Since Beck, Katz, and Tucker (1998), the standard method for modeling time dependence in binary data has been to incorporate time dummies or splined time in logistic regressions. Although we agree with the need for modeling time dependence, we demonstrate that time dummies can induce estimation problems due to separation. Splines do not suffer from these problems. However, the complexity of splines has led substantive researchers (1) to use knot values that may be inappropriate for their data and (2) to ignore any substantive discussion concerning temporal dependence. We propose a relatively simple alternative: including t, t2, and t3 in the regression. This cubic polynomial approximation is trivial to implement—and, therefore, interpret—and it avoids problems such as quasi-complete separation. Monte Carlo analysis demonstrates that, for the types of hazards one often sees in substantive research, the polynomial approximation always outperforms time dummies and generally performs as well as splines or even more flexible autosmoothing procedures. Due to its simplicity, this method also accommodates nonproportional hazards in a straightforward way. We reanalyze Crowley and Skocpol (2001) using nonproportional hazards and find new empirical support for the historical-institutionalist perspective.

The pattern of alliances among states is commonly assumed to reflect the extent to which states have common or conflicting security interests. For the past twenty years, Kendall's τb has been used to measure the similarity of nations' "portfolios" of alliance commitments. Widely employed indicators of systemic polarity, state utility, and state risk propensity all rely on τ b . We demonstrate that τ b is inappropriate for measuring the similarity of states' alliance policies. We develop an alternative measure of policy portfolio similarity, S, which avoids many of the problems associated with τb, and we use data on alliances among European states to compare S to τ b . Finally, we identify several problems with inferring state interests from alliances alone, and we provide a method to overcome those problems using S in combination with data on alliances, trade, UN votes, diplomatic missions, and other types of state interaction. We demonstrate this by comparing the calculated similarity of foreign policy positions based solely on alliance data to that based on alliance data supplemented with UN voting data.

Although strategic interaction is at the heart of most international relations theory, it has largely been missing from much empirical analysis in the field. Typical applications of logit and probit to theories of international conflict generally do not capture the structure of the strategic interdependence implied by those theories. I demonstrate how to derive statistical discrete choice models of international conflict that directly incorporate the theorized strategic interaction. I show this for a simple crisis interaction model and then use Monte Carlo analysis to show that logit provides estimates with incorrect substantive interpretations as well as fitted values that can be far from the true values. Finally, I reanalyze a well-known game-theoretic model of war, Bueno de Mesquita and Lalman's (1992) international interaction game. My results indicate that there is at best modest empirical support for their model.

Social scientists are often confronted with theories in which one or more actors make choices over a discrete set of options. In this article, I generalize a broad class of statistical discrete choice models, with both well-known and new nonstrategic and strategic special cases. I demonstrate how to derive statistical models from theoretical discrete choice models and, in doing so, I address the statistical implications of three sources of uncertainty: agent error, private information about payoffs, and regressor error. For strategic and some nonstrategic choice models, the three types of uncertainty produce different statistical models. In these cases, misspecifying the type of uncertainty leads to biased and inconsistent estimates, and to incorrect inferences based on estimated probabilities.

Common regression models are often structurally inconsistent with strategic interaction. We demonstrate that this "strategic misspecification" is really an issue of structural (or functional form) (Signorino 1999(Signorino , 2000Smith 1999) suggests that, when analyzing strategic behavior on the part of individuals or states, failure to reflect that strategic interaction in one's statistical model can result in invalid inferences. Signorino (1999) demonstrates this with a Monte Carlo example in which the inferences from logit regressions are far from (at times completely opposite to) the strategic data-generating process. Signorino (1999), however, is not a complete analysis of the misspecification, but more a warning and demonstration that the misspecification exists. As of yet, the form of the misspecification has not been characterized in a way that most practitioners readily understand or in a manner that allows us to state when the effects of strategic misspecification should be mild versus severe. The primary goal of this article is to do exactly that.As we demonstrate in this article, strategic misspecification is really an issue of structural (or functional form) misspecification. Because this type of misspecification is not well known among political scientists, we begin in the next section by illustrating the problem of functional form misspecification as it applies to the classical linear regression model. It is easy to show in this case that functional form misspecification is actually a type of omitted variable bias, where the omitted variables are nonlinear terms in a Taylor series approximation of the true functional form.We then move to the strategic setting and construct what we believe is the simplest model possible: a twoplayer deterrence game. We assume the data in this case represents whether a particular outcome (war) has occurred or not, and we analyze the misspecification of using logit or probit with the ubiquitous linear X B specification of the latent variable equation. As in the OLS case, it is easy to rewrite the strategic misspecification as a form of omitted variable bias, where the omitted variables are nonlinear terms in a Taylor series expansion of the true functional form and where the nonlinearity is due to the players' expected utility calculations. Because of the misspecification, parameter estimates are not only biased, but inconsistent. Therefore, throwing more data at the problem does not make it go away.In the third section, we analyze the misspecification when the dependent variable is the action taken by the first player, the attacker. By construction, this choice is

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Common regression models are often structurally inconsistent with strategic interaction. We demonstrate that this "strategic misspecification" is really an issue of structural (or functional form) misspecification. The misspecification can be equivalently written as a form of omitted variable bias, where the omitted variables are nonlinear terms arising from the players' expected utility calculations and often from data aggregation. We characterize the extent of the specification error in terms of model parameters and the data and show that typical regressions models can at times give exactly the opposite inferences versus the true strategic data-generating process. Researchers are recommended to pay closer attention to their theoretical models, the implications of those models concerning their statistical models, and vice versa.

We present a simple method for estimating regressions based on recursive extensive-form games. Our procedure, which can be implemented in most standard statistical packages, involves sequentially estimating standard logits (or probits) in a manner analogous to backwards induction. We demonstrate that the technique produces consistent parameter estimates and show how to calculate consistent standard errors. To illustrate the method, we replicate Leblang's (2003) study of speculative attacks by financial markets and government responses to these attacks.