Unifying Statistical Analysis

Development of a unified approach to statistical modeling, inference, interpretation, presentation, analysis, and software; integrated with most of the other projects listed here.
A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results
Beau Coker, Cynthia Rudin, and Gary King. 2021. “A Theory of Statistical Inference for Ensuring the Robustness of Scientific Results.” Management Science, Pp. 1-24. Publisher's VersionAbstract
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting uncertainty. Any one theory of inference is neither right nor wrong, but merely an axiom that may or may not be useful. Each of the many diverse theories of inference can be valuable for certain applications. However, no existing theory of inference addresses the tendency to choose, from the range of plausible data analysis specifications consistent with prior evidence, those that inadvertently favor one's own hypotheses. Since the biases from these choices are a growing concern across scientific fields, and in a sense the reason the scientific community was invented in the first place, we introduce a new theory of inference designed to address this critical problem. We derive "hacking intervals," which are the range of a summary statistic one may obtain given a class of possible endogenous manipulations of the data. Hacking intervals require no appeal to hypothetical data sets drawn from imaginary superpopulations. A scientific result with a small hacking interval is more robust to researcher manipulation than one with a larger interval, and is often easier to interpret than a classical confidence interval. Some versions of hacking intervals turn out to be equivalent to classical confidence intervals, which means they may also provide a more intuitive and potentially more useful interpretation of classical confidence intervals. 

Unifying Approaches to Statistical Analysis

Twitter: Big data opportunities—Response
David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani. 2014. “Twitter: Big data opportunities—Response.” Science, 345, 6193, Pp. 148-149. Publisher's VersionAbstract
WE THANK BRONIATOWSKI, Paul, and Dredze for giving us the opportunity to reemphasize the potential of big data and make the more obvious point that not all big data projects have the problems currently plaguing Google Flu Trends (GFT), nor are these problems inherent to the field in general.

See our original papers: "The Parable of Google Flu: Traps in Big Data Analysis," and "Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season"
Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season
David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani. 2014. “Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season”.Abstract
Last year was difficult for Google Flu Trends (GFT). In early 2013, Nature reported that GFT was estimating more than double the percentage of doctor visits for influenza like illness than the Centers for Disease Control and Prevention s (CDC) sentinel reports during the 2012 2013 flu season (1). Given that GFT was designed to forecast upcoming CDC reports, this was a problematic finding. In March 2014, our report in Science found that the overestimation problem in GFT was also present in the 2011 2012 flu season (2). The report also found strong evidence of autocorrelation and seasonality in the GFT errors, and presented evidence that the issues were likely, at least in part, due to modifications made by Google s search algorithm and the decision by GFT engineers not to use previous CDC reports or seasonality estimates in their models what the article labeled algorithm dynamics and big data hubris respectively. Moreover, the report and the supporting online materials detailed how difficult/impossible it is to replicate the GFT results, undermining independent efforts to explore the source of GFT errors and formulate improvements.

See our original paper, "The Parable of Google Flu: Traps in Big Data Analysis"
The Parable of Google Flu: Traps in Big Data Analysis
David Lazer, Ryan Kennedy, Gary King, and Alessandro Vespignani. 2014. “The Parable of Google Flu: Traps in Big Data Analysis.” Science, 343, 14 March, Pp. 1203-1205. Publisher's VersionAbstract
Large errors in flu prediction were largely avoidable, which offers lessons for the use of big data.

In February 2013, Google Flu Trends (GFT) made headlines but not for a reason that Google executives or the creators of the flu tracking system would have hoped. Nature reported that GFT was predicting more than double the proportion of doctor visits for influenza-like illness (ILI) than the Centers for Disease Control and Prevention (CDC), which bases its estimates on surveillance reports from laboratories across the United States ( 1, 2). This happened despite the fact that GFT was built to predict CDC reports. Given that GFT is often held up as an exemplary use of big data ( 3, 4), what lessons can we draw from this error?

