Christopher Zorn

Generalized Estimating Equation Models for Correlated Data: A Review with Applications:

Political scientists are often called upon to estimate models in which the standard assumption that the data are conditionally independent can be called into question. I review the method of generalized estimating equations (GEE) for dealing with such correlated data. The GEE approach offers a number of advantages to researchers interested in modeling correlated data, including applicability to data in which the outcome variable takes on a wide range of forms. In addition, GEE models allow for substantial flexibility in specifying the correlation structure within cases and offer the potential for valuable substantive insights into the nature of that correlation. Moreover, GEE models are estimable with many currently available software packages, and the interpretation of model estimates is identical to that for commonly used models for uncorrelated data (e.g., logit and probit). I discuss practical issues relating to the use of GEE models and illustrate their usefulness for analyzing correlated data through three applications in political science. mpirical political science is most often interested in estimating the effect of some set of explanatory covariates on an outcome variable of interest. At the same time, in many cases, the data on which we observe the phenomena of interest are likely to be correlated. The most common instances of correlated data are those involving repeated observations over time, either in the form of panel studies or time-series of crosssections.1 Correlated data can also arise in other ways, including dyadic studies (e.g., Oneal and Russett 1997; Hojnacki and Kimball 1998; Huckfeldt, Sprague, and Levine 2000) and examinations of individual decisions in a collegial context, for example, voting decisions in a legislature (e.g., Levitt 1996; Snyder and Groseclose 2000) or a court (e.g., Traut and Emmert 1998). While issues relating to temporal correlation have recently received a good deal of attention among political scientists (Beck and Katz 1995; Beck, Katz, and Tucker 1998; Box-Steffensmeier and Jones 1997; see also Stimson 1985), the latter form of correlation often goes unaddressed. Moreover, few of the methods for dealing with correlation over time are appropriate for use with data where the interdependence is not of a temporal nature, and fewer still are capable of dealing with noncontinuous dependent variables (for example, dichotomous variables or event counts). In this article, I review a general method for dealing with correlated data: the technique of generalized estimating equations (GEEs).2 GEEs of-

Duration Models and Proportional Hazards in Political Science

period. In recent years political scientists have increasingly adopted a wide range of techniques for modeling duration data. But while the use of duration models by political scientists has increased dramatically, a concomitant examination of the modeling assumptions underlying these methods has not accompanied this growth. An important characteristic of most of these models is the assumption that the relative hazards over different covariate values are proportional. This consideration is important because, as has been widely shown in the statistics literature, estimation of proportional hazards models when hazards are, in fact, nonproportional can result in biased estimates, incorrect standard errors, and faulty inferences about the substantive impact of independent variables (e.g., Kalbfleisch and Prentice 1980; Schemper 1992; Collett 1994; Klein and Moeschberger 1997). But while the proportional hazards assumption is central to the proper estimation and interpretation of these models, it has received little attention by political scientists modeling duration data. This is unfortunate because, absent explicit examinations of the validity of these assumptions, the reader is often unable to infer whether or not the assumption holds for any particular analysis. This difficulty is exacerbated by the fact that, in many circumstances, both substantive theories and empirical data suggest that the assumption itself is of dubious accuracy. In fact, it is often the case that many substantively interesting hypotheses imply time-dependence or other forms of nonproportionality in the conditional probability of failure. Thus, it is important that, as political scientists begin to use these models more often in applied research, they take care to examine the extent to which this assumption is consistent with their data and to be aware of methods for analyzing duration data in which hazards are not proportional.

Duration Models for Repeated Events

An important feature of most political events is their repeatability: nearly all political events reoccur, and theories of learning, path dependence, and institutional change all suggest that later events will differ from earlier ones. Yet, most models for event history analysis fail to account for repeated events, a fact that can yield misleading results in practice. We present a class of duration models for analyzing repeated events, discuss their properties and implementation, and offer recommendations for their use by applied researchers. We illustrate these methods through an application to widely used data on international conflict.

Nonproportional Hazards and Event History Analysis in International Relations

Event history models have become a dominant method of analysis in the study of international relations. Conventional event history models, however, retain the assumption that the effects of the covariates remain proportional to each other throughout the duration of the subjects phase. Nonproportional hazard (NPH) models are used, which allow for the effects of covariates to vary over time. These models are then applied to three previously established data sets on the duration of postwar peace, civil wars, and alliances. Results show that NPH analysis is a useful method for testing new hypotheses, as well as removing possible sources of bias from existing analyses.

