<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We extend the twofold small-area model of Stukel and Rao (1997; 1999) to accommodate binary data. An example is the Third International Mathematics and Science Study (TIMSS), in which pass-fail data for mathematics of students from US schools (clusters) are available at the third grade by regions and communities (small areas). We compare the finite population proportions of these small areas. We present a hierarchical Bayesian model in which the firststage binary responses have independent Bernoulli distributions, and each subsequent stage is modeled using a beta distribution, which is parameterized by its mean and a correlation coefficient. This twofold small-area model has an intracluster correlation at the first stage and an intercluster correlation at the second stage. The final-stage mean and all correlations are assumed to be noninformative independent random variables. We show how to infer the finite population proportion of each area. We have applied our models to synthetic TIMSS data to show that the twofold model is preferred over a onefold small-area model that ignores the clustering within areas. We further compare these models using a simulation study, which shows that the intracluster correlation is particularly important.</p></abstract>

We extend the twofold small-area model of Stukel and Rao (1997; 1999) to accommodate binary data. An example is the Third International Mathematics and Science Study (TIMSS), in which pass-fail data for mathematics of students from US schools (clusters) are available at the third grade by regions and communities (small areas). We compare the finite population proportions of these small areas. We present a hierarchical Bayesian model in which the firststage binary responses have independent Bernoulli distributions, and each subsequent stage is modeled using a beta distribution, which is parameterized by its mean and a correlation coefficient. This twofold small-area model has an intracluster correlation at the first stage and an intercluster correlation at the second stage. The final-stage mean and all correlations are assumed to be noninformative independent random variables. We show how to infer the finite population proportion of each area. We have applied our models to synthetic TIMSS data to show that the twofold model is preferred over a onefold small-area model that ignores the clustering within areas. We further compare these models using a simulation study, which shows that the intracluster correlation is particularly important.

Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model

Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, U.S.A.

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model"}

We extend the twofold small-area model of Stukel and Rao (1997; 1999) to accommodate binary data. An example is the Third International Mathematics and Science...

Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model

Published Online: Mar 10, 2016

Page range: 187 - 208

Received: Dec 01, 2012

Accepted: Oct 01, 2015

DOI: https://doi.org/10.1515/jos-2016-0009

Keywords
Intracluster and intercluster correlations, credible intervals, goodness of fit, hierarchical model, simulation study

© by Balgobin Nandram

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model

Published Online: Mar 10, 2016

Page range: 187 - 208

Received: Dec 01, 2012

Accepted: Oct 01, 2015

DOI: https://doi.org/10.1515/jos-2016-0009

KeywordsIntracluster and intercluster correlations, credible intervals, goodness of fit, hierarchical model, simulation study

© by Balgobin Nandram

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Intracluster and intercluster correlations, credible intervals, goodness of fit, hierarchical model, simulation study