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Random Coefficient Models for Time-Series--Cross-Section Data: The 2001 Version Beck, Nathaniel Katz, Jonathan Uploaded 07-17-2001 Keywords random coefficients generalized least squares empirical Bayesian Stein-rule TCSC Abstract This paper considers random coefficient models (RCMs) for time-series--cross-section data. These models allow for unit to unit variation in the model parameters. After laying out the various models, we assess several issues in specifying RCMs. We then consider the finite sample properties of some standard RCM estimators, and show that the most common one, associated with Hsaio, has very poor properties. These analyses also show that a somewhat awkward combination of estimators based on Swamy's work performs reasonably well; this awkward estimator and a Bayes estimator with an uninformative prior (due to Smith) seem to perform best. But we also see that estimators which assume full pooling perform well unless there is a large degree of unit to unit parameter heterogeneity. We also argue that the various data driven methods (whether classical or empirical Bayes or Bayes with gentle priors) tends to lead to much more heterogeneity than most political scientists would like. We speculate that fully Bayesian models, with a variety of informative priors, may be the best way to approach RCMs.

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Multiculturalism, Diversity, and Prejudice Branton, Regina P. Jones, Bradford S. Uploaded 03-27-1999 Keywords random coefficients multilevel analysis multiculturalism racial politics Abstract In this paper, we consider the relationship between racial and ethnic diversity and individuals' assessments of racial and ethnic groups measured on several public opinion items. To examine these issues, we merge 1992 National Election Study data with U.S. Census Bureau demographic data measured at the congressional district level. We then develop an index of diversity that is based on the distribution of racial and ethnic groups in the congressional district. To examine the relationship between diversity and individual-level attitudes toward racial and ethnic groups, we estimate a series of models treating the response variable as a function of both individual-level attributes and district-level attributes. This approach allows us to assess, among other things, if diversity is associated with more positive or negative evaluations of racial and ethnic groups. The models herein are all estimated as mixed effects models to account for the clustering of observations within congressional districts. We find that diversity is associated with group affect and individuals' placement on policy issues; however, in contrast to some of the extant literature, we find that racial and ethnic diversity is nonlinearly associated with group affect: extremely low and extremely high levels of racial and ethnic diversity are associated with lower racial and ethnic group evaluations, while districts that are moderately diverse are associated with higher evaluations. This result also holds for some of the policy items examined. Specifically, we find that support for government assistance to blacks, and to a lesser extent, support for affirmative action, exhibits this nonlinearity with regard to racial and ethnic diversity. We also find this pattern for individuals' assessment of welfare recipients.

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Modeling Multilevel Data Structures Jones, Bradford S. Steenbergen, Marco R. Uploaded 07-17-1997 Keywords multilevel models random coefficients contextual analysis comparative Abstract Although integrating multiple levels of data into an analysis can often yield better inferences about the phenomenon under study, traditional methodologies used to combine multiple levels of data are problematic. In this paper, we discuss several methodologies under the rubric of multilevel analysis. Multilevel methods, we argue, provide researchers, particularly researchers using comparative data, substantial leverage in overcoming the typical problems associated with either ignoring multiple levels of data, or problems associated with combining lower-level and higher-level data (including overcoming implicit assumptions of fixed and constant effects). The paper discusses several variants of the multilevel model and provides an application of individual-level support for European integration using comparative political data from Western Europe.

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New Empirical Strategies to Model the Government Formation Process Glasgow, Garrett Golder, Matt Golder, Sona Uploaded 07-15-2010 Keywords discrete choice mixed logit IIA random coefficients government formation Abstract Over the past decade, a "standard approach" to the quantitative study of government formation has developed. This approach involves the use of a conditional (CL) logit model to examine government choice with the government formation opportunity as the unit of analysis. In this paper, we reconsider this approach and make three methodological contributions. First, we demonstrate that the existing procedure used to test for the independence of irrelevant alternatives (IIA) is flawed and severely biased against finding IIA violations. Our new testing procedure reveals that many government alternatives share unobserved attributes, thereby violating the IIA assumption and making the CL model inappropriate. Second, we employ a mixed logit with random coefficients that allows us to take account of unobserved heterogeneity and IIA violations. Third, we return to a question that originally motivated this literature, namely, what determines the likelihood that a particular party enters government? Although scholars have generally abandoned this question due to perceived methodological limitations in our ability to address it, we demonstrate that calculating probabilities for parties entering office rather than governments is straightforward in a mixed logit framework.