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34
Bayesian multilevel estimation with poststratification: Statelevel estimates from national polls
 Political Analysis
, 2004
"... 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 smallarea estimation with the population information used in poststratification (see Gelman and Little 1997, S ..."
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Cited by 38 (5 self)
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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 smallarea 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 statelevel 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
Rich state, poor state, red state, blue state: what’s the matter with Connecticut
, 2005
"... 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 ..."
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Cited by 32 (12 self)
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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 statelevel 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.
Type S error rates for classical and Bayesian single and multiple comparison procedures
 COMPUTATIONAL STATISTICS
, 2000
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How Should We Estimate Public Opinion in The States?
"... We compare two approaches for estimating statelevel 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 ..."
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Cited by 20 (1 self)
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We compare two approaches for estimating statelevel 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 statelevel opinion are therefore needed to study a wide range of related political issues, issues at the heart
Analysis of variance—why it is more important than ever. The Annals of Statistics
, 2005
"... Analysis of variance (Anova) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (for example, splitplot designs), it is not always easy to set up an appropriate Anova. We propose a hierarchical analysis that automatically gives the corr ..."
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Cited by 18 (0 self)
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Analysis of variance (Anova) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (for example, splitplot designs), it is not always easy to set up an appropriate Anova. We propose a hierarchical analysis that automatically gives the correct Anova comparisons even in complex scenarios. The inferences for all means and variances are performed under a model with a separate batch of effects for each row of the Anova table. We connect to classical Anova by working with finitesample variance components: fixed and random effects models are characterized by inferences about existing levels of a factor and new levels, respectively. We also introduce a new graphical display showing inferences about the standard deviations of each batch of effects. We illustrate with two examples from our applied data analysis, first illustrating the usefulness of our hierarchical computations and displays, and second showing how the ideas of Anova are helpful in understanding a previouslyfit hierarchical model.
The Democratic Deficit in the States
"... We study how well states translate public opinion into policy. Using national surveys and advances in subnational opinion estimation, we estimate statelevel support for 39 policies across eight issue areas, including abortion, law enforcement, health care, and education. We show that policy is high ..."
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Cited by 17 (2 self)
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We study how well states translate public opinion into policy. Using national surveys and advances in subnational opinion estimation, we estimate statelevel support for 39 policies across eight issue areas, including abortion, law enforcement, health care, and education. We show that policy is highly responsive to policyspecific opinion, even controlling for other influences. But we also uncover a striking “democratic deficit”: policy is congruent with majority will only half the time. The analysis considers the influence of institutions, salience, partisan control of government, and interest groups on the magnitude and ideological direction of this democratic deficit. We find the largest influences to be legislative professionalization, term limits, and issue salience. Partisanship and interest groups affect the ideological balance of incongruence more than the aggregate degree thereof. Finally, policy is overresponsive to ideology and party—leading policy to be polarized relative to state electorates. How responsive is state policy to public opinion? Erikson, Wright, and McIver (1993) overturned the longstanding view that the public had little influence and established a clear correlation between voter ideology and aggregate state policy. Simply put, liberal states have more liberal policy. Subsequent studies of
Deep Interactions with MRP ∗ Election Turnout and Voting Patterns Among Small Electoral Subgroups
, 2012
"... Using multilevel regression and poststratification (MRP), we estimate voter turnout and vote choice within deeply interacted subgroups: subsets of the population that are defined by multiple demographic and geographic characteristics. This article lays out the models and statistical procedures we us ..."
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Cited by 16 (5 self)
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Using multilevel regression and poststratification (MRP), we estimate voter turnout and vote choice within deeply interacted subgroups: subsets of the population that are defined by multiple demographic and geographic characteristics. This article lays out the models and statistical procedures we use, along with the steps required to fit the model for the 2004 and 2008 Presidential elections. Though MRP is an increasingly popular method, we improve upon it in numerous ways: deeper levels of covariate interaction, allowing for nonlinearity and nonmonotonicity, accounting for unequal inclusion probabilities that are conveyed in survey weights, postestimation adjustments to turnout and voting levels, and informative multidimensional graphical displays as a form of model checking. We use a series of examples to demonstrate the flexibility of our method, including an illustration of turnout and vote choice as subgroups become increasingly detailed, and an analysis of both vote choice changes and turnout changes
Gay rights in the states: public opinion and policy responsiveness. American Political Science Review 103
, 2009
"... We study the effects of policyspecific 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 statelevel support for eight policies including c ..."
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Cited by 15 (0 self)
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We study the effects of policyspecific 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 statelevel support for eight policies including civil unions and nondiscrimination 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 policyspecific opinion (directly and relative to general voter ideology). There is, however, a surprising amount of noncongruence—for some policies, even clear supermajority support seems insufficient for adoption. When noncongruent, policy tends to be more conservative than desired by voters; that is, there is little progay policy bias. State political institutions have no significant effect on policy responsiveness; legislative professionalization affects congruence.
Poststratification and Weighting Adjustments
 In
, 2000
"... 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 ..."
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Cited by 15 (3 self)
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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 modelbased (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 modelbased 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
Using redundant parameterizations to fit hierarchical models
 Journal of Computational and Graphical Statistics
, 2008
"... 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 repar ..."
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Cited by 11 (0 self)
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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 overparameterization. We begin with parameter expansion using working parameters, a strategy developed for the EM algorithm. 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: oneatatime 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