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Stochastic Dependence in Competing Risks Gordon, Sanford C. Uploaded 09-05-2001 Keywords Competing risks duration models survival models event history random effects frailty models unobserved heterogeneity Monte Carlo simulation Congress legislative position-taking cabinet survival numeric integration Markov Chain Monte Carlo Abstract The term "Competing Risks" describes duration models in which spells may terminate via multiple outcomes: The term of a cabinet, for example, may end with or without an election; wars persist until the loss or victory of the aggressor. Analysts typically assume stochastic independence among risks, the duration modeling equivalent of independence of irrelevant alternatives. However, many political examples violate this assumption. I review competing risks as a latent variables approach. After discussing methods for modeling dependence that place restrictions on the nature of association, I introduce a parametric generalized dependent risks model in which inter-risk correlation may be estimated and its significance tested. The method employs risk-specific random effects drawn from a multivariate normal distribution. Estimation is conducted using numerical methods and/or Bayesian simulation. Monte Carlo simulation reveals desirable large sample properties of the estimator. Finally, I examine two applications using data on cabinet survival and legislative position taking.

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Mixed Logit Models in Political Science Glasgow, Garrett Uploaded 07-08-2001 Keywords mixed logit discrete choice heterogeneity Abstract Mixed logit (MXL) is a general discrete choice model that is applicable to a wide range of political science problems. Mixed logit assumes the unobserved portions of utility are a mixture of an IID extreme value term and another multivariate distribution selected by the researcher. This general specification allows MXL to avoid imposing the independence of irrelevant alternatives (IIA) property on the choice probabilities. Further, and more importantly, MXL is a flexible tool for examining heterogeneity in individual behavior through random-coefficients specifications. Three empirical examples are presented. Two are drawn from studies of voting behavior. The first uses data from the 1987 British general election and examines heterogeneity in the impact of social class on voting, and the second uses data from the 1992 U.S. presidential election and examines heterogeneity in the impact of union membership on voting. A third example examines heterogeneity in the factors that lead to various Congressional career decisions. These empirical examples demonstrate the utility of mixed logit in political science research. This paper has both a methodological and substantive contribution for political science. Methodologically, it expands the tool set available to researchers for studying various phenomena in political science. More importantly, this paper contributes substantively by allowing for more realistic models of individual behavior. Most models currently used in political science assume the independent variables have a homogeneous effect on the dependent variable. This assumption is usually made to keep models tractable, even though few believe it is an accurate description of behavior. MXL is a tractable way to relax this assumption and study heterogeneity in a variety of settings.

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Bayesian Inference for Heterogeneous Event Counts Martin, Andrew D. Uploaded 04-20-2000 Keywords hierarchical models Poisson event count heterogeneity Abstract This paper presents a handful of Bayesian tools one can use to model heterogeneous event counts. In many political science applications we are interested in modeling the number of times a particular event takes place. While models for event count cross-sections are now widely used in political science (King, 1988, 1989b), little has been written about how to model counts when contextual factors introduce heterogeneity. I begin with a discussion of Bayesian cross-sectional count models and introduce an alternative model for counts with overdispersion. To illustrate the Bayesian framework, I model event counts of the number of discharge petitions from the 61st to the 105th House, and the number of women's rights bills cosponsored by each member in the 92nd House. I then generalize the model to allow for contextual heterogeneity and posit a hierarchical Poisson regression model, fitting this model to the number of women rights cosponsorships for each member of the 83rd to 102nd House. I demonstrate the advantages of this approach over pooled and independent Poisson regressions. The hierarchical model allows one to explicitly model contextual factors and test alternative contextual explanations. Additionally, I discuss software one can use to easily implement these models with little start-up cost.

