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A Random Effects Approach to Legislative Ideal Point Estimation Bailey, Michael Uploaded 04-21-1998 Keywords ideal points random effects models Bayesian estimation em algorithm Abstract Conventionally, scholars use either standard probit/logit techniques or fixed-effect methods to estimate legislative ideal points. However, these methods are unsatisfactory when a limited number of votes are available: standard probit/logit methods are poorly equipped to handle multiple votes and fixed-effect models disregard serious ``incidental parameter'' problems. In this paper I present an alternative approach that moves beyond single-vote probit/logit analysis without requiring the large number of votes needed for fixed-effects models. The method is based on a random effects, panel logit framework that models ideal points as stochastic functions of legislator characteristics. Monte Carlo results and an application to trade politics demonstrate the practical usefulness of the method.

2

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Do Voters Learn from Presidential Election Campaigns? Alvarez, R. Michael Glasgow, Garrett Uploaded 10-27-1997 Keywords random effects panel models content analysis presidential election campaigns voter decisionmaking voter learning Abstract We present a model of voter campaign learning which is based on Bayesian learning models. This model assumes voters are imperfectly informed and that they incorporate new information into their existing perceptions about candidate issue positions in a systematic manner. Additional information made available to voters about candidate issue positions during the course of a political campaign will lead voters to have more precise perceptions of the issue positions of the candidates involved. We use panel survey data from the 1976 and 1980 presidental elections, combined with content analyses of the media during these same elections. Our primary analysis is conducted using random effects panel models. We find that during each of these campaigns many voters became better informed about the positions of candidates on many issues and that these changes in voter information are directly related to the information flow during each presidential campaign.

3

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Voter Turnout and the Life Cycle: A Latent Growth Curve Analysis Plutzer, Eric Uploaded 04-09-1997 Keywords turnout life-cycle random effects model HLM latent growth models Abstract The distinctive relationship between age and voter turnout has intrigued students of electoral behavior since at least the early 1960s. Nevertheless, political scientists actually know little about how individuals acquire the habit of voting during young adulthood. Moreover, previous speculations and explanations are all questionable because they are based on data and models that are inappropriate for what is essentially a developmental process. Problems include confounding age with generational effects, assumptions of reversibility of gains in participation from key life events, and a failure account for the fact that an individual's probability of turnout at any particular age is a function of two distinct latent variables: their turnout rate in the very first elections, and their subsequent rate of increase. Theory construction is muddled because these two variables are negatively correlated and have different predictors. This study uses longitudinal data covering young voters over their first four presidential elections and uses latent growth curve models -- a special case of multi-level or Hierarchical Linear Models which are finding wide applicability in the social sciences. Given appropriate data, this approach permits statistical models that better correspond to life-cycle hypotheses. The findings clarify the role of parental influence, marriage and parenthood, while raising questions about the costs of mobility.

4

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Problems with and Solutions for Two-dimensional Models of Continuous Dependent Variables Goodrich, Ben Uploaded 05-24-2005 Keywords TSCS fixed effects random effects between estimator pooled OLS Abstract This paper addresses hierarchical models with continuous dependent variables, such as time-series-cross-section models. Building on the argument in Zorn (2001), the main point of this paper is that the pooled OLS estimator is deeply flawed – especially for time-series-cross-section data – but for reasons that have not explicitly been raised in previous papers. The pooled OLS estimator, the within-estimator, the between-estimator, and the random effects estimator can be seen as special cases of the fractionally pooled estimator presented in Bartels (1996), which allows all of these estimators to be evaluated in a common framework. Taking bias and efficiency into account, using both the within-estimator and the between-estimator is likely to be the best estimation strategy for the vast majority of applications in political science.

5

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Fitting Multilevel Models When Predictors and Group Effects Correlate Bafumi, Joseph Uploaded 04-27-2006 Keywords Multilevel models random effects fixed effects unit effects group effects Gauss-Markov Abstract Random effects models (that is, regressions with varying intercepts that are modeled with error) are avoided by some social scientists because of potential issues with bias and uncertainty estimates. Particularly, when one or more predictors correlate with the group or unit effects, a key Gauss-Markov assumption is violated and estimates are compromised. However, this problem can easily be solved by including the average of each individual-level predictors in the group-level regression. We explain the solution, demonstrate its effectiveness using simulations, show how it can be applied in some commonly-used statistical software, and discuss its potential for substantive modeling.

