vast bodies of literature in theoretical rational choice and empirical political behavior have been built. We demonstrate here that the empirical tests in the large and growing body of literature on this subject amount to theoretical debates about which statistical assumption is right. The key statistical assumptions have not been empirically tested and, indeed, turn out to be effectively untestable with existing methods and data. Unfortunately, these assumptions are also crucial since changing them leads to different conclusions about voter decision processes.

A statistic—the similarity coefficient—is developed for assessing the property that a set of scale items measures one and only one construct. This statistic is rooted in an explicit measurement model and is flexible enough to be used in exploratory scale analyses, even in small samples. Methods for analyzing similarity coefficients are described and illustrated in analyses of Stimson's (1991) policy mood data and Markus' (1990) popular individualism items. The Appendix discusses the statistical properties of similarity coefficients.

High levels of nonresponse plague all three waves of the National Election Studies' Senate Studies. Each of the studies failed to elicit interviews from close to one of every two selected sample persons, a rate far worse than the NES regular Pre- and Post-Election Studies. This paper addresses three interdependent problems: Given limited data about the nonrespondents, how can we model the causes of nonresponse? Using these models, how can we adjust our analysis of the Senate Study data to compensate for nonresponse? What difference does nonresponse make for our understanding of the dynamics of Senate elections?

As applications of duration analysis have burgeoned in political science, scholars have become increasingly aware of the potential substantive importance of duration dependence: the extent to which the conditional hazards of the events of interest are rising or falling over time. Here I discuss the issue of duration dependence, focusing on the distinction between “spurious” dependence due to unobserved heterogeneity and “true” duration dependence due to state dependence in the process of interest. I present a simple extension of a commonly used parametric duration model—the Weibull model—which allows researchers to assess the influence of causal variables on the nature and extent of duration dependence in their data. I then illustrate the application of this “generalized Weibull” model using data on the duration of international alliances.

In recent years, political scientists have tested for the existence of rational expectations (RE) using survey-based aggregate data on subjective economic perceptions. These tests suffer from several conceptual shortcomings of a nontrivial nature. In this study, the meaning of RE is clarified, and also a test for strong rational expectations (SRE) where citizens possess heterogeneous information levels is set forth. These empirical tests provide insights into what kinds of information citizens use in forming expectations from that which they do not utilize but could employ to arrive at more accurate forecasts. Using inflation expectations data for the period January 1978—December 1993, the empirical findings indicate that citizens can benefit from greater reliance on objective economic and political conditions when formulating their inflation expectations. The broader implications of this work pertain not only to the execution of RE tests in political science, but also to distinguishing which types of information people do and do not (but could) incorporate in their decision-making calculus.

This paper shows that agnostic spatial models that simultaneously attempt to estimate legislators' preferred points and ideological locations for the proposals on which they vote, such as the well-known NOMINATE model of Poole and Rosenthal, are not identified. The problem arises because the agnostic estimators inherit the granularity of the voting data and, so, cannot recapture the underlying continuous parameter space. I propose an alternative estimator that achieves identification by modeling the agenda.

Political knowledge has emerged as one of the central variables in political behavior research, with numerous scholars devoting considerable effort to explaining variance in citizens' levels of knowledge and to understanding the consequences of this variance for representation. Although such substantive matters continue to receive exhaustive study, questions of measurement also warrant attention. I demonstrate that conventional measures of political knowledge—constructed by summing a respondent's correct answers on a battery of factual items—are of uncertain validity. Rather than collapsing incorrect and “don't know” responses into a single absence-of-knowledge category, I introduce estimation procedures that allow these effects to vary. Grouped-data multinomial logistic regression results demonstrate that incorrect answers and don't knows perform dissimilarly, a finding that suggests deficiencies in the construct validity of conventional knowledge measures. The likely cause of the problem is traced to two sources: knowledge may not be discrete, meaning that a simple count of correct answers provides an imprecise measure; and, as demonstrated by the wealth of research conducted in the field of educational testing and psychology since the 1930s, measurement procedures used in political science potentially result in “knowledge” scales contaminated by systematic personality effects.

A ranking exists in electoral systems research of different electoral formulas—the mathematical functions governing the conversion of votes into legislative seats—in terms of both proportionality of seats and votes and favorability to the largest party. I reexamine this issue with new methods and new evidence, attempting to cross-validate previous rankings using a larger and more controlled data set and more precise parametric methods than have been applied previously. The results by and large confirm previous knowledge but also illuminate several important new facets obscured in previous investigations. For example, at common ranges of district magnitude (from 5 to 15 seats), it is shown that electoral formula may matter at least as much as district magnitude in shaping proportionality.

In political science and many other disciplines, statistically significant results—rejections of the null hypothesis—are achieved more frequently in published than in unpublished studies. Such “publication bias” is generally seen as the consequence of a widespread prejudice against statistically nonsignificant results. I argue that evidence of such a prejudice is in surprisingly short supply and that publication bias can occur even in the absence of such a prejudice and even if the review process is functioning perfectly. More importantly, publication bias may stem from dutiful application of standards of scientific inquiry rather than from irrational prejudice.