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Heterogeneity in the Impact of Issues on Vote Choice Glasgow, Garrett Uploaded 04-18-1999 Keywords random parameters logit heterogeneity issue salience Abstract There is a great deal of diversity in the issues than members of the American electorate are concerned with. It seems logical that these different concerns will lead voters to evaluate political candidates in different ways when voting. Unfortunately, the models currently employed by political scientists ignore the possibility of heterogeneity in the weights that individuals place on issues when voting. In order to create a tractable model of vote choice, most researchers assume that the weights placed on issues are homogeneous across voters. Estimating such a model tells us if an issue was salient to the electorate on average, but gives us no information about heterogeneity in the use of the issue. Allowing for heterogeneity in issue weights allows for a much more complete picture of the impact of issues on vote choice. I assume that issue weights are distributed among voters by some known probability distribution, and estimate the parameters of that distribution. This assumption leads to random parameters logit. I present the results of a random parameters logit model for the 1996 presidential election, and compare these results to those from a conditional logit model with the homogeneity assumption. I show that random parameters logit contains all of the information that models that assume homogeneity do, plus I uncover evidence of heterogeneity in the weights placed on issues by voters.

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Modeling Heterogeneity in Duration Models Box-Steffensmeier, Janet M. Zorn, Christopher Uploaded 07-11-1999 Keywords heterogeneity survival models split-population variance correction frailty random effects Abstract As increasing numbers of political scientists have turned to event history models to analyze duration data, there has been growing awareness of the issue of heterogeneity: instances in which subpopulations in the data vary in ways not captured by the systematic components of standard duration models. We discuss the general issue of heterogeneity, and offer techniques for dealing with it under various conditions. One special case of heterogeneity arises when the population under study consists of one or more subpopulations which will never experience the event of interest. Split-population, or "cure" models, account for this heterogeneity by permitting separate analysis of the determinants of whether an event will occur and the timing of that event, using mixture distributions. We use the split-population model to reveal additional insights into the strategies of political action committees' allocation decisions, and compare split-population and standard duration models of Congressional responses to Supreme Court decisions. We then go on to explore the general issue of heterogeneity in survival data by considering two broad classes of models for dealing with the lack of independence among failure times: variance correction models and "frailty" (or random effects) duration models. The former address heterogeneity by adjusting the variance matrix of the estimates to allow for correct inference in the presence of that heterogeneity, while the latter approach treats heterogeneity as an unobservable, random, multiplicative factor acting on the baseline hazard function. Both types of models allow us to deal with heterogeneity that results, for example, from correlation at multiple levels of data, or from repeated events within units of analysis. We illustrate these models using data on international conflicts. In sum, we explore the issue of heterogeneity in event history models from a variety of perspectives, using a host of examples from contemporary political science. Our techniques and findings will therefore be of substantial interest to both political methodologists and others engaged in empirical work across a range of subfields.

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Poisson-Normal Dynamic Generalized Linear Mixed Models of U.S. House Campaign Contributions Mebane, Walter R. Wand, Jonathan Uploaded 07-11-1999 Keywords GLMM MCEM count model heterogeneity FEC campaign contributions campaign finance U.S. House of Representatives 1984 election Abstract We develop generalized linear mixed models to analyze itemized contributions to U.S. House campaigns. Our basic model is a system of Poisson processes that have means that are log-linear functions of normally distributed random effects. Our model permits multiple random effects, including serially correlated effects. The mixed model specification involves an integration over the random effects that is analytically intractable. When there is only one, serially independent random effect, the model may be estimated using quadrature to evaluate the integral. With multiple random effects, quadrature is infeasible but the model may be estimated using the Monte Carlo EM (MCEM) algorithm proposed by McCulloch (1997). We illustrate these various estimation methods. The system we analyze includes contributions to Democratic and Republican candidates from different sources, including individuals and PACs. We estimate dynamic effects both within and across contributions series. The cross-series dynamics measure how contributions to one candidate react to contributions to the other. The cross-series dynamics also measure how contributions to a candidate from one source can mobilize contributions from other sources. We use a combination of observed variables and random effects to test the hypothesis of dynamic mobilization against several hypotheses that imply constant differences between candidates and between districts. One such hypothesis is that some candidates received persistently higher contributions from all sources because of PAC endorsements. Another is that some candidates are simply better at raising money than others. We also test how national expectations about presidential election outcomes affect contributions. We apply our model to itemized contributions data for open seat races in the 1984 election.

