Logistic Regression in Rare Events Data

We study rare events data, binary dependent variables with dozensto thousands of times fewer ones (events, such as wars, vetoes,cases of political activism, or epidemiological infections)than zeros ("nonevents"). In many literatures, these variableshave proven difficult to explain and predict, a problem thatseems to have at least two sources. First, popular statisticalprocedures, such as logistic regression, can sharply underestimatethe probability of rare events. We recommend corrections thatoutperform existing methods and change the estimates of absoluteand relative risks by as much as some estimated effects reportedin the literature. Second, commonly used data collection strategiesare grossly inefficient for rare events data. The fear of collectingdata with too few events has led to data collections with hugenumbers of observations but relatively few, and poorly measured,explanatory variables, such as in international conflict datawith more than a quarter-million dyads, only a few of whichare at war. As it turns out, more efficient sampling designsexist for making valid inferences, such as sampling all availableevents (e.g., wars) and a tiny fraction of nonevents (peace).This enables scholars to save as much as 99% of their (nonfixed)data collection costs or to collect much more meaningful explanatoryvariables. We provide methods that link these two results, enablingboth types of corrections to work simultaneously, and softwarethat implements the methods developed.     

Empirical versus Theoretical Claims about Extreme Counterfactuals: A Response

Langche Zeng Department of Political Science, University of California, San Diego, La Jolla, CA 92093 e-mail: lazeng{at}ucsd.edu In response to the data-based measures of model dependence proposedin King and Zeng (2006), Sambanis and Michaelides (2008) proposealternative measures that rely upon assumptions untestable inobservational data. If these assumptions are correct, then theirmeasures are appropriate and ours, based solely on the empiricaldata, may be too conservative. If instead, and as is usuallythe case, the researcher is not certain of the precise functionalform of the data generating process, the distribution from whichthe data are drawn, and the applicability of these modelingassumptions to new counterfactuals, then the data-based measuresproposed in King and Zeng (2006) are much preferred. After all,the point of model dependence checks is to verify empirically,rather than to stipulate by assumption, the effects of modelingassumptions on counterfactual inferences. Author’s note: Easy-to-use software to implement the methodsdiscussed here, called "WhatIf: Software for Evaluating Counterfactuals,"is available at http://gking.harvard.edu/whatif. All informationnecessary to replicate the analyses herein can be found in King and Zeng (2008).Conflict of interest statement. None declared.     

Some properties of Hare voting with strategic voters

From the perspective of some common criteria for evaluating voting procedures, the results we offer in this essay will almost certainly be interpreted as inditments of STV. Even if we restrict preferences with conditions R1 and R2, STV is not necessarily incentive compatible. Moreover, strategic voting does not ensure the selection of Condorcet winning candidates or of Condorcet outcomes. This fact, moreover is not dependent on the existence of bogus equilibria — outcomes that exclude Condorcet candidates cannot be avoided under all circumstances even if we limit our analysis to strong or to individually stable equilibria.It is not the case, though, that the Condorcet criterion is the unique or even the most important criterion with which to evaluate election procedures. For example, we have not examined the extent to which STV ensures proportionality and we have not compared STV to other procedures. Despite the apparent deficiencies described in this essay, STV may yet prove to be a viable alternative to systems that seek to ensure proportionality by other means.     

Analyzing Censored and Sample-Selected Data with Tobit and Heckit Models

Political scientists are making increasing use of the Tobitand Heckit models. This paper addresses some common problemsin the application and interpretation of these models. Throughnumerical experiments and reanalysis of data from a study byRomer and Snyder (1994), we illustrate the consequences of usingthe standard Tobit model, which assumes a censoring point atzero, when the zeros are not due to censoring mechanisms orwhen actual censoring is not at zero. In the latter case, wealso show that Greene's (1981) well-known results on the directionand size of the bias of the OLS estimator in the standard Tobitmodel do not necessarily hold. Because the Heckit model is oftenused as an alternative to Tobit, we examine its assumptionsand discuss the proper interpretation of the Heckit/Tobit estimationresults using Grier and co-workers' (1994) Heckit model of campaigncontribution data. Sensitivity analyses of the Heckit estimationresults suggest some conclusions rather different from thosereached by Grier et al.