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The Binomial-Beta Hierarchical Model for Ecological Inference: Methodological Issues and Fast Implementation via the ECM Algorithm de Mattos, Rogerio S. Veiga, Alvaro Uploaded 10-17-2002 Keywords ecological inference hierarchical models binomial-beta distribution ECM Algorithm Abstract The binomial-beta hierarchical model from King, Rosen, and Tanner (1999) is a recent contribution to ecological inference. Developed for the 2x2 tables case and from a bayesian perspective, the model is featured by the compounding of binomial and beta distributions into a hierarchical structure. From a sample of aggregate observations, inference with this model can be made regarding values of unobservable disaggregate variables. The paper reviews this EI model with two purposes: First, a faster approach to use it in practice, based on explicit modeling of the disaggregate data generation process along with posterior maximization implemented via the ECM algorithm, is proposed and illustrated with an application to a real dataset; second, limitations concerning the use of marginal posteriors for binomial probabilities as the vehicle of inference (basically, the failure to respect the accounting identity) instead of the predictive distributions for the disaggregate proportions are pointed. In the concluding section, principles for EI model building in general and directions for further research are suggested.

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Pre-Election Polls in Nation and State: A Dynamic Bayesian Hierarchical Model Franklin, Charles Uploaded 07-17-2001 Keywords campaigns polling aggregation Bayesian hierarchical models Abstract A vast number of national trial heat polls are conducted in the months preceding a presidential election. But as was dramatically demonstrated in 2000, candidates must win states to win the presidency, not just win popular votes. The density of state level polling is much less than that for the nation as a whole. This makes efforts to track candidate support at the state level, and to estimate campaign effects in the states, very difficult. This paper develops a Bayesian hierarchical model of trial heat polls which uses state and national polling data, plus measures of campaign effort in each state, to estimate candidate support between observed state polls. At a technical level, the Bayesian approach provides not only estimates of support but also easily understood estimates of the uncertainty of those estimates. At an applied level, this method can allow campaigns to target polling in states that are most likely to be changing while being alerted to potential shifts in states that are not as frequently polled.

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The Binomial-Beta Hierarchical Model for Ecological Inference Revisited and Implemented via the ECM Algorithm Mattos, Rogerio Veiga, Alvaro Uploaded 05-21-2001 Keywords ecological inference hierarchical models binomial-beta distribution ECM Algorithm Abstract The binomia-beta hierarchical model is a recent contribution to ecological inference. Developed for the 2x2 tables case and under a bayesian perspective, the model is based on compounding the binomial and the beta distributions into a hierarchical structure to describe the behavior of aggregate variables. From a sample of aggregate observations, inference with this model can be made with regard to the values of the unobservable disaggregate variables. The paper discusses some issues regarding the construction of this EI model: First, previous uses of compounded binomial and beta distributions in the EI literature are reviewed; second, a faster approach to use the model in practice, based on posterior maximization implemented via the ECM algorithm, is proposed and illustrated with an application to a real dataset; finally, limitations regarding the use of marginal posteriors for binomial probabilities as elements of inference (basically, the failure to respect the accounting identity) instead of the predictive densities for the binomial proportions are pointed, together with suggestions of principles for EI model building in general.

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Bayesian Inference for Heterogeneous Event Counts Martin, Andrew D. Uploaded 04-20-2000 Keywords hierarchical models Poisson event count heterogeneity Abstract This paper presents a handful of Bayesian tools one can use to model heterogeneous event counts. In many political science applications we are interested in modeling the number of times a particular event takes place. While models for event count cross-sections are now widely used in political science (King, 1988, 1989b), little has been written about how to model counts when contextual factors introduce heterogeneity. I begin with a discussion of Bayesian cross-sectional count models and introduce an alternative model for counts with overdispersion. To illustrate the Bayesian framework, I model event counts of the number of discharge petitions from the 61st to the 105th House, and the number of women's rights bills cosponsored by each member in the 92nd House. I then generalize the model to allow for contextual heterogeneity and posit a hierarchical Poisson regression model, fitting this model to the number of women rights cosponsorships for each member of the 83rd to 102nd House. I demonstrate the advantages of this approach over pooled and independent Poisson regressions. The hierarchical model allows one to explicitly model contextual factors and test alternative contextual explanations. Additionally, I discuss software one can use to easily implement these models with little start-up cost.

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Campaign Timing and Vote Determinants Peterson, David A.M. Uploaded 09-07-1999 Keywords Campaign effects hierarchical models random coefficient Markov chain Monte Carlo Abstract Questions about the role of campaigns in making different considerations more important for voters have been central to the study of political behavior for fifty years (Lazardsfeld et al 1948). The basic concern is does the information presented during the campaign alter how voters evaluate and choose between candidates. This paper develops a random coefficient or hierarchical logit model to analyze the 1984 NES Continuous Monitoring Survey. The specification treats the effect of partisanship, policy distance and candidate character traits as a function of the campaign timing. Of the theories tested in this paper, the attitude strength model best predicts the changes in vote determinants across the campaign.