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Candidate Viability and Voter Learning in the Presidential Nomination Process Paolino, Philip Uploaded 08-30-1999 Keywords beta distribution maximum likelihood heterogeneity Bayesian Abstract Candidates' viability and momentum are important features of the presidential nomination process in the United States, and much work has examined how both influence the outcome of the nomination campaign (e.g. Aldrich 1980a, Aldrich 1980b, Bartels 1988, Brady and Johnston 1987) Previous treatments, however, have focused upon candidates' expectations of winning or losing the nomination. A critical feature that has been mentioned, but not addressed directly is the volatility of these expectations. In this paper, I use a view of viability and momentum that considers both expectations and the variance of the public's perceptions about candidates' viability which allows us to examine how voters use new information to update their beliefs about both elements of candidates' viability and provides a basis for assessing candidates' potential momentum.

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GEE Models of Judicial Behavior Zorn, Christopher Uploaded 04-02-1998 Keywords generalized estimating equations time-series cross-sectional data temporal dependence heterogeneity judicial decision making Abstract The assumption of independent observations in judicial decision making flies in the face of our theoretical understanding of the topic. In particular, two characteristics of judicial decision making on collegial courts introduce heterogeneity into successive decisions: individual variation in the extent to which different jurists maintain consistency in their voting behavior over time, and the ability of one judge or justice to influence another in their decisions. This paper addresses these issues by framing judicial behavior in a time-series cross-section context and using the recently developed technique of generalized estimating equations (GEE) to estimate models of that behavior. Because the GEE approach allows for flexible estimation of the conditional correlation matrix within cross-sectional observations, it permits the researcher to explicitly model interjustice influence or over-time dependence in judicial decisions. I utilize this approach to examine two issues in judicial decision making: latent interjustice influence in civil rights and liberties cases during the Burger Court, and temporal consistency in Supreme Court voting in habeas corpus decisions in the postwar era. GEE estimators are shown to be comparable to more conventional pooled and TSCS techniques in estimating variable effects, but have the additional benefit of providing empirical estimates of time- and panel- based heterogeneity in judicial behavior.

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Cosponsorship Coalitions in the U.S. House of Representatives Grant, J. Tobin Pellegrini, Pasquale (Pat) A. Uploaded 04-22-1998 Keywords clustering coalitions cosponsorship duration models hazard models heterogeneity spatial models Abstract urrent theories and methods for studying of cosponsorship assume that the decision to cosponsor is identical to decision to vote. In this paper we develop a new theory of cosponsorship that identifies where along the ideological spectrum cosponsors of a bill are more likely to be. Moreover, we predict that members with organizational ties to the sponsor are more likely to cosponsor than other members. To test this theory, we employ a spatial duration model. This method has recently been used by geographers to estimate areas that are more likely to experience an "event." Using this technique permits a statistical test that supports our substantive hypotheses that cosponsorship coalitions are shaped by the characteristics of the location of the bill, the shared ties to the sponsor, and the policy area. In addition, more active sponsors are associated with wider and less clustered coalitions. These findings demonstrate that theories of the voting decision are not applicable to cosponsorship.

