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Abstract:
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We consider making inference about several small areas with data obtained in the form of multino- mial counts. The cell probabilities have the same unimodal order restriction across areas, and these cell probabilities share a common effect. Therefore, a hierarchical multinomial-Dirichlet model, used to model the cell probabilities and the cell counts, allows a borrowing of strength across areas. We used the Gibbs sampler to make inference about the order-restricted multinomial parameters. We show how to perform the computations because there are difficulties poised by the order re- strictions. An application on body mass index showed that the order restriction is necessary and it provides increased precision over the scenario without the restriction.
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