We look at conventional methods for removing endogeneity bias in regression models, including the linear model and the probit model. It is known that the usual Heckman two-step procedure should not be used in the probit model: from a theoretical perspective, it is unsatisfactory, and likelihood methods are superior. However, serious numerical problems occur when standard software packages try to maximize the biprobit likelihood function, even if the number of covariates is small. We draw conclusions for statistical practice. Finally, we prove the conditions under which parameters in the model are identifiable. The conditions for identification are delicate; we believe these results are new.

Ideal point estimators are typically based on an assumption that all legislators are equally responsive to modeled dimensions of legislative disagreement; however, particularistic constituency interests and idiosyncrasies of individual legislators introduce variation in the degree to which legislators cast votes predictably. I introduce a Bayesian heteroskedastic ideal point estimator and demonstrate by Monte Carlo simulation that it outperforms standard homoskedastic estimators at recovering the relative positions of legislators. In addition to providing a refinement of ideal point estimates, the heteroskedastic estimator recovers legislator-specific error variance parameters that describe the extent to which each legislator's voting behavior is not conditioned on the primary axes of disagreement in the legislature. Through applications to the roll call histories of the U.S. Congress, the E.U. Parliament, and the U.N. General Assembly, I demonstrate how to use the heteroskedastic estimator to study substantive questions related to legislative incentives for low-dimensional voting behavior as well as diagnose unmodeled dimensions and nonconstant ideal points.

Although sample selection bias is a frequent problem of applied research, there has been no generalization of sample selection models with binary dependent variables of interest to data with temporal error correlations. We suggest a generalized estimating equation approach to panel data selection models, considering binary responses in both equations. We demonstrate the utility of this model by a simulation study and by analyzing highly unbalanced annual panel data taken from the German Socio-Economic Panel Study covering two decades of Green party support.

The Cox proportional hazards model is widely used to model durations in the social sciences. Although this model allows analysts to forgo choices about the form of the hazard, it demands careful attention to the proportional hazards assumption. To this end, a standard diagnostic method has been developed to test this assumption. I argue that the standard test for nonproportional hazards has been misunderstood in current practice. This test detects a variety of specification errors, and these specification errors must be corrected before one can correctly diagnose nonproportionality. In particular, unmodeled nonlinearity can appear as a violation of the proportional hazard assumption for the Cox model. Using both simulation and empirical examples, I demonstrate how an analyst might be led astray by incorrectly applying the nonproportionality test.

The polity2 variable from the Polity IV project is the most popular measure of a country's political regime. This article contends that the coding rules employed to create a polity2 score during years of so-called interregnum and affected transitions produce a measure of democracy that lacks face validity. Using both single and multiple imputation methods, we construct and evaluate several variables that offer alternative measures to polity2 during such periods. We recommend that scholars using polity2 test whether their results are robust to using our alternatives and using multiple imputation techniques instead. Where robustness cannot be established, scholars need to theoretically justify the choice of either polity2 or one of the alternatives.

This paper extends the Calculus of Voting of McKelvey and Ordeshook, providing the first direct derivation of the conditions under which voters will vote strategically: choose their second-most preferred candidate in order to prevent their least-preferred candidate from winning. Addressing this theoretical problem is important, as nearly all empirical research on strategic voting either implicitly or explicitly tests hypotheses which originate from this seminal model. The formal result allows us to isolate the subset of voters to which strategic voting hypotheses properly apply and in turn motivates a critical reevaluation of past empirical work. In making this argument, we develop a unified and parsimonious framework for understanding competing models of tactical voter choice. The typology helps to elucidate the methodological difficulties in studying tactical behavior when faced with heterogeneous explanatory models and suggests the need for both theoretical caution and more precise data instruments in future empirical work.

Political science researchers typically conduct an idiosyncratic search of possible model configurations and then present a single specification to readers. This approach systematically understates the uncertainty of our results, generates fragile model specifications, and leads to the estimation of bloated models with too many control variables. Bayesian model averaging (BMA) offers a systematic method for analyzing specification uncertainty and checking the robustness of one's results to alternative model specifications, but it has not come into wide usage within the discipline. In this paper, we introduce important recent developments in BMA and show how they enable a different approach to using the technique in applied social science research. We illustrate the methodology by reanalyzing data from three recent studies using BMA software we have modified to respect statistical conventions within political science.