Methods

We highlight common problems in the application of random treatment assignment in large scale program evaluation. Random assignment is the defining feature of modern experimental design. Yet, errors in design, implementation, and analysis often result in real world applications not benefiting from the advantages of randomization. The errors we highlight cover the control of variability, levels of randomization, size of treatment arms, and power to detect causal effects, as well as the many problems that commonly lead to post-treatment bias. We illustrate with an application to the Medicare Health Support evaluation, including recommendations for improving the design and analysis of this and other large scale randomized experiments.

We attempt to clarify, and suggest how to avoid, several serious misunderstandings about and fallacies of causal inference in experimental and observational research. These issues concern some of the most basic advantages and disadvantages of each basic research design. Problems include improper use of hypothesis tests for covariate balance between the treated and control groups, and the consequences of using randomization, blocking before randomization, and matching after treatment assignment to achieve covariate balance. Applied researchers in a wide range of scientific disciplines seem to fall prey to one or more of these fallacies, and as a result make suboptimal design or analysis choices. To clarify these points, we derive a new four-part decomposition of the key estimation errors in making causal inferences. We then show how this decomposition can help scholars from different experimental and observational research traditions better understand each other’s inferential problems and attempted solutions.

In this article, we introduce a Stata implementation of coarsened exact matching, a new method for improving the estimation of causal effects by reducing imbalance in covariates between treated and control groups. Coarsened exact matching is faster, is easier to use and understand, requires fewer assumptions, is more easily automated, and possesses more attractive statistical properties for many applications than do existing matching methods. In coarsened exact matching, users temporarily coarsen their data, exact match on these coarsened data, and then run their analysis on the uncoarsened, matched data. Coarsened exact matching bounds the degree of model dependence and causal effect estimation error by ex ante user choice, is monotonic imbalance bounding (so that reducing the maximum imbalance on one variable has no effect on others), does not require a separate procedure to restrict data to common support, meets the congruence principle, is approximately invariant to measurement error, balances all nonlinearities and interactions in sample (i.e., not merely in expectation), and works with multiply imputed datasets. Other matching methods inherit many of the coarsened exact matching method’s properties when applied to further match data preprocessed by coarsened exact matching. The cem command implements the coarsened exact matching algorithm in Stata.

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.

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.

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 introduce a new framework for forecasting age-sex-country-cause-specific mortality rates that incorporates considerably more information, and thus has the potential to forecast much better, than any existing approach. Mortality forecasts are used in a wide variety of academic fields, and for global and national health policy making, medical and pharmaceutical research, and social security and retirement planning. As it turns out, the tools we developed in pursuit of this goal also have broader statistical implications, in addition to their use for forecasting mortality or other variables with similar statistical properties. First, our methods make it possible to include different explanatory variables in a time series regression for each cross-section, while still borrowing strength from one regression to improve the estimation of all. Second, we show that many existing Bayesian (hierarchical and spatial) models with explanatory variables use prior densities that incorrectly formalize prior knowledge. Many demographers and public health researchers have fortuitously avoided this problem so prevalent in other fields by using prior knowledge only as an ex post check on empirical results, but this approach excludes considerable information from their models. We show how to incorporate this demographic knowledge into a model in a statistically appropriate way. Finally, we develop a set of tools useful for developing models with Bayesian priors in the presence of partial prior ignorance. This approach also provides many of the attractive features claimed by the empirical Bayes approach, but fully within the standard Bayesian theory of inference.

This paper presents analytical, Monte Carlo, and empirical evidence on models for event count data. Event counts are dependent variables that measure the number of times some event occurs. Counts of international events are probably the most common, but numerous examples exist in every empirical field of the discipline. The results of the analysis below strongly suggest that the way event counts have been analyzed in hundreds of important political science studies have produced statistically and substantively unreliable results. Misspecification, inefficiency, bias, inconsistency, insufficiency, and other problems result from the unknowing application of two common methods that are without theoretical justification or empirical unity in this type of data. I show that the exponential Poisson regression (EPR) model provides analytically, in large samples, and empirically, in small, finite samples, a far superior model and optimal estimator. I also demonstrate the advantage of this methodology in an application to nineteenth-century party switching in the U.S. Congress. Its use by political scientists is strongly encouraged.