6

Paper

The Future of Partisan Symmetry as a Judicial Test for Partisan Gerrymandering after LULAC v. Perry Grofman, Bernard King, Gary Uploaded 08-04-2006 Keywords Gerrymandering redistricting random effects partisan symmetry Abstract While the Supreme Court in Bandemer v. Davis found partisan gerrymandering to be justiciable, no challenged redistricting plan in the subsequent 20 years has been held unconstitutional on partisan grounds. Then, in Vieth v. Jubilerer, five justices concluded that some standard might be adopted in a future case, if a manageable rule could be found. When gerrymandering next came before the Court, in LULAC v. Perry, we along with our colleagues filed an Amicus Brief (King et al., 2005), proposing that a test be based in part on the partisan symmetry standard. Although the issue was not resolved, our proposal was discussed and positively evaluated in three of the opinions, including the plurality judgment, and for the first time for any proposal the Court gave a clear indication that a future legal test for partisan gerrymandering will likely include partisan symmetry. A majority of Justices now appear to endorse the view that the measurement of partisan symmetry may be used in partisan gerrymandering claims as “a helpful (though certainly not talismanic) tool” (Justice Stevens, joined by Justice Breyer), provided one recognizes that “asymmetry alone is not a reliable measure of unconstitutional partisanship” and possibly that the standard would be applied only after at least one election has been held under the redistricting plan at issue (Justice Kennedy, joined by Justices Souter and Ginsburg). We use this essay to respond to the request of Justices Souter and Ginsburg that “further attention … be devoted to the administrability of such a criterion at all levels of redistricting and its review.” Building on our previous scholarly work, our Amicus Brief, the observations of these five Justices, and a supporting consensus in the academic literature, we offer here a social science perspective on the conceptualization and measurement of partisan gerrymandering and the development of relevant legal rules based on what is effectively the Supreme Court’s open invitation to lower courts to revisit these issues in the light of LULAC v. Perry. (Forthcoming, January 2007 Election Law Journal. Comments welcome.)

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Paper

Beyond "Fixed Versus Random Effects": A Framework for Improving Substantive and Statistical Analysis of Panel, TSCS, and Multilevel Data Bartels, Brandon Uploaded 09-30-2008 Keywords random effects fixed effects pooling time-series cross-sectional data panel data multilevel modeling Abstract Researchers analyzing panel, time-series cross-sectional, and multilevel data often choose between a random effects, fixed effects, or complete pooling modeling approach. While pros and cons exist for each approach, I contend that some core issues concerning clustered data continue to be ignored. I present a unified and simple modeling framework for analyzing clustered data that solves many of the substantive and statistical problems inherent in extant approaches. The approach: (1) solves the substantive interpretation problems associated with cluster confounding, which occurs when one assumes that within- and between-cluster effects are equal; (2) accounts for cluster-level unobserved heterogeneity via a random intercept model; (3) satisfies the controversial statistical assumption that level-1 variables be uncorrelated with the random effects term; (4) allows for the inclusion of level-2 variables; and (5) allows for statistical tests of cluster confounding. I illustrate this approach using three substantive examples: global human rights abuse, oil production for OPEC countries, and Senate voting on Supreme Court nominations. Reexaminations of these data produce refined interpretations of some of the core substantive conclusions.

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Paper

Sampling Schemes for Generalized Linear Dirichlet Random Effects Models Kyung, Minjung Gill, Jeff Casella, George Uploaded 02-18-2009 Keywords generalized linear mixed Dirchlet model Markov chain Monte Carlo Dirichlet process priors for random effects precision parameters Scottish Social Attitudes Survey terrorism targeting Abstract We evaluate MCMC sampling schemes for a variety of link functions in generalized linear models with Dirichlet random effects. We find that models using Dirichlet process priors for the random effects tend to capture information in the data in a nonparametric fashion. In fitting the the Dirichlet process, dealing with the precision parameter has troubled model specifications in the past. Here we find that incorporating this parameter into the MCMC sampling scheme is not only computationally feasible, but also results in a more robust set of estimates, in that they are marginalized-over rather than conditioned-upon. Applications are provided with social science problems in areas where the data can be difficult to model. In all, we find that these models provide superior Bayesian posterior results in theory, simulation, and application.

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Estimation in Dirichlet Random Effects Models Kyung, Minjung Gill, Jeff Casella, George Uploaded 04-28-2009 Keywords generalized linear mixed model Dirichlet process random effects model precision parameter likelihood Gibbs sampling importance sampling probit mixed Dirichlet random effects model Abstract We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distribution, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date. Forthcoming: Annals of Statistics.