The Strategic Timing of Position Taking in Congress: A Study of the North American Free Trade Agreement

A critical element of decision making is the timing of choices political actors make; often when a decision is made is as critical as the decision itself. We posit a dynamic model of strategic position announcement based on signaling theories of legislative politics. We suggest that members who receive clear signals from constituents, interest groups, and policy leaders will announce their positions earlier. Those with conflicting signals will seek more information, delaying their announcement. We test several expectations by examining data on when members of the House of Representatives announced their positions on the North American Free Trade Agreement. We also contrast the timing model with a vote model, and find that there are meaningful differences between the factors influencing the timing of position announcements and vote choice. Our research allows analysts to interpret the process leading up to the House action and the end state of that process.

Comparing GEE and Robust Standard Errors for Conditionally Dependent Data

In recent years political scientists have become increasingly sensitive to questions of conditional dependence in their data. I outline and compare two general, widely-used approaches for addressing such dependence—robust variance estimators and generalized estimating equations (GEEs)—using data on votes in Supreme Court search and seizure decisions between 1963 and 1981. The results make clear that choices about the unit on which data are grouped, i.e., clustered, are typically of far greater significance than are decisions about which type estimator is used.

Violent Conflict and the Spread of HIV/AIDS in Africa

It has been widely speculated that violent conflict acts as a key contributor to the transmission of human immunodeficiency virus (HIV). Yet to date no empirical examination of the conflict-HIV relationship has been conducted. Drawing on work in political science and public health, we set forth a theoretical framework for understanding this potential relationship and go on to present data on the spatio-temporal dispersion of HIV/AIDS in 43 African countries during the period from 1997 to 2005. We then assess the association between domestic and international conflict and levels of HIV/AIDS infection while controlling for a range of other influential factors. Our analyses support a clear positive relationship between both international and domestic conflict and climbing HIV/AIDS prevalence, as well as significant palliative effects for education and economic development on the incidence of HIV/AIDS.

Explaining the Incidence and Timing of Congressional Responses to the U.S. Supreme Court

Sparked by interest in game-theoretic representations of the separation of powers, empirical work examining congressional overrides of Supreme Court statutory decisions has burgeoned in recent years. Much of this work has been hampered, however, by the relative rarity of such events; as has long been noted, congressional attention to the Court is limited, and most Court decisions represent the last word on statutory interpretation. With this fact foremost in our minds, we examine empirically a number of theories regarding such reversals. By adopting an approach that allows us to separate the factors that lead to the event itself (that is, the presence or absence of an override in a particular case) from those that influence the timing of the event, we find that case-specific factors are an important influence in the incidence of overrides, whereas Congress- and Court-specific political influences dominate the timing at which those overrides occur. By separating the incidence and timing of overrides, our study yields a more accurate and nuanced understanding of this aspect of the separation-of-powers system.

Estimating between‐ and within‐cluster covariate effects, with an application to models of international disputes

Students of international politics often use data in which the covariates vary both within and across units of observation. This is particularly true for dyadic data, which has come to dominate quantitative studies of international conflict, but is also a concern in any work involving a time‐series cross‐sectional component. Standard regression methods treat both types of covariates as equivalent with respect to their influence on the dependent variable, ignoring possible differences between cross‐dyad and within‐dyad effects. Here, I discuss the potential pitfalls of this approach, and show how between‐ and within‐dyad effects can be separated and estimated. I then illustrate the approach in the context of a logistic regression, using data on international disputes.

U.S. government litigation strategies in the federal appellate courts

I examine the decisions of the Department of Justice appellate sections and the Office of the Solicitor General to appeal unfavorable U.S. court of appeals decisions to which the federal government is a party during 1993 and 1994. I hypothesize that factors relating to the cost, reviewability and likelihood of victory in the appeal will be influential in the governments decision, and that the influence of each of these types of factors will vary depending upon the actor making the decision. Multivariate analysis supports these hypotheses, indicating that those factors which have been shown to influence both the Courts decision to grant certiorari and its decisions on the merits also operate in the governments decision to bring an appeal. Overall, my research suggests that the case selection process has a substantial influence on the success of the United States in the federal appellate courts.