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The Impact of Political Campaigns on the Effects of Political Sophistication Fournier, Patrick P. Uploaded 09-18-1997 Keywords campaign sophistication information heterogeneity individual deviation aggregate deviation Canadian politics Abstract [none provided]

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Heterogeneity and Individual Party Identification Box-Steffensmeier, Janet M. Smith, Renee M. Uploaded 05-01-1997 Keywords heterogeneity party identification macropartisanship panel data Wiley-Wiley Monte Carlo beta-logistic Markov Abstract Box-Steffensmeier and Smith (1996) suggest that heterogeneity in individual-level party identification accounts for aggregate dynamics in macropartisanship. Wiley-Wiley estimates of partisan persistence suggesting a very high degree of individual-level partisan persistence have been made under the assumption of no heterogeneity. Stratifying panel data by subgroups based on information, interest, and age, shows some heterogeneity in persistence even when the Wiley-Wiley estimator is used. Analytical and Monte Carlo results show, however, that the Wiley-Wiley estimator is biased upward when heterogeneity is present. Given these problems, we estimate a beta-logistic model of heterogeneity and persistence in individual-level party identification and show (a) heterogeneity in the probabilities of persistent response does exist and (b) a portion of that heterogeneity is systematically explained by interest in political campaigns in the 1990-91-92 ANES panel three-wave panel. Our estimates indicate Markov models assuming true state dependence may not be needed. Further, we find that our estimate of one of the parameters of the beta distribution is consistent with the estimate of that parameter that would be derived from our previous aggregate-level analysis.

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Testing the Pooling Assumption with Cross-Sectional Time Series Data: A Proposal and an Assesment with Simulation Experiments Stanig, Piero Uploaded 07-17-2005 Keywords Cross-Sectional Time Series Data heterogeneity of coefficients Abstract I propose to use the loss of fit of the cross-validated predictions relative to the fit of the predictions from a pooled regression to test the assumption of constant betas across countries in a CSTS setting. The performance of this measure is a) evaluated in several simulation experiments that reproduce research situations common in comparative politics, and b) compared to the “cross-validated standard error of the regression”, proposed by Franzese(2002). I show that the measure I propose depends much less on the stochastic component in the DGP, and is better able to detect the country-specificity of the betas. I calculate the critical values that can be used to test the pooling assumption in some typical comparative politics CSTS situations. Finally, to evaluate the behavior of the measure with an actual dataset, I replicate the results of Alvarez et al. (1991) as replicated in Beck et al. (1993), calculate the proposed measure, and show that the pooling assumption does not seem to be inappropriate for the model they estimate.

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Heterogeneity in Supreme Court Decision-Making: How Case-Level Factors Alter Preference-Based Behavior Bartels, Brandon Uploaded 07-19-2005 Keywords Supreme Court decision-making multilevel modeling heterogeneity Abstract Many theoretical perspectives of Supreme Court decision-making, most notably the attitudinal model, assume that justices’ policy preferences exhibit a uniform impact on their decisions across a wide variety of situations. I argue that there exists meaningful heterogeneity in the impact of policy preferences that can be explained theoretically and tested empirically. Adopting social psychological insights from theories of the attitude-behavior relationship, I develop a theoretical framework specifying the mechanisms--attitude strength and accountability--that explain variation in the preference-behavior relationship for justices. Case-level factors associated with each mechanism are hypothesized to moderate the impact of preferences. To test the hypotheses, I use a multilevel (hierarchical) modeling framework and conceive of Supreme Court voting data from the 1994-2002 terms as a two-level hierarchy: justices’ choices nested within cases. Estimates from a random coefficient model indicate that case-level variables associated with both attitude strength and accountability systematically explain variation in the preference-behavior relationship. Using an average partial effects post-estimation procedure, I present in-depth substantive interpretations of the results that highlight the compelling ways in which these case-level factors alter the nature of preference-based behavior. In addition to providing important substantive conclusions about Supreme Court decision-making, the paper also illustrates how a multilevel modeling framework is well-qualified to test heterogeneity-related hypotheses in social and behaviorial processes.

