In this study, we are interested in comparing various computational approaches to
\nBayesian small area estimation of proportions in logistic regression models. The
\nbasic idea consists of incorporating into such a model nested random e\u000bects that
\nre ect the complex structure of the data in a multistage sample design. As com-
\npared to the ordinary linear regression model, it is not feasible to obtain a closed
\nform expression for the posterior distribution of the parameters. However, the
\nproven optimality properties of empirical Bayes methods and their documented
\nsuccessful performance have made them popular (cf. Efron 1998). The EM algo-
\nrithm has proven to be an extremely useful computational tool here for empirical
\nBayes estimation. The approximation often used in the M step is that proposed
\nby Laird (1978), where the posterior is expressed as a multivariate normal distri-
\nbution having its mean at the mode and covariance matrix equal to the inverse
\nof the information matrix evaluated at the mode. Inspired by the work of Zeger
\nand Karim (1991), Wei and Tanner (1990), Gu and Li (1998) and Nielsen (2000)
\nwe also study a stochastic simulation method to approximate the posterior dis-
\ntribution. Alternatively, a hierarchical Bayes approach based on Gibbs sampling
\ncan also be employed. We present here the results of a Monte Carlo simulation
\nstudy to compare point and interval estimates of small area proportions based on
\nthese three estimation methods. As the empirical Bayes estimators obtained are
\nknown to be biased, we use the bootstrap to correct for this.
\nKeywords and phrases: Logistic Regression, Generalized Linear Models, Overdis-
\npersion, Random E\u000bects, Stochastic Simulation, EM algorithm, Gibbs Sampling.<\/p>\n