Supporting Tables for
In chapter 3, we refer to a comprehensive hierarchical regression model. In this model, the dependent variable is the General Social Survey (GSS) spending preference question, which is scored +1 for those who believe that current spending is too low, 0 for those who say spending is about right, and –1 for those who believe current spending is too high.1 The effects of all variables are modeled as random effects that vary across the forty-four states included in the GSS sampling frame. As is common in the estimation of hierarchical models, each independent variable is state centered. In other words, each respondent's score is calculated as the difference between their raw score and the mean score for their state (centering or “de-meaning” does not affect the magnitudes of the regression slopes; e.g., if Scholastic Aptitude Tests were scored –300 to +300, rather than 200 to 800, the estimated impact on the freshman grade point average would be precisely the same). In this way, the mean of all independent variables is zero, and the intercept represents the average opinion in the average state (for helpful discussions of centering, see Aiken and West 1991; Bryk and Raudenbush 1992). The model estimates are reported in table A3.1. The model serves as the basis for selecting the relevant demographic factors to be utilized in our application of small polity inference.
In the following four subsections, we provide background on the method of small polity inference. In the first three, we explain the simulation, aggregation, and Bayesian approaches to inferring state-level public opinion. We then show how the three major approaches are related; and from this, the logic of small polity inference becomes readily apparent. The details of the computations are provided in subsequent sections.
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Publication information: Book title: Ten Thousand Democracies: Politics and Public Opinion in America's School Districts. Contributors: Michael B. Berkman - Author, Eric Plutzer - Author. Publisher: Georgetown University Press. Place of publication: Washington, DC. Publication year: 2005. Page number: 161.
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