This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number of wars or coups d’etat in a year. I discuss several generalizations of the Poisson regression model, presented in King (1988), to allow for substantively interesting stochastic processes that do not fit into the Poisson framework. Individual models that cope with, and help analyze, heterogeneity, contagion, and negative contagion are each shown to lead to specific statistical models for event count data. In addition, I derive a new generalized event count (GEC) model that enables researchers to extract significant amounts of new information from existing data by estimating features of these unobserved substantive processes. Applications of this model to congressional challenges of presidential vetoes and superpower conflict demonstrate the dramatic advantages of this approach.

International relations theorists tend to think in terms of continuous processes. Yet we observe only discrete events, such as wars or alliances, and summarize them in terms of the frequency of occurrence. As such, most empirical analyses in international relations are based on event count variables. Unfortunately, analysts have generally relied on statistical techniques that were designed for continuous data. This mismatch between theory and method has caused bias, inefficiency, and numerous inconsistencies in both theoretical arguments and empirical findings throughout the literature. This article develops a much more powerful approach to modeling and statistical analysis based explicity on estimating continuous processes from observed event counts. To demonstrate this class of models, I present several new statistical techniques developed for and applied to different areas of international relations. These include the influence of international alliances on the outbreak of war, the contagious process of multilateral economic sanctions, and reciprocity in superpower conflict. I also show how one can extract considerably more information from existing data and relate substantive theory to empirical analyses more explicitly with this approach.

This article introduces a new estimator for the analysis of two contemporaneously correlated endogenous event count variables. This seemingly unrelated Poisson regression model (SUPREME) estimator combines the efficiencies created by single equation Poisson regression model estimators and insights from "seemingly unrelated" linear regression models.

We use an analogy with the normal distribution and linear regression to demonstrate the need for the Generalize Event Count (GEC) model. We then show how the GEC provides a unified framework within which to understand a diversity of distributions used to model event counts, and how to express the model in one simple equation. Finally, we address the points made by Christopher Achen, Timothy Amato, and John Londregan. Amato's and Londregan's arguments are consistent with ours and provide additional interesting information and explanations. Unfortunately, the foundation on which Achen built his paper turns out to be incorrect, rendering all his novel claims about the GEC false (or in some cases irrelevant).

We demonstrate that the expected value and variance commonly given for a well-known probability distribution are incorrect. We also provide corrected versions and report changes in a computer program to account for the known practical uses of this distribution.

Three articles, published in the leading journals of three disciplines over the last five decades, have each used the Poisson probability distribution to help describe the frequency with which presidents were able to appoint United States Supreme Court Justices. This work challenges these previous findings with a new model of Court appointments. The analysis demonstrates that the number of appointments a president can expect to make in a given year is a function of existing measurable variables.

Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all 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 single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut 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 set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.

The literature on cabinet duration is split between two apparently irreconcilable positions. The attributes theorists seek to explain cabinet duration as a fixed function of measured explanatory variables, while the events process theorists model cabinet durations as a product of purely stochastic processes. In this paper we build a unified statistical model that combines the insights of these previously distinct approaches. We also generalize this unified model, and all previous models, by including (1) a stochastic component that takes into account the censoring that occurs as a result of governments lasting to the vicinity of the maximum constitutional interelection period, (2) a systematic component that precludes the possibility of negative duration predictions, and (3) a much more objective and parsimonious list of explanatory variables, the explanatory power of which would not be improved by including a list of indicator variables for individual countries.

King, Alt, Burns, and Laver (1990) proposed and estimated a unified model in which cabinet durations depended on seven explanatory variables reflecting features of the cabinets and the bargaining environments in which they formed, along with a stochastic component in which the risk of a cabinet falling was treated as a constant across its tenure. Two recent research reports take issue with one aspect of this model. Warwick and Easton replicate the earlier findings for explanatory variables but claim that the stochastic risk should be seen as rising, and at a rate which varies, across the life of the cabinet. Bienen and van de Walle, using data on the duration of leaders, allege that random risk is falling. We continue in our goal of unifying this literature by providing further estimates with both cabinet and leader duration data that confirm the original explanatory variables’ effects, showing that leaders’ durations are affected by many of the same factors that affect the durability of the cabinets they lead, demonstrating that cabinets have stochastic risk of ending that is indeed constant across the theoretically most interesting range of durations, and suggesting that stochastic risk for leaders in countries with cabinet government is, if not constant, more likely to rise than fall.