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Binomial-Beta Hierarchical Models for Ecological Inference King, Gary Rosen, Ori Tanner, Martin A. Uploaded 05-28-1998 Keywords ecological inference aggregation MCMC hierarchical models iterative simulation Abstract We develop a binomial-beta hierarchical model for ecological inference, using insights from King's (1997) ecological inference model and from the literature on hierarchical models based on Markov chain Monte Carlo algorithms (Tanner, 1996). Models in the framework we provide appear to scale up well, to have few numerical difficulties, and to recognize and avoid automatically problems with multiple modes and some other statistical issues.

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Not Asked and Not Answered: Multiple Imputation for Multiple Surveys Gelman, Andrew King, Gary Liu, Chuanhai Uploaded 10-27-1997 Keywords Bayesian inference cluster sampling diagnostics hierarchical models ignorable nonresponse missing data political science sample surveys stratified sampling multiple imputation Abstract We present a method of analyzing a series of independent cross-sectional surveys in which some questions are not answered in some surveys and some respondents do not answer some of the questions posed. The method is also applicable to a single survey in which different questions are asked, or different sampling methods used, in different strata or clusters. Our method involves multiply-imputing the missing items and questions by adding to existing methods of imputation designed for single surveys a hierarchical regression model that allows covariates at the individual and survey levels. Information from survey weights is exploited by including in the analysis the variables on which the weights were based, and then reweighting individual responses (observed and imputed) to estimate population quantities. We also develop diagnostics for checking the fit of the imputation model based on comparing imputed to non-imputed data. We illustrate with the example that motivated this project --- a study of pre-election public opinion polls, in which not all the questions of interest are asked in all the surveys, so that it is infeasible to impute each survey separately.

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Validation of software for Bayesian models using posterior quantiles Cook, Samantha Gelman, Andrew Rubin, Donald Uploaded 08-16-2005 Keywords Bayesian inference Markov chain Monte Carlo simulation computation hierarchical models Abstract We present a simulation-based method designed to establish the computational correctness of software developed to fit a specific Bayesian model, capitalizing on properties of Bayesian posterior distributions. We illustrate the validation technique with two examples. The validation method is shown to find errors in software when they exist and, moreover, the validation output can be informative about the nature and location of such errors.

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Prior distributions for Bayesian data analysis in political science Gelman, Andrew Uploaded 02-25-2009 Keywords Bayesian inference hierarchical models mixture models prior information Abstract Prior information is often what makes Bayesian inference work. In the political science examples of which we are aware aware, information needs to come in, whether as regression predictors or regularization (that is, prior distributions) on parameters. We illustrate with a few examples from our own research.

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Penalized Regression, Standard Errors, and Bayesian Lassos Kyung, Minjung Gill, Jeff Ghosh, Malay Casella, George Uploaded 02-23-2010 Keywords model selection lassos Bayesian hierarchical models LARS algorithm EM/Gibbs sampler Geometric Ergodicity Gibbs Sampling Abstract Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of Tibshirani (1996), have received a great deal of attention in recent years, mostly through frequentist models. Properties such as consistency have been studied, and are achieved by different lasso variations. Here we look at a fully Bayesian formulation of the problem, which is flexible enough to encompass most versions of the lasso that have been previously considered. The advantages of the hierarchical Bayesian formulations are many. In addition to the usual ease-of-interpretation of hierarchical models, the Bayesian formulation produces valid standard errors (which can be problematic for the frequentist lasso), and is based on a geometrically ergodic Markov chain. We compare the performance of the Bayesian lassos to their frequentist counterparts using simulations and data sets that previous lasso papers have used, and see that in terms of prediction mean squared error, the Bayesian lasso performance is similar to and, in some cases, better than, the frequentist lasso.

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Bayesian Methods: A Social and Behavioral Sciences Approach, ANSWER KEY TO THE SECOND EDITION. Odd Numbers. Park, Hong Min Gill, Jeff Uploaded 09-14-2010 Keywords Bayes modeling simulation Bayesian inference MCMC prior posterior Bayes Factor DIC GLM Markov chain Monte Carlo hierarchical models linear nonlinear Abstract This is the odd-numbered exercise answers to the second edition of Bayesian Methods: A Social and Behavioral Sciences Approach (minus Chapter 13). Course Instructors can get the full set from Chapman & Hall/CRC upon request.

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Treatment effects in before-after data Gelman, Andrew Uploaded 04-27-2004 Keywords correlation experiments interactions hierarchical models observational studies variance components Abstract In experiments and observations with before-after data, the correlation between "before" and "after" measurements is typically higher among the controls than among the treated units, violating the usual assumptions of equal variance and a constant treatment effect. We illustrate with three applied examples and then discuss models that could be used to fit this phenomenon, which we argue is related to the