Dirichlet-multinomial Model with Varying Response Rates over Time

10.6339/JDS.2007.05(3).282

Jeffrey R. Wilson；Grace S. C. Chen

Dirichlet-multinomial ； extravariation ； overdispersion

Journal of Data Science

5卷3期（2007 / 07 / 01）

413 - 423

英文

It is believed that overdispersion or extravariation as often referred is present more in survey data due to the existence of heterogeneity among and between the units. One approach to address such a phenomenon is to use a generalized Dirichlet-multinomial model. In its application the generalized Dirichlet-multinomial model assumes that the clusters are of equal sizes and the number of clusters remains the same from time to time. In practice this may rarely ever be the case when clusters are observed over time. In this paper the random variability and the varying response rates are accounted for in the model. This requires modeling another level of variation. In effect, this can be considered a hierarchical model that allows varying response rates in the presence of overdispersed multinomial data. The model and its applicability are demonstrated through an illustrative application to a subset of the well known High School and Beyond survey data.

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