We address the problem that occurs when inferences about counterfactuals – predictions, "what if" questions, and causal effects – are attempted far from the available data. The danger of these extreme counterfactuals is that substantive conclusions drawn from statistical models that fit the data well turn out to be based largely on speculation hidden in convenient modeling assumptions that few would be willing to defend. Yet existing statistical strategies provide few reliable means of identifying extreme counterfactuals. We offer a proof that inferences farther from the data are more model-dependent, and then develop easy-to-apply methods to evaluate how model-dependent our answers would be to specified counterfactuals. These methods require neither sensitivity testing over specified classes of models nor evaluating any specific modeling assumptions. If an analysis fails the simple tests we offer, then we know that substantive results are sensitive to at least some modeling choices that are not based on empirical evidence.
The widely used methods for estimating adult mortality rates from sample survey responses about the survival of siblings, parents, spouses, and others depend crucially on an assumption that we demonstrate does not hold in real data. We show that when this assumption is violated – so that the mortality rate varies with sibship size – mortality estimates can be massively biased. By using insights from work on the statistical analysis of selection bias, survey weighting, and extrapolation problems, we propose a new and relatively simple method of recovering the mortality rate with both greatly reduced potential for bias and increased clarity about the source of necessary assumptions.
I show herein how to write a publishable paper by beginning with the replication of a published article. This strategy seems to work well for class projects in producing papers that ultimately get published, helping to professionalize students into the discipline, and teaching them the scientific norms of the free exchange of academic information. I begin by briefly revisiting the prominent debate on replication our discipline had a decade ago and some of the progress made in data sharing since.
Does the U.S. Supreme Court curtail rights and liberties when the nation’s security is under threat? In hundreds of articles and books, and with renewed fervor since September 11, 2001, members of the legal community have warred over this question. Yet, not a single large-scale, quantitative study exists on the subject. Using the best data available on the causes and outcomes of every civil rights and liberties case decided by the Supreme Court over the past six decades and employing methods chosen and tuned especially for this problem, our analyses demonstrate that when crises threaten the nation’s security, the justices are substantially more likely to curtail rights and liberties than when peace prevails. Yet paradoxically, and in contradiction to virtually every theory of crisis jurisprudence, war appears to affect only cases that are unrelated to the war. For these cases, the effect of war and other international crises is so substantial, persistent, and consistent that it may surprise even those commentators who long have argued that the Court rallies around the flag in times of crisis. On the other hand, we find no evidence that cases most directly related to the war are affected. We attempt to explain this seemingly paradoxical evidence with one unifying conjecture: Instead of balancing rights and security in high stakes cases directly related to the war, the Justices retreat to ensuring the institutional checks of the democratic branches. Since rights-oriented and process-oriented dimensions seem to operate in different domains and at different times, and often suggest different outcomes, the predictive factors that work for cases unrelated to the war fail for cases related to the war. If this conjecture is correct, federal judges should consider giving less weight to legal principles outside of wartime but established during wartime, and attorneys should see it as their responsibility to distinguish cases along these lines.
We address two long-standing survey research problems: measuring complicated concepts, such as political freedom or efficacy, that researchers define best with reference to examples and and what to do when respondents interpret identical questions in different ways. Scholars have long addressed these problems with approaches to reduce incomparability, such as writing more concrete questions – with uneven success. Our alternative is to measure directly response category incomparability and to correct for it. We measure incomparability via respondents’ assessments, on the same scale as the self-assessments to be corrected, of hypothetical individuals described in short vignettes. Since actual levels of the vignettes are invariant over respondents, variability in vignette answers reveals incomparability. Our corrections require either simple recodes or a statistical model designed to save survey administration costs. With analysis, simulations, and cross-national surveys, we show how response incomparability can drastically mislead survey researchers and how our approach can fix them.