See also "Google Flu Trends Still Appears Sick: An Evaluation of the 2013‐2014 Flu Season"

 

How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It
Gary King and Margaret E. Roberts. 2015. “How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It.” Political Analysis, 23, 2, Pp. 159–179. Publisher's VersionAbstract

"Robust standard errors" are used in a vast array of scholarship to correct standard errors for model misspecification. However, when misspecification is bad enough to make classical and robust standard errors diverge, assuming that it is nevertheless not so bad as to bias everything else requires considerable optimism. And even if the optimism is warranted, settling for a misspecified model, with or without robust standard errors, will still bias estimators of all but a few quantities of interest. The resulting cavernous gap between theory and practice suggests that considerable gains in applied statistics may be possible. We seek to help researchers realize these gains via a more productive way to understand and use robust standard errors; a new general and easier-to-use "generalized information matrix test" statistic that can formally assess misspecification (based on differences between robust and classical variance estimates); and practical illustrations via simulations and real examples from published research. How robust standard errors are used needs to change, but instead of jettisoning this popular tool we show how to use it to provide effective clues about model misspecification, likely biases, and a guide to considerably more reliable, and defensible, inferences. Accompanying this article is open source software that implements the methods we describe. 

Calculating Standard Errors of Predicted Values based on Nonlinear Functional Forms
Gary King. 1991. “Calculating Standard Errors of Predicted Values based on Nonlinear Functional Forms.” The Political Methodologist, 4.Abstract

Whenever we report predicted values, we should also report some measure of the uncertainty of these estimates. In the linear case, this is relatively simple, and the answer well-known, but with nonlinear models the answer may not be apparent. This short article shows how to make these calculations. I first present this for the familiar linear case, also reviewing the two forms of uncertainty in these estimates, and then show how to calculate these for any arbitrary function. An example appears last.

 

Making the Most of Statistical Analyses: Improving Interpretation and Presentation
Generalizes the unification in the book (replacing its Section 5.2 with simulation to compute quantities of interest). This paper, which was originally titled "Enough with the Logit Coefficients, Already!", explains how to compute any quantity of interest from almost any statistical model; and shows, with replications of several published works, how to extract considerably more information than standard practices, without changing any data or statistical assumptions. Gary King, Michael Tomz, and Jason Wittenberg. 2000. “Making the Most of Statistical Analyses: Improving Interpretation and Presentation.” American Journal of Political Science, 44, Pp. 341–355. Publisher's VersionAbstract
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.
CLARIFY: Software for Interpreting and Presenting Statistical Results
Software that accompanies the above article and implements its key ideas in easy-to-use Stata macros. Michael Tomz, Jason Wittenberg, and Gary King. 2003. “CLARIFY: Software for Interpreting and Presenting Statistical Results.” Journal of Statistical Software.Abstract

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 https://gking.harvard.edu/clarify (https://gking.harvard.edu/clarify)" at the Stata command line.

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.

URL: https://scholar.harvard.edu/gking/clarify

Zelig: Everyone's Statistical Software
A generalization of Clarify, and much other software, implemented in R. The extensive manual encompasses most of the above works and can be read independently as an introduction to wide range of models. Under active development. Kosuke Imai, Gary King, and Olivia Lau. 2006. “Zelig: Everyone's Statistical Software”.
Toward A Common Framework for Statistical Analysis and Development
A paper that describes the advances underlying Zelig software: Kosuke Imai, Gary King, and Olivia Lau. 2008. “Toward A Common Framework for Statistical Analysis and Development.” Journal of Computational Graphics and Statistics, 17, Pp. 1–22.Abstract
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.

Related Materials

The Changing Evidence Base of Social Science Research
Gary King. 2009. “The Changing Evidence Base of Social Science Research.” In The Future of Political Science: 100 Perspectives, edited by Gary King, Kay Schlozman, and Norman Nie. New York: Routledge Press.Abstract

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

How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science
Gary King. 1986. “How Not to Lie With Statistics: Avoiding Common Mistakes in Quantitative Political Science.” American Journal of Political Science, 30, Pp. 666–687.Abstract
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.
On Political Methodology
Gary King. 1991. “On Political Methodology.” Political Analysis, 2, Pp. 1–30.Abstract
"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.
What to do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation
Jeff Gill and Gary King. 2004. “What to do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation.” Sociological Methods and Research, 32, Pp. 54-87.Abstract
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.