Small Area Prediction for Exponential Dispersion Families under Informative Sampling

Small area estimates are usually constructed from complex survey data. If the design is informative for the model, then procedures that ignore the sample design can suffer from important biases. Past work on small area estimation under informative sampling has focused heavily on linear models or on the prediction of means. We propose to generalize existing small area procedures for an informative sample design. We develop procedures in the context of a broad class of exponential dispersion families with random small area effects. We consider two models for the survey weights. We construct predictions of means as well as more general parameters that are nonlinear functions of the model response variable. We evaluate the procedures through simulation using a logistic mixed model. We then apply the methods to construct small area estimates of several functions of a wetlands indicator using data from the National Resources Inventory, a large scale agricultural survey.