We thank Scott de Marchi, Christopher Gelpi, and Jeffrey Grynaviski (2003 and hereinafter dGG) for their careful attention to our work (Beck, King, and Zeng, 2000 and hereinafter BKZ) and for raising some important methodological issues that we agree deserve readers’ attention. We are pleased that dGG’s analyses are consistent with the theoretical conjecture about international conflict put forward in BKZ –- "The causes of conflict, theorized to be important but often found to be small or ephemeral, are indeed tiny for the vast majority of dyads, but they are large stable and replicable whenever the ex ante probability of conflict is large" (BKZ, p.21) –- and that dGG agree with our main methodological point that out-of-sample forecasting performance should always be one of the standards used to judge studies of international conflict, and indeed most other areas of political science. However, dGG frequently err when they draw methodological conclusions. Their central claim involves the superiority of logit over neural network models for international conflict data, as judged by forecasting performance and other properties such as ease of use and interpretation ("neural networks hold few unambiguous advantages... and carry significant costs" relative to logit and dGG, p.14). We show here that this claim, which would be regarded as stunning in any of the diverse fields in which both methods are more commonly used, is false. We also show that dGG’s methodological errors and the restrictive model they favor cause them to miss and mischaracterize crucial patterns in the causes of international conflict. We begin in the next section by summarizing the growing support for our conjecture about international conflict. The second section discusses the theoretical reasons why neural networks dominate logistic regression, correcting a number of methodological errors. The third section then demonstrates empirically, in the same data as used in BKZ and dGG, that neural networks substantially outperform dGG’s logit model. We show that neural networks improve on the forecasts from logit as much as logit improves on a model with no theoretical variables. We also show how dGG’s logit analysis assumed, rather than estimated, the answer to the central question about the literature’s most important finding, the effect of democracy on war. Since this and other substantive assumptions underlying their logit model are wrong, their substantive conclusion about the democratic peace is also wrong. The neural network models we used in BKZ not only avoid these difficulties, but they, or one of the other methods available that do not make highly restrictive assumptions about the exact functional form, are just what is called for to study the observable implications of our conjecture.
What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertable? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest exists in the data, through the likelihood function. We explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.
Although not widely known until much later, Al Gore received 202 more votes than George W. Bush on election day in Florida. George W. Bush is president because he overcame his election day deficit with overseas absentee ballots that arrived and were counted after election day. In the final official tally, Bush received 537 more votes than Gore. These numbers are taken from the official results released by the Florida Secretary of State's office and so do not reflect overvotes, undervotes, unsuccessful litigation, butterfly ballot problems, recounts that might have been allowed but were not, or any other hypothetical divergence between voter preferences and counted votes. After the election, the New York Times conducted a six month long investigation and found that 680 of the overseas absentee ballots were illegally counted, and no partisan, pundit, or academic has publicly disagreed with their assessment. In this paper, we describe the statistical procedures we developed and implemented for the Times to ascertain whether disqualifying these 680 ballots would have changed the outcome of the election. The methods involve adding formal Bayesian model averaging procedures to King's (1997) ecological inference model. Formal Bayesian model averaging has not been used in political science but is especially useful when substantive conclusions depend heavily on apparently minor but indefensible model choices, when model generalization is not feasible, and when potential critics are more partisan than academic. We show how we derived the results for the Times so that other scholars can use these methods to make ecological inferences for other purposes. We also present a variety of new empirical results that delineate the precise conditions under which Al Gore would have been elected president, and offer new evidence of the striking effectiveness of the Republican effort to convince local election officials to count invalid ballots in Bush counties and not count them in Gore counties.
Despite widespread recognition that aggregated summary statistics on international conflict and cooperation miss most of the complex interactions among nations, the vast majority of scholars continue to employ annual, quarterly, or occasionally monthly observations. Daily events data, coded from some of the huge volume of news stories produced by journalists, have not been used much for the last two decades. We offer some reason to change this practice, which we feel should lead to considerably increased use of these data. We address advances in event categorization schemes and software programs that automatically produce data by "reading" news stories without human coders. We design a method that makes it feasible for the first time to evaluate these programs when they are applied in areas with the particular characteristics of international conflict and cooperation data, namely event categories with highly unequal prevalences, and where rare events (such as highly conflictual actions) are of special interest. We use this rare events design to evaluate one existing program, and find it to be as good as trained human coders, but obviously far less expensive to use. For large scale data collections, the program dominates human coding. Our new evaluative method should be of use in international relations, as well as more generally in the field of computational linguistics, for evaluating other automated information extraction tools. We believe that the data created by programs similar to the one we evaluated should see dramatically increased use in international relations research. To facilitate this process, we are releasing with this article data on 4.3 million international events, covering the entire world for the last decade.
