Bayesian Predictive Inference of a Proportion Under a Twofold Small-Area Model
TLDR
A hierarchical Bayesian model is presented 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 to infer the finite population proportion of each area.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.read more
Citations
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References
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BookDOI
Density estimation for statistics and data analysis
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Book
Small Area Estimation
TL;DR: In this paper, the authors proposed a model-based approach for estimating small area statistics based on direct and indirect estimates of the total population of a given region in a given domain.
Journal ArticleDOI
The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables
J. N. K. Rao,Alastair Scott +1 more
TL;DR: The effect of stratification and clustering on the asymptotic distributions of standard Pearson chi-squared test statistics for goodness of fit and independence in a two-way contingency table, denoted as X 2 and XI 2, respectively, is investigated in this article.
Journal ArticleDOI
A Predictive Approach to Model Selection
Seymour Geisser,William F. Eddy +1 more
TL;DR: In this article, a synthesis of Bayesian and sample-reuse approaches to the problem of high structure model selection geared to prediction is presented. But this approach is not suitable for high-dimensional models.
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