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Joint Modeling of Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models Park, Jong Hee Uploaded 07-14-2009 Keywords Bayesian statistics Fixed-effects Hidden Markov models Markov chain Monte Carlo methods Random-effects Reversible jump Markov chain Monte Carlo Abstract Researchers working with panel data sets often face situations where changes in unobserved factors have produced changes in the cross-sectional heterogeneity across time periods. Unfortunately, conventional statistical methods for panel data are based on the assumption that the unobserved cross-sectional heterogeneity is time constant. In this paper, I introduce statistical methods to diagnose and model changes in the unobserved heterogeneity. First, I develop three combinations of a hidden Markov model with panel data models using the Bayesian framework; (1) a baseline hidden Markov panel model with varying fixed effects and varying random effects; (2) a hidden Markov panel model with varying fixed effects; and (3) a hidden Markov panel model with varying intercepts. Second, I present model selection methods to diagnose the dynamic heterogeneity using the marginal likelihood method and the reversible jump Markov chain Monte Carlo method. I illustrate the utility of these methods using two important ongoing political economy debates; the relationship between income inequality and economic growth and the effect of institutions on income inequality.

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Paper

Should I Use Fixed or Random Effects? Clark, Tom Linzer, Drew Uploaded 03-26-2012 Keywords Fixed effects Random effects Panel data TSCS multilevel simulation Abstract Empirical analyses in political science very commonly confront data that are grouped---multiple votes by individual legislators, multiple years in individual states, multiple conflicts during individual years, and so forth. Modeling these data presents a series of potential challenges, of which accounting for differences across the groups is perhaps the most well-known. Two widely-used methods are the use of either "fixed" or "random" effects models. However, how best to choose between these approaches remains unclear in the applied literature. We employ a series of simulation experiments to evaluate the relative performance of fixed and random effects estimators for varying types of datasets. We further investigate the commonly-used Hausman test, and demonstrate that it is neither a necessary nor sufficient statistic for deciding between fixed and random effects. We summarize the results into a typology of datasets to offer practical guidance to the applied researcher.

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Explaining Fixed Effects: Random Effects modelling of Time-Series Cross-Sectional and Panel Data Bell, Andrew Jones, Kelvyn Uploaded 07-13-2012 Keywords Random Effects models Fixed Effects models Random coefficient models Mundlak formulation Fixed effects vector decomposition Hausman test Endogeneity Panel Data Time-Series Cross-Sectional Data Abstract This article challenges Fixed Effects (FE) modelling’s status as the ‘default option’ when using time-series-cross-sectional and panel data. We argue that understanding the difference between within- and between-effects of predictor variables is important when considering what modelling strategy to use. The downside of Random Effects (RE) compared to FE modelling – correlation between lower-level covariates and higher-level residuals - is a case of omitted variable bias, readily solvable using a variant of Mundlak’s (1978a) formulation. Consequently, RE modelling provides everything that FE modelling promises, and more. It allows time-invariant variables to be modelled, more parsimoniously than Plümper and Troeger’s (2007) suggested method. It is also readily extendable to Random Coefficients Models, allowing reliable, differential effects of variables without heavy parameterisation, the use of cross-level interactions between time-variant and invariant variables, and the modelling of complex variance functions. We are arguing not simply for technical solutions to endogeneity, but for the substantive importance of modelling context, and RE models’ ability to do so. Two empirical examples show that failing to do this can lead to misleading results. This paper is distinctive in stressing the substantive interpretations of within- and between-effects. This has implications beyond political science, to all datasets with multilevel structures.

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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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Sweeping fewer things under the rug: tis often (usually?) better to model than be robust Beck, Nathaniel Uploaded 07-16-2012 Keywords Cluster Robust Standard Errors Moulton Problem Time Series Cross Section Data Difference in Difference Random Effects Abstract The use of ``robust'' standard errors is now commonplace in political science. This paper considers one such type of errors, those that are robust to clustering of the data. While these give accurate estimates of parameter variability, we often can do better by direct modeling of the clustering process; such modeling can give insight into important sources of cluster effects. Applications are to grouped data with group level variables, difference in difference designs and time-series--cross-section data. Analysts should always ask whether clustering can be no more than an estimation nuisance before simply resorting to cluster robust standard errors.

