1We appreciate the generosity and insight of Ron Lee and Nan Li for help in understanding their approach and the demographic literature in general. Many thanks also to John Wilmoth for very helpful comments.

Social scientific theories frequently posit that multiple causal mechanisms may produce the same outcome. Unfortunately, it is not always possible to observe which mechanism was responsible. For example, IMF scholars conjecture that nations enter IMF agreements both out of economic need and for discretionary domestic political reasons. Typically, though, all we observe is the fact of agreement, not its cause. Partial observability probit models (Poirier 1980, Journal of Econometrics 12:209–217; Braumoeller 2003, Political Analysis 11:209– 233) provide one method for the statistical analysis of such phenomena. Unfortunately, they are often plagued by identification and labeling difficulties. Sometimes, however, qualitative studies of particular cases enlighten us about causes when quantitative studies cannot. We propose exploiting this information to lend additional structure to the partial observability approach. Monte Carlo simulation reveals that by anchoring ‘‘discernible’ ’ causes for a handful of cases about which we possess qualitative information, we obtain greater efficiency. More important, our method proves reliable at recovering unbiased parameter estimates when the partial observability model fails. The paper concludes with an analysis of the determinants of IMF agreements. A member shall be entitled to purchase the currencies of other members from the Fund...[provided] the member represents that it has a need to make the purchase because of its balance of payments or its reserve position or developments in its reserves. —International Monetary Fund Articles of Agreement [IMF] negotiations sometimes enable government leaders to do what they privately wish to do, but are powerless to do domestically. —Robert Putnam (1988, p. 457)

Binary, count, and duration data all code for discrete events occurring at points in time. Although a single data generation process can produce any of these three data types, the statistical literature is not very helpful in providing methods to estimate parameters of the same process from each. In fact, only a single theoretical process exists for which known statistical methods can estimate the same parameters --- and it is generally limited to count and duration data. The result is that seemingly trivial decisions about which level of data to use can have important consequences for substantive interpretations. We describe the theoretical event process for which results exist, based on time-independence. We also derive a new set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical mode...

Nearly all hierarchical linear models presented to political science audiences are estimated using maximum likelihood under a repeated sampling interpretation of the results of hypothesis tests. Maximum likelihood estimators have excellent asymptotic properties but less than ideal small sample properties. Multilevel models common in political science have relatively large samples of units like individuals nested within relatively small samples of units like countries. Often these level-2 samples will be so small as to make inference about level-2 effects uninterpretable in the likelihood framework from which they were estimated. When analysts do not have enough data to make a compelling argument for repeated sampling based probabilistic inference, we show how visualization can be a useful way of allowing scientific progress to continue despite lack of fit between research design and asymptotic properties of maximum likelihood estimators.

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Despite immense data collections, prestigious journals, and sophisticated analyses, empirical findings in the literature on international conflict are frequently unsatisfying. Statistical results appear to change from article to article and specification to specification. Very few relationships hold up to replication with even minor respecification. Accurate forecasts are nonexistent. We provide a simple conjecture about what accounts for this problem, and offer a statistical framework that better matches the substantive issues and types of data in this field. Our model, a version of a "neural network" model, forecasts substantially better than any previous effort, and appears to uncover some structural features of international conflict. 1 Introduction Despite immense data collections, prestigious journals, and sophisticated analyses, empirical findings in the literature on international conflict are frequently unsatisfying. Statistical results appear to change from article to arti...

Unknown to most world politics scholars and political scientists in general, traditional methods of model discrimination such as likelihood ratio tests, F-tests, and artificial nesting fail when applied to nonnested models. That the vast majority of models used throughout international relations research have nonlinear functional forms complicates the problem. The purpose of this research is to suggest methods of properly discriminating between nonnested models and then to demonstrate how these techniques can shed light on substantive debates in international relations. Re-analysis of two well-known articles that compare structural realism to various alternatives suggests that the evidence against realism in both articles is overstated. 1

This paper discusses the modeling of over- and under-dispersion for grouped binary (proportions or frequency) data in binomial regression models (logit and probit). The sources of non-binomial variance in heterogeneity and dependence across or within units is described. Even when point predictions in conventional logit and probit analyses are only slightly affected, standard errors, and inferences based on them, will be incorrect. Particular attention is paid to the extended beta-binomial model. Using the extended beta binomial distribution, the non-binomial variance can be explicitly modeled. Another benefit of modeling the non-binomial variance with the EBB distribution is that negative correlations which lead to under-dispersion can be accommodated. Although common in some disciplines, EBB in conjunction with binary regressions (logit, probit) has only recently been used in political science applications. Some example analyses are presented and the results are compared to those from other models and post-analysis fixes.

Background: Studies have revealed large variations in average health status across social, economic, and other groups. No study exists on the distribution of the risk of ill-health across individuals, either within groups or across all people in a society, and as such a crucial piece of total health inequality has been overlooked. Some of the reason for this neglect has been that the risk of death, which forms the basis for most measures, is impossible to observe directly and difficult to estimate.

We examine whether the conditions affecting initial expressions of hostility are similar to those affecting militarized disputes, which are not only more serious but also represent subsequent stages in the conflict process. Using data on dyadic interactions covering the 1951-1992 period, we estimate two models, one designed to take into account selection effects and the other allowing for conjunctive causation. Both provide closer approximations to theoretical models of the conflict process, and both yield similar results. Overall, our findings correspond with Kant's understanding that all states are subject to the realist conditions of interstate competition that makes disputes likely, but that the liberal influences, where present, can constrain the escalation of such disputes to war. The investigation also provides support for our argument that the effects of various influences on the conflict process are nonmonotonic over the range of hostile state behavior. We find that geopolitical factors affecting the opportunity for conflict are relatively more important in earlier stages of the conflict process, when less information is available regarding acceptable settlements and the resolve of actors to achieve them, than in later stages. By contrast, the importance of factors affecting willingness -- democratic norms and institutions and economic interdependence -- increase as the conflict process unfolds because they facilitate the flow of information relevant to the ongoing dispute. Fortunately, militarized conflict between states is rare. Nevertheless, diplomatic and other forms of low-level interstate conflict surely are not rare and these have the potential to escalate to more violent forms of dispute -- so scholars and policymakers have great interest in the tools o...