In every discipline in which "empirical research" has become commonplace, scholars have formed a subfield devoted to solving the methodological problems unique to that discipline’s data and theoretical questions. Although students of economics, political science, psychology, sociology, business, education, medicine, public health, and so on primarily focus on specific substantive questions, they cannot wait for those in other fields to solve their methoodological problems or to teach them "new" methods, wherever they were initially developed. In "The Rules of Inference," we argued for the creation of an analogous methodological subfield devoted to legal scholarship. We also had two other objectives: (1) to adapt the rules of inference used in the natural and social sciences, which apply equally to quantitative and qualitative research, to the special needs, theories, and data in legal scholarship, and (2) to offer recommendations on how the infrastructure of teaching and research at law schools might be reorganized so that it could better support the creation of first-rate quantitative and qualitative empirical research without compromising other important objectives. Published commentaries on our paper, along with citations to it, have focused largely on the first-our application of the rules of inference to legal scholarship. Until now, discussions of our second goal-suggestions for the improvement of legal scholarship, as well as our argument for the creation of a group that would focus on methodological problems unique to law-have been relegated to less public forums, even though, judging from the volume of correspondence we have received, they seem to be no less extensive.
Since the replication standard was proposed for political science research, more journals have required or encouraged authors to make data available, and more authors have shared their data. The calls for continuing this trend are more persistent than ever, and the agreement among journal editors in this Symposium continues this trend. In this article, I offer a vision of a possible future of the replication movement. The plan is to implement this vision via the Virtual Data Center project, which – by automating the process of finding, sharing, archiving, subsetting, converting, analyzing, and distributing data – may greatly facilitate adherence to the replication standard.
Since Herron and Shotts (2003a and hereinafter HS), Adolph and King (2003 andhereinafter AK), and Herron and Shotts (2003b and hereinafter HS2), the four of us have iterated many more times, learned a great deal, and arrived at a consensus on this issue. This paper describes our joint recommendations for how to run second-stage ecological regressions, and provides detailed analyses to back up our claims.
We present new statistical methods for evaluating information extraction systems. The methods were developed to evaluate a system used by political scientists to extract event information from news leads about international politics. The nature of this data presents two problems for evaluators: 1) the frequency distribution of event types in international event data is strongly skewed, so a random sample of newsleads will typically fail to contain any low frequency events. 2) Manual information extraction necessary to create evaluation sets is costly, and most effort is wasted coding high frequency categories . We present an evaluation scheme that overcomes these problems with considerably less manual effort than traditional methods, and also allows us to interpret an information extraction system as an estimator (in the statistical sense) and to estimate its bias.
Classic (or "cumulative") case-control sampling designs do not admit inferences about quantities of interest other than risk ratios, and then only by making the rare events assumption. Probabilities, risk differences, and other quantities cannot be computed without knowledge of the population incidence fraction. Similarly, density (or "risk set") case-control sampling designs do not allow inferences about quantities other than the rate ratio. Rates, rate differences, cumulative rates, risks, and other quantities cannot be estimated unless auxiliary information about the underlying cohort such as the number of controls in each full risk set is available. Most scholars who have considered the issue recommend reporting more than just the relative risks and rates, but auxiliary population information needed to do this is not usually available. We address this problem by developing methods that allow valid inferences about all relevant quantities of interest from either type of case-control study when completely ignorant of or only partially knowledgeable about relevant auxiliary population information.
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. Methods: We develop a measure of total health inequality – encompassing all inequalities among people in a society, including variation between and within groups – by adapting a beta-binomial regression model. We apply it to children under age two in 50 low- and middle-income countries. Our method has been adopted by the World Health Organization and is being implemented in surveys around the world and preliminary estimates have appeared in the World Health Report (2000). Results: Countries with similar average child mortality differ considerably in total health inequality. Liberia and Mozambique have the largest inequalities in child survival, while Colombia, the Philippines and Kazakhstan have the lowest levels among the countries measured. Conclusions: Total health inequality estimates should be routinely reported alongside average levels of health in populations and groups, as they reveal important policy-related information not otherwise knowable. This approach enables meaningful comparisons of inequality across countries and future analyses of the determinants of inequality.