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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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Coordination, Moderation and Institutional Balancing in American House Elections at Midterm Mebane, Walter R. Wand, Jonathan Uploaded 09-02-1999 Keywords campaign finance itemized contributions congressional elections generalized linear mixed model Monte Carlo EM random effects conditional compound Poisson process Abstract We use Federal Election Commission itemized contributions data from 1984 to estimate a model of campaign contributions in U.S. House elections. The model is a dynamic system of conditional compound Poisson processes in which there are contributions from both individuals and political action committees (PACs). The model includes random effects to allow for unobserved heterogeneity among districts and candidates. The dynamic effects measure how contributions to one candidate react to contributions to other candidates, as well as how contributions from individuals interact with contributions from PACs. We test the hypothesis that some candidates received higher contributions because of PAC endorsements. We also test whether national expectations about presidential election outcomes affect contributions to House candidates, as predicted by a policy moderating model. We use a Monte Carlo EM algorithm to optimize the likelihood of the model in specifications that include more than one random effect.

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Paper

A Panel Probit Analysis of Campaign Contributions and Roll Call Votes Wawro, Gregory Uploaded 09-07-1999 Keywords campaign finance panel data methods logit probit random effects GMM estimators Abstract Political scientists have long been concerned with the effects of campaign contributions on roll call voting. However, methodological problems have hampered attempts to assess the degree to which contributions affect voting. One of the key problems is that it is difficult to untangle the effect of contributions from the effect of a member's predisposition to vote one way or another. That is, political action committees (PACs) contribute to members of Congress who are likely to vote the way the PACs favor even in the absence of contributions. A PAC donation to a friendly member might be misconstrued as causing a member to vote a particular way, when in reality the member would have voted that way to begin with. It is therefore crucial to account for a member's propensity to vote in a particular way in order to assess the influence of contributions. One way that studies have done this is to use ideological ratings developed by interest groups. This approach is problematic, however, because the ratings are built from roll call votes and thus will introduce bias if campaign contributions affect the votes used to compute the ratings. In order to circumvent the problem of accounting for voting predispositions, I use panel data methods which, unfortunately, have seen almost no application in political science. These methods enable us to account for individual specific effects which are difficult or impossible to measure, such as the predisposition to vote for or against a particular type of legislation. To employ these methods, I build panels of roll call votes on legislation that business and labor groups have indicated are important for their interests. Using panel data estimators, I determine the effects of contributions from corporate and labor PACs on the probability of voting ``aye'' or ``nay'', while accounting for members' propensities to vote in particular directions. I find that contributions have minimal to no effects on roll call votes, while short-term factors including monthly unemployment and support for the president in the district have substantial effects.

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Poster

Political Regimes and Infant Death: Democratization and Its Consequences for Infant Mortality, 1970-2008. Ramos, Antonio Pedro Uploaded 04-10-2013 Keywords child mortality democratization longitudinal models random effects models bent lines Abstract In this study, I investigate the causal linkage between political regimes and health outcomes over 180 countries between 1970 and 2010. While there are a number of previous empirical studies on this topic, the results of those studies are mixed and even contradictory. Missing data and measurement error present a major challenge. The main outcome of interest---child mortality--was until very recently poorly measured or unmeasured for many countries, specially for dictatorships and low-income countries. A lack of comparable measures of political regimes across time periods and countries also contributes to the contradictory findings in the existing literature. Finally, new statistical techniques that capture the important over-time dynamics that we expect to find in the translation of regime type into health outcomes have not previously been applied. Thus, though there are many examples of wealthy democracies with low infant mortality and high infant mortality countries are disproportionally autocratic, it remains unclear whether regime type causes lower levels of child mortality. Recently a group of health scholars compiled a high resolution data set based on 16,174 measurements of mortality rate of children younger than 5 years old for 187 countries from 1970 to 2009. There measurements are based upon information from all available sources, including vital registration systems, summary birth histories in censuses and surveys, and complete birth histories ([CITE]). I revisit the connection between regime type and infant mortality using this data set and flexible Bayesian statistical techniques that are specially tailored for the problem. To gain greater leverage on the causal effect of political regime on health outcomes, I focus on democratization episodes occurring since 1970. I present hierarchical longitudinal models tracking over-time changes in mean child mortality and investigate whether democratization episodes are followed by systematics changes from previous trend in infant mortality. I also apply matching techniques to compare changes in infant mortality following democratization episodes to change in infant mortality in similar countries which did not democratized during the same period. I find that there is little if any effect of democracy on health outcomes.