A stand-alone, easy-to-use program for running event count and duration regression models, developed by and/or discussed in a series of journal articles by me. (Event count models have a dependent variable measured as the number of times something happens, such as the number of uncontested seats per state or the number of wars per year. Duration models explain dependent variables measured as the time until some event, such as the number of months a parliamentary cabinet endures.) Winner of the APSA Research Software Award.

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.

The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and King’s ecological inference model. The new approach reveals some features of the data that King’s approach does not, can easily be generalized to more complicated problems such as general R x C tables, allows the data analyst to adjust for covariates, and provides a formal evaluation of the significance of the covariates. It may also be better suited to cases in which the observed aggregate cells are estimated from very few observations or have some forms of measurement error. This article also provides an example of a hierarchical model in which the statistical idea of "borrowing strength" is used not merely to increase the efficiency of the estimates but to enable the data analyst to obtain estimates.

In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R x C contingency tables, including a covariate. The proposed Bayesian model extends the binomial-beta hierarchical model developed by King, Rosen and Tanner (1999) from the 2 x 2 case to the R x C case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on first moments rather than on the entire likelihood, provides quick inference via nonlinear least-squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the final section of the paper we provide an overview of a range of alternative inferential approaches which trade-off computational intensity for statistical efficiency.

Binary, count and duration data all code discrete events occurring at points in time. Although a single data generation process can produce all 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 single theoretical process exists for which know statistical methods can estimate the same parameters - and it is generally used only for count and duration data. The result is that seemingly trivial decisions abut 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 set of models for a time-dependent process and compare their predictions to those of a commonly used model. Any hope of understanding and avoiding the more serious problems of aggregation bias in events data is contingent on first deriving a much wider arsenal of statistical models and theoretical processes that are not constrained by the particular forms of data that happen to be available. We discuss these issues and suggest an agenda for political methodologists interested in this very large class of aggregation problems.

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.

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.

This is an invited response to an article by Anselin and Cho. I make two main points: The numerical results in this article violate no conclusions from prior literature, and the absence of the deterministic information from the bounds in the article’s analyses invalidates its theoretical discussion of spatial autocorrelation and all of its actual simulation results. An appendix shows how to draw simulations correctly.

I am grateful for such thoughtful review from these three distinguished geographers. Fotheringham provides an excellent summary of the approach offered, including how it combines the two methods that have dominated applications (and methodological analysis) for nearly half a century– the method of bounds (Duncan and Davis, 1953) and Goodman’s (1953) least squares regression. Since Goodman’s regression is the only method of ecological inference "widely used in Geography" (O’Loughlin), adding information that is known to be true from the method of bounds (for each observation) would seem to have the chance to improve a lot of research in this field. The other addition that EI provides is estimates at the lowest level of geography available, making it possible to map results, instead of giving only single summary numbers for the entire geographic region. Whether one considers the combined method offered "the" solution (as some reviewers and commentators have portrayed it), "a" solution (as I tried to describe it), or, perhaps better and more simply, as an improved method of ecological inference, is not importatnt. The point is that more data are better, and this method incorporates more. I am gratified that all three reviewers seem to support these basic points. In this response, I clarify a few points, correct some misunderstandings, and present additional evidence. I conclude with some possible directions for future research.

I appreciate the editor’s invitation to reply to Freedman et al.’s (1998) review of "A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data" (Princeton University Press.) I welcome this scholarly critique and JASA’s decision to publish in this field. Ecological inference is a large and very important area for applications that is especially rich with open statistical questions. I hope this discussion stimulates much new scholarship. Freedman et al. raise several interesting issues, but also misrepresent or misunderstand the prior literature, my approach, and their own empirical analyses, and compound the problem, by refusing requests from me and the editor to make their data and software available for this note. Some clarification is thus in order.

Social scientists typically devote considerable effort to reducing measurement error during data collection and then ignore the issue during data analysis. Although many statistical methods have been proposed for reducing measurement error-induced biases, few have been widely used because of implausible assumptions, high levels of model dependence, difficult computation, or inapplicability with multiple mismeasured variables. We develop an easy-to-use alternative that generalizes the popular multiple imputation (MI) framework by treating missing data problems as a special case of extreme measurement error and correcting for both. Like MI, the proposed "multiple overimputation" (MO) framework is a simple two-step procedure. First, multiple (≈5) completed copies of the data set are created where cells measured without error are held constant, those missing are imputed from the distribution of predicted values, and cells (or entire variables) with measurement error are "overimputed," that is imputed from a predictive distribution with observation-level priors defined by the mismeasured values and available external information, if any. In the second step, analysts can then run whatever statistical method they would have run on each of the overimputed data sets as if there had been no missingness or measurement error; the results are then combined via a simple procedure. We also (will) offer open source software that implements all the methods described herein.

