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Strategic Interaction and Interstate Crises: A Fixed-Effects Bayesian Quantal Response Estimator for Incomplete Information Games Esarey, Justin Mukherjee, Subhanan Moore, Will Uploaded 07-12-2007 Keywords fixed effects quantal response crisis bargaining EITM Abstract Two strategies have been laid out by a growing literature on how to properly test the hypotheses implied by a theory of strategic interaction. The first strategy focuses on conventional comparative statics and the proper specification of standard statistical models (OLS, logit or probit). The second strategy requires deriving a novel likelihood function directly from the model or theory and estimating the parameters with maximum likelihood or Bayesian methods. Both approaches have largely limited their attention to games of perfect information, though many important phenomena are studied using games of incomplete information. This study develops a statistical model for incomplete information games that we term the Fixed Effects Bayesian Quantal Response Model. Our FE-BQRE model, which lies in the domain of the second strategy, offers three advantages over existing efforts: it directly incorporates (i) Bayesian updating and (ii) signaling dynamics, and (iii) it mimics the temporal learning process that we believe takes place in international politics.

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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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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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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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Lagging the Dog?: The Robustness of Panel Corrected Standard Errors in the Presence of Serial Correlation and Observation Specific Effects Kristensen, Ida Wawro, Gregory Uploaded 07-13-2003 Keywords time-series cross-section data serial correlation fixed effects panel data lag models Monte Carlo experiments Abstract This paper examines the performance of the method of panel corrected standard errors (PCSEs) for time-series cross-section data when a lag of the dependent variable is included as a regressor. The lag specification can be problematic if observation-specific effects are not properly accounted for, leading to biased and inconsistent estimates of coefficients and standard errors. We conduct Monte Carlo studies to assess how problematic the lag specification is, and find that, although the method of PCSEs is robust when there is little to no correlation between unit effects and explanatory variables, the method's performance declines as that correlation increases. A fixed effects estimator with robust standard errors appears to do better in these situations.

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Populists in the Pluralist Heaven: How Direct Democracy Reduces Bias in Interest Representation Boehmke, Frederick Uploaded 10-15-1999 Keywords Initiative direct democracy interest groups lobbying fixed effects representation Abstract This paper explores the effect of direct democracy on state interest group populations, providing an empirical test of a formal model of how access to the initiative process affects group formation and activities (Boehmke 1999), which predicts that more groups will mobilize and become active in initiative states. This prediction is supported by the findings in this paper, which also suggest that the effect of the initiative on group mobilizations has increased from the late 1970s to 1990. The prediction that groups that face a greater collective action problem are influenced more by the initiative is also confirmed since government and social groups are among those most affected. Counterfactual analysis indicates that the initiative process makes a state's interest group population more diverse, though the gains are decreasing from 1975 to 1990.

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Legislative Entrepreneurship and Campaign Finance Wawro, Gregory Uploaded 07-21-1997 Keywords campaign finance fixed effects panel data selection bias Abstract Drawing on models of service--induced and investor PAC campaign contributions, I analyze the role that legislative entrepreneurship plays in PACs' contribution decisions. I explore the possibility that PACs use campaign contributions to invest in members of Congress with the expectation that members will reciprocate by engaging in entrepreneurial behavior to the benefit of PACs. To determine whether a relationship exists between legislative entrepreneurship and PAC contributions I compute measures of entrepreneurial behavior for individual members of the U.S. House using detailed data on bill sponsorship and congressional hearings from the 97th through the 101st Congress. In order to cleanly estimate the effects of legislative entrepreneurship, we need to account for unobservable member--specific factors that enter into the PAC contribution calculus. To account for such factors I employ panel data methods which require very few assumptions about the data and provide a way to test whether the manipulations of the data that are required for a panel analysis introduce bias.

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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.

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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.