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.
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.
Ecological Inference: New Methodological Strategies brings together a diverse group of scholars to survey the latest strategies for solving ecological inference problems in various fields. The last half decade has witnessed an explosion of research in ecological inference – the attempt to infer individual behavior from aggregate data. The uncertainties and the information lost in aggregation make ecological inference one of the most difficult areas of statistical inference, but such inferences are required in many academic fields, as well as by legislatures and the courts in redistricting, by businesses in marketing research, and by governments in policy analysis.
Gelman, Andrew, Jonathan Katz, and Gary King. 2004. Empirically Evaluating the Electoral College. In Rethinking the Vote: The Politics and Prospects of American Electoral Reform, Ann N Crigler, Just, Marion R, and McCaffery, Edward J, 75-88. New York: Oxford University Press.Abstract
The 2000 U.S. presidential election rekindled interest in possible electoral reform. While most of the popular and academic accounts focused on balloting irregularities in Florida, such as the now infamous "butterfly" ballot and mishandled absentee ballots, some also noted that this election marked only the fourth time in history that the candidate with a plurality of the popular vote did not also win the Electoral College. This "anti-democratic" outcome has fueled desire for reform or even outright elimination of the electoral college. We show that after appropriate statistical analysis of the available historical electoral data, there is little basis to argue for reforming the Electoral College. We first show that while the Electoral College may once have been biased against the Democrats, the current distribution of voters advantages neither party. Further, the electoral vote will differ from the popular vote only when the average vote shares of the two major candidates are extremely close to 50 percent. As for individual voting power, we show that while there has been much temporal variation in relative voting power over the last several decades, the voting power of individual citizens would not likely increase under a popular vote system of electing the president.
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.
YourCast is (open source and free) software that makes forecasts by running sets of linear regressions together in a variety of sophisticated ways. YourCast avoids the bias that results when stacking datasets from separate cross-sections and assuming constant parameters, and the inefficiency that results from running independent regressions in each cross-section.
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.
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.
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.
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.
This is a set of easy-to-use Stata macros that implement the techniques described in Gary King, Michael Tomz, and Jason Wittenberg's "Making the Most of Statistical Analyses: Improving Interpretation and Presentation". To install Clarify, type "net from http://gking.harvard.edu/clarify" at the Stata command line. The documentation [ HTML | PDF ] explains how to do this. We also provide a zip archive for users who want to install Clarify on a computer that is not connected to the internet. Winner of the Okidata Best Research Software Award. Also try -ssc install qsim- to install a wrapper, donated by Fred Wolfe, to automate Clarify's simulation of dummy variables.
Although the term "empirical research" has become commonplace in legal scholarship over the past two decades, law professors have, in fact, been conducting research that is empirical – that is, learning about the world using quantitative data or qualitative information – for almost as long as they have been conducting research. For just as long, however, they have been proceeding with little awareness of, much less compliance with, the rules of inference, and without paying heed to the key lessons of the revolution in empirical analysis that has been taking place over the last century in other disciplines. The tradition of including some articles devoted to exclusively to the methododology of empirical analysis – so well represented in journals in traditional academic fields – is virtually nonexistent in the nation’s law reviews. As a result, readers learn considerably less accurate information about the empirical world than the studies’ stridently stated, but overconfident, conclusions suggest. To remedy this situation both for the producers and consumers of empirical work, this Article adapts the rules of inference used in the natural and social sciences to the special needs, theories, and data in legal scholarship, and explicate them with extensive illustrations from existing research. The Article also offers suggestions for how the infrastructure of teaching and research at law schools might be reorganized so that it can better support the creation of first-rate empirical research without compromising other important objectives.
Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. This model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here improves on Katz and King’s (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that implements our suggestions.