We propose a comprehensive statistical model for analyzing multiparty, district-level elections. This model, which provides a tool for comparative politics research analagous to that which regression analysis provides in the American two-party context, can be used to explain or predict how geographic distributions of electoral results depend upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or aggregate areas. We also provide new graphical representations for data exploration, model evaluation, and substantive interpretation. We illustrate the use of this model by attempting to resolve a controversy over the size of and trend in electoral advantage of incumbency in Britain. Contrary to previous analyses, all based on measures now known to be biased, we demonstrate that the advantage is small but meaningful, varies substantially across the parties, and is not growing. Finally, we show how to estimate the party from which each party’s advantage is predominantly drawn.

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.

We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked or different sampling methods are used in different strata or clusters. Our method involves multiply imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights are based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed data to nonimputed data. We illustrate with the example that motivated this project: a study of pre-election public opinion polls in which not all the questions of interest are asked in all the surveys, so that it is infeasible to impute within each survey separately.

This program multiply imputes missing data in cross-sectional, time series, and time series cross-sectional data sets. It includes a Windows version (no knowledge of R required), and a version that works with R either from the command line or via a GUI.

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.

Amelia II is a complete R package for multiple imputation of missing data. The package implements a new expectation-maximization with bootstrapping algorithm that works faster, with larger numbers of variables, and is far easier to use, than various Markov chain Monte Carlo approaches, but gives essentially the same answers. The program also improves imputation models by allowing researchers to put Bayesian priors on individual cell values, thereby including a great deal of potentially valuable and extensive information. It also includes features to accurately impute cross-sectional datasets, individual time series, or sets of time series for different cross-sections. A full set of graphical diagnostics are also available. The program is easy to use, and the simplicity of the algorithm makes it far more robust; both a simple command line and extensive graphical user interface are included. Amelia II software web site

Before every presidential election, journalists, pollsters, and politicians commission dozens of public opinion polls. Although the primary function of these surveys is to forecast the election winners, they also generate a wealth of political data valuable even after the election. These preelection polls are useful because they are conducted with such frequency that they allow researchers to study change in estimates of voter opinion within very narrow time increments (Gelman and King 1993). Additionally, so many are conducted that the cumulative sample size of these polls is large enough to construct aggregate measures of public opinion within small demographic or geographical groupings (Wright, Erikson, and McIver 1985).

Receiving five serious reviews in this symposium is gratifying and confirms our belief that research design should be a priority for our discipline. We are pleased that our five distinguished reviewers appear to agree with our unified approach to the logic of inference in the social sciences, and with our fundamental point: that good quantitative and good qualitative research designs are based fundamentally on the same logic of inference. The reviewers also raised virtually no objections to the main practical contribution of our book– our many specific procedures for avoiding bias, getting the most out of qualitative data, and making reliable inferences. However, the reviews make clear that although our book may be the latest word on research design in political science, it is surely not the last. We are taxed for failing to include important issues in our analysis and for dealing inadequately with some of what we included. Before responding to the reviewers’ more direct criticisms, let us explain what we emphasize in Designing Social Inquiry and how it relates to some of the points raised by the reviewers.

We highlight, and suggest ways to avoid, a large number of common misunderstandings in the literature about best practices in qualitative research. We discuss these issues in four areas: theory and data, qualitative and quantitative strategies, causation and explanation, and selection bias. Some of the misunderstandings involve incendiary debates within our discipline that are readily resolved either directly or with results known in research areas that happen to be unknown to political scientists. Many of these misunderstandings can also be found in quantitative research, often with different names, and some of which can be fixed with reference to ideas better understood in the qualitative methods literature. Our goal is to improve the ability of quantitatively and qualitatively oriented scholars to enjoy the advantages of insights from both areas. Thus, throughout, we attempt to construct specific practical guidelines that can be used to improve actual qualitative research designs, not only the qualitative methods literatures that talk about them.

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.

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.

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.