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Detecting heterogeneous treatment effects in large-scale experiments using Bayesian Additive Regression Trees Green, Donald Kern, Holger Uploaded 07-16-2010 Keywords causal inference heterogeneity ATE ensemble methods BART tree models MCMC Abstract We present a method that largely automates the search for systematic treatment effect heterogeneity in large-scale experiments. We introduce an estimator recently proposed in the statistical learning literature, Bayesian Additive Regression Trees (BART), to model treatment effects that vary as a function of covariates. BART has two important advantages over commonly employed parametric modeling strategies: it automates the search for treatment-covariate interactions and models them in a very flexible manner. To increase the reliability and credibility of the resulting conditional average treatment effect estimates, we suggest the use of a split sample analysis, which randomly divides the data into two equally-sized parts. The first part is used to search for systematic treatment effect heterogeneity; the second part is used to confirm the results. This approach permits a relatively unstructured exploration of systematic treatment effect heterogeneity while avoiding the pitfalls of data dredging and multiple comparisons. We illustrate the value of our approach by offering two empirical examples, a survey experiment on Americans' support for social welfare spending and a voter mobilization field experiment. In both applications, our approach provides robust insights into the nature and extent of systematic treatment effect heterogeneity.

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A Monte Carlo Analysis for Recurrent Events Data Box-Steffensmeier, Janet M. De Boef, Suzanna Uploaded 07-13-2002 Keywords survival analysis repeated events heterogeneity event dependence simulations Abstract Scholars have long known that multiple events data, which occur when subjects experience more than one event, cause a problem when analyzed without taking into consideration the correlation among the events. In particular there has not been a solution about the best way to model the common occurrence of repeated events, where the subject experiences the same type of event more than once. Many event history model variations based on the Cox proportional hazards model have been proposed for the analysis of repeated events and it is well known that these models give different results (Clayton 1994; Lin 1994; Gao and Zhou 1997; Klein and Moeschberger 1997; Therneau and Hamilton 1997; Wei and Glidden 1997; Box-Steffensmeier and Zorn 1999; Hosmer and Lemeshow 1999; Kelly and Lim 2000). Our paper focuses on the two main alternatives for modeling repeated events data, variance corrected and frailty (also referred to as random effects) approaches, and examines the consequences these different choices have for understanding the interrelationship between dynamic processes in multivariate models, which will be useful across disciplines. Within political science, the statistical work resulting from this project will help resolve some important theoretical and policy debates about political dynamics, such as the liberal peace, by commenting on the reliability of the different modeling strategies used to test those theories and applying those models. Specifically, the results of the project will help assess whether one of the two primary approaches is better able to account for within-subject correlation. We evaluate the various modeling strategies using Monte Carlo evidence to determine whether and under what conditions alternative modeling strategies for repeated events are appropriate. The question as to the best modeling strategy for repeated events data is an important one. Our understanding of political processes, as in all studies, depends on the quality of the inferences we can draw from our models. There is currently little guidance about which approach or model is appropriate and so, not surprisingly, we see analysts unsure of the best way to analyze their data. Given the dramatic substantive differences that result from using the different models and approaches, this is a problem that will be of interest across research communities.

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Heterogeneity in Discrete Choice Models Glasgow, Garrett Uploaded 12-12-2001 Keywords heterogeneity discrete choice logit probit ambivalence Abstract Nearly all empirical studies of individual behavior in political science have sought to estimate the mean relationship between some variables of interest. While such studies are vital for determining aggregate relationships between variables of interest, they are an incomplete picture of individual behavior. In particular, we generally do not pay attention to the possibility of heterogeneity, or individual-level variation in the relationships we estimate. Ignoring heterogeneity in our models means we are ignoring valuable information about individual behavior. This paper demonstrates that examining heterogeneity in discrete choice models is both important substantively and feasible methodologically. Possible sources of heterogeneity are discussed, and it is shown that these sources of heterogeneity are observationally equivalent in most cases, meaning it is generally not possible to determine the source of heterogeneity in our empirical models. Several empirical models for examining heterogeneity are described. An empirical example studying heterogeneity in union voting in the 1992 US presidential election demonstrates the