For decades, the Democrats have been viewed as the party of the poor, with the Republicans representing the rich. Recent presidential elections, however, have shown a reverse pattern, with Democrats performing well in the richer blue states in the northeast and coasts, and Republicans dominating in the red states in the middle of the country and the south. Through multilevel modeling of individuallevel survey data and county- and state-level demographic and electoral data, we reconcile these patterns. Furthermore, we find that income matters more in red America than in blue America. In poor states, rich people are much more likely than poor people to vote for the Republican presidential candidate, but in rich states (such as Connecticut), income has a very low correlation with vote preference.

Hierarchical linear and generalized linear models can be fit using Gibbs samplers and Metropolis algorithms; these models, however, often have many parameters, and convergence of the seemingly most natural Gibbs and Metropolis algorithms can sometimes be slow. We examine solutions that involve reparameterization and over-parameterization. We begin with parameter expansion using working parameters, a strategy developed for the EM algorithm by Meng and van Dyk (1997) and Liu, Rubin, and Wu (1998). This strategy can lead to algorithms that are much less susceptible to becoming stuck near zero values of the variance parameters than are more standard algorithms. Second, we consider a simple rotation of the regression coefficients based on an estimate of their posterior covariance matrix. This leads to a Gibbs algorithm based on updating the transformed parameters one at a time or a Metropolis algorithm with vector jumps; either of these algorithms can perform much better (in terms of total CPU time) than the two standard algorithms: one-at-a-time updating of untransformed parameters or vector updating using a linear regression at each step. We present an innovative evaluation of the algorithms in terms of how quickly they can get away from remote areas of parameter space, along with some more standard evaluation of computation and convergence speeds. We illustrate our methods with examples from our applied work. Our ultimate goal is to develop a fast and reliable method for fitting a hierarchical linear model as easily as one can now fit a non-hierarchical model, and to increase understanding of Gibbs samplers for hierarchical models in general. Keywords: Bayesian computation, blessing of dimensionality, Markov chain Monte Carlo, multilevel modeling, mixed effects models, PX-EM algorithm, random effects regression, redundant

We fit a multilevel logistic regression model for the mean of a binary response variable conditional on poststratification cells. This approach combines the modeling approach often used in small-area estimation with the population information used in poststratification (see Gelman and Little 1997, Survey Methodology 23:127–135). To validate the method, we apply it to U.S. preelection polls for 1988 and 1992, poststratified by state, region, and the usual demographic variables. We evaluate the model by comparing it to state-level election outcomes. The multilevel model outperforms more commonly used models in political science. We envision the most important usage of this method to be not forecasting elections but estimating public opinion on a variety of issues at the state level. 1

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We study the effects of policy-specific public opinion on state adoption of policies affecting gays and lesbians, and the factors that condition this relationship. Using national surveys and advances in opinion estimation, we create new estimates of state-level support for eight policies including civil unions and non-discrimination laws. We differentiate between responsiveness to opinion and congruence with opinion majorities. We find a high degree of responsiveness, controlling for interest group pressure and the ideology of voters and elected officials. Policy salience strongly increases the influence of policy-specific opinion (directly and relative to general voter ideology). There is, however, a surprising amount of non-congruence—for some policies, even clear super-majority support seems insufficient for adoption. When non-congruent, policy tends to be more conservative than desired by voters; that is, there is little pro-gay policy bias. State political institutions have no significant effect on policy responsiveness; legislative professionalization affects congruence.

We compare two approaches for estimating state-level public opinion: disaggregation by state of national surveys and a simulation approach using multilevel modeling of individual opinion and poststratification by population share. We present the first systematic assessment of the predictive accuracy of each and give practical advice about when and how each method should be used. To do so, we use an original data set of over 100 surveys on gay rights issues as well as 1988 presidential election data. Under optimal conditions, both methods work well, but multilevel modeling performs better generally. Compared to baseline opinion measures, it yields smaller errors, higher correlations, and more reliable estimates. Multilevel modeling is clearly superior when samples are smaller—indeed, one can accurately estimate state opinion using only a single large national survey. This greatly expands the scope of issues for which researchers can study subnational opinion directly or as an influence on policymaking. Democratic theory suggests that the varying attitudes and policy preference of citizens across states should play a large role in shaping both electoral outcomes and policymaking. Accurate measurements of state-level opinion are therefore needed to study a wide range of related political issues, issues at the heart

Introduction 1.1 Overview Poststratification and weighting are used to adjust for known or expected discrepancies between sample and population. In this chapter, we aim to review current methods for using these techniques in survey analysis, and to critically examine the methods in the context of new ideas for extending model-based (Bayesian) methods to handle some of the more difficult problems that arise in practice. In particular, we distinguish among several different types of weights that are commonly used and clarify the relationship between poststratification and weighting. Difficulties that arise with these concepts motivate further development of the model-based poststratification approach (Holt and Smith, 1979; Little, 1991, 1993), which is usefully linked to the more traditional approaches via what we call the basic poststratification identity. Some progress is illustrated with examples, and the need for further development of these ideas is emphasized. We

The standard analysis of unit nonresponse in sample surveys is to assume missing at random--- that is, that the probability a person responds is independent of their response to the question of interest, y, conditional on fully-observed covariates x or on sampling weights w. In this paper, we discuss weakening these assumptions without the use of additional covariates in the special case of a binary outcome variable, y = 0 or 1. We note frequentist confidence bounds that do not rely on strong assumptions about the response mechanism. From a Bayesian perspective, we discuss using prior distributions to average over uncertainty in the missing data mechanism. Surprisingly, a natural-looking "noninformative" prior distribution yields unappealing posterior inferences. We discuss methods of constructing informative prior distributions using hierarchical data structures. We also show how to incorporate unequal sampling weights into the model using design-based sampling theory. This is importa...

Does public opinion influence Supreme Court confirmation politics? We present the first direct evidence that state-level public opinion on whether a particular Supreme Court nominee should be confirmed affects the roll call votes of senators. Using national polls and applying recent advances in opinion estimation, we produce state-ofthe-art estimates of public support for the confirmation of 10 recent Supreme Court nominees in all 50 states. We find that greater home-state public support does significantly and strikingly increase the probability that a senator will vote to approve a nominee, even controlling for other predictors of roll call voting. These results establish a systematic and powerful link between constituency opinion and voting on Supreme Court nominees. We connect this finding to larger debates on the role of majoritarianism and representation.

Large-scale social surveys are an important source of information for a wide range of topics. In analyzing such surveys, it is important to be aware of the complexity of the sampling design and the data adjustments that are used by survey organizations, including weighting to adjust for differences between sample and population and imputation to fill in missing responses. For estimating population means and proportions, the analyst should calculate weighted averages, using survey weights. In regression analysis, it is best to include, among the predictors, the variables that are used in the design and the weighting. Hierarchical models can be used to obtain inferences for small subpopulations. In general, analyzing survey data as if they had been obtained through simple random sampling can result in biased point estimates and underestimated standard errors. These calculations can often be adjusted reasonably well by using design effects reported in the survey documentation...