When respondents use the ordinal response categories of standard survey questions in different ways, the validity of analyses based on the resulting data can be biased. Anchoring vignettes is a survey design technique, introduced by King, Murray, Salomon, and Tandon (2004), intended to correct for some of these problems. We develop new methods both for evaluating and choosing anchoring vignettes, and for analyzing the resulting data. With surveys on a diverse range of topics in a range of countries, we illustrate how our proposed methods can improve the ability of anchoring vignettes to extract information from survey data, as well as saving in survey administration costs.

We report the results of several randomized survey experiments designed to evaluate two intended improvements to anchoring vignettes, an increasingly common technique used to achieve interpersonal comparability in survey research.  This technique asks for respondent self-assessments followed by assessments of hypothetical people described in vignettes. Variation in assessments of the vignettes across respondents reveals interpersonal incomparability and allows researchers to make responses more comparable by rescaling them. Our experiments show, first, that switching the question order so that self-assessments follow the vignettes primes respondents to define the response scale in a common way.  In this case, priming is not a bias to avoid but a means of better communicating the question’s meaning.  We then demonstrate that combining vignettes and self-assessments in a single direct comparison induces inconsistent and less informative responses.  Since similar combined strategies are widely employed for related purposes, our results indicate that anchoring vignettes could reduce measurement error in many applications where they are not currently used.  Data for our experiments come from a national telephone survey and a separate on-line survey.

Before every presidential election, journalists, pollsters, and politicians commission dozens of public opinion polls. Although the primary function of these surveys is to forecast the election winners, they also generate a wealth of political data valuable even after the election. These preelection polls are useful because they are conducted with such frequency that they allow researchers to study change in estimates of voter opinion within very narrow time increments (Gelman and King 1993). Additionally, so many are conducted that the cumulative sample size of these polls is large enough to construct aggregate measures of public opinion within small demographic or geographical groupings (Wright, Erikson, and McIver 1985).

As most political scientists know, the outcome of the U.S. Presidential election can be predicted within a few percentage points (in the popular vote), based on information available months before the election. Thus, the general election campaign for president seems irrelevant to the outcome (except in very close elections), despite all the media coverage of campaign strategy. However, it is also well known that the pre-election opinion polls can vary wildly over the campaign, and this variation is generally attributed to events in the campaign. How can campaign events affect people’s opinions on whom they plan to vote for, and yet not affect the outcome of the election? For that matter, why do voters consistently increase their support for a candidate during his nominating convention, even though the conventions are almost entirely predictable events whose effects can be rationally forecast? In this exploratory study, we consider several intuitively appealing, but ultimately wrong, resolutions to this puzzle, and discuss our current understanding of what causes opinion polls to fluctuate and yet reach a predictable outcome. Our evidence is based on graphical presentation and analysis of over 67,000 individual-level responses from forty-nine commercial polls during the 1988 campaign and many other aggregate poll results from the 1952–1992 campaigns. We show that responses to pollsters during the campaign are not generally informed or even, in a sense we describe, "rational." In contrast, voters decide which candidate to eventually support based on their enlightened preferences, as formed by the information they have learned during the campaign, as well as basic political cues such as ideology and party identification. We cannot prove this conclusion, but we do show that it is consistent with the aggregate forecasts and individual-level opinion poll responses. Based on the enlightened preferences hypothesis, we conclude that the news media have an important effect on the outcome of Presidential elections–-not due to misleading advertisements, sound bites, or spin doctors, but rather by conveying candidates’ positions on important issues.

``Robust standard errors'' are used in a vast array of scholarship across all fields of empirical political science and most other social science disciplines. The popularity of this procedure stems from the fact that estimators of certain quantities in some models can be consistently estimated even under particular types of misspecification; and although classical standard errors are inconsistent in these situations, robust standard errors can sometimes be consistent. However, in applications where misspecification is bad enough to make classical and robust standard errors diverge, assuming that misspecification is nevertheless not so bad as to bias everything else requires considerable optimism. And even if the optimism is warranted, we show that settling for a misspecified model (even with robust standard errors) can be a big mistake, in that all but a few quantities of interest will be impossible to estimate (or simulate) from the model without bias. We suggest a different practice: Recognize that differences between robust and classical standard errors are like canaries in the coal mine, providing clear indications that your model is misspecified and your inferences are likely biased. At that point, it is often straightforward to use some of the numerous and venerable model checking diagnostics to locate the source of the problem, and then modern approaches to choosing a better model. With a variety of real examples, we demonstrate that following these procedures can drastically reduce biases, improve statistical inferences, and change substantive conclusions.

