Binomial-Beta Hierarchical Models for Ecological Inference

Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo

“…In these situations, hundreds of thousands of iterations of the MCMC sampler may be required, if not more. For instance, the King, Rosen, and Tanner (1999) treatment of the ecological inference problem has all these features and was implemented using Fortran on an extremely powerful UNIX workstation. Perhaps all this is to say that pathbreaking work is hard and that not everyone will do it!…”

“…estimating a logit model with a generalized link function (e.g., Carlin and Louis 1996, 176 and following): Given the model the resulting conditional distributions for P and m do not have closed form expressions and are only known up to constants of proportionality. estimating precinct-level proportions in an "ecological" or "cross-level" model (King, Rosen, and Tanner 1999):With precincts i = 1, . .…”

“…Western (1998) uses the Gibbs sampler to estimate a two-level hierarchical model of GDP in the OECD with pooled cross-sectional timeseries data; the hierarchical structure of the model makes the country-specific effects of covariates conditional on (time-invariant and country-specific) levels of labor organization. Hierarchical models are an obvious and frequent area of application for MCMC; I refer readers to the summaries in Western (1998) and King, Rosen, and Tanner (1999) and the treatments in the statistical literature: e.g., Gelman et al (1995, chapters 5, 13-14), Carlin and Louis (1996, chapter 7), and the book length treatment by Draper (1999). Smith (1999) uses MCMC to estimate an orderedprobit model in a strategic choice setting (crisis escalation in international relations), subject to the assumption that observed crisis behavior (e.g., escalation and acquiescence) provides strategically censored insights as to each player's true underlying level of resolve.…”

eco:RPackage for Ecological Inference in 2×2 Tables

“…First, one may collect additional covariates Z i and assume no contextual effect after conditioning on Z i . Such a strategy is often employed in the literature (e.g., King 1997;King et al 1999). Thus, we can extend our CAR model to the following CCAR (conditionally coarsened at random) model,…”

Bayesian and Frequentist Inference for Ecological Inference: The R×C Case

“…The proposed Bayesian model extends the binomial-beta hierarchical model developed by KING, ROSEN and TANNER (1999) from the 2 3 2 case to the R 3 C case. As in the 2 3 2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods.…”