Social Scientists rarely take full advantage of the information available in their statistical results. As a consequence, they miss opportunities to present quantities that are of greatest substantive interest for their research and express the appropriate degree of certainty about these quantities. In this article, we offer an approach, built on the technique of statistical simulation, to extract the currently overlooked information from any statistical method and to interpret and present it in a reader-friendly manner. Using this technique requires some expertise, which we try to provide herein, but its application should make the results of quantitative articles more informative and transparent. To illustrate our recommendations, we replicate the results of several published works, showing in each case how the authors’ own conclusions can be expressed more sharply and informatively, and, without changing any data or statistical assumptions, how our approach reveals important new information about the research questions at hand. We also offer very easy-to-use Clarify software that implements our suggestions.

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.

We describe some progress toward a common framework for statistical analysis and software development built on and within the R language, including R’s numerous existing packages. The framework we have developed offers a simple unified structure and syntax that can encompass a large fraction of statistical procedures already implemented in R, without requiring any changes in existing approaches. We conjecture that it can be used to encompass and present simply a vast majority of existing statistical methods, regardless of the theory of inference on which they are based, notation with which they were developed, and programming syntax with which they have been implemented. This development enabled us, and should enable others, to design statistical software with a single, simple, and unified user interface that helps overcome the conflicting notation, syntax, jargon, and statistical methods existing across the methods subfields of numerous academic disciplines. The approach also enables one to build a graphical user interface that automatically includes any method encompassed within the framework. We hope that the result of this line of research will greatly reduce the time from the creation of a new statistical innovation to its widespread use by applied researchers whether or not they use or program in R.

This (two-page) article argues that the evidence base of political science and the related social sciences are beginning an underappreciated but historic change.

This article identifies a set of serious theoretical mistakes appearing with troublingly high frequency throughout the quantitative political science literature. These mistakes are all based on faulty statistical theory or on erroneous statistical analysis. Through algebraic and interpretive proofs, some of the most commonly made mistakes are explicated and illustrated. The theoretical problem underlying each is highlighted, and suggested solutions are provided throughout. It is argued that closer attention to these problems and solutions will result in more reliable quantitative analyses and more useful theoretical contributions.

"Politimetrics" (Gurr 1972), "polimetrics" (Alker 1975), "politometrics" (Hilton 1976), "political arithmetic" (Petty [1672] 1971), "quantitative Political Science (QPS)," "governmetrics," "posopolitics" (Papayanopoulos 1973), "political science statistics (Rai and Blydenburgh 1973), "political statistics" (Rice 1926). These are some of the names that scholars have used to describe the field we now call "political methodology." The history of political methodology has been quite fragmented until recently, as reflected by this patchwork of names. The field has begun to coalesce during the past decade and we are developing persistent organizations, a growing body of scholarly literature, and an emerging consensus about important problems that need to be solved. I make one main point in this article: If political methodology is to play an important role in the future of political science, scholars will need to find ways of representing more interesting political contexts in quantitative analyses. This does not mean that scholars should just build more and more complicated statistical models. Instead, we need to represent more of the essence of political phenomena in our models. The advantage of formal and quantitative approaches is that they are abstract representations of the political world and are, thus, much clearer. We need methods that enable us to abstract the right parts of the phenomenon we are studying and exclude everything superfluous. Despite the fragmented history of quantitative political analysis, a version of this goal has been voiced frequently by both quantitative researchers and their critics (Sec. 2). However, while recognizing this shortcoming, earlier scholars were not in the position to rectify it, lacking the mathematical and statistical tools and, early on, the data. Since political methodologists have made great progress in these and other areas in recent years, I argue that we are now capable of realizing this goal. In section 3, I suggest specific approaches to this problem. Finally, in section 4, I provide two modern examples, ecological inference and models of spatial autocorrelation, to illustrate these points.

A set of Gauss programs and datasets (annotated for pedagogical purposes) to implement many of the maximum likelihood-based models I discuss in Unifying Political Methodology: The Likelihood Theory of Statistical Inference, Ann Arbor: University of Michigan Press, 1998, and use in my class. All datasets are real, not simulated.

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.