Model checking techniques for small area estimation
Yahia S. El-Horbaty · ePrints Soton (University of Southampton) · 2015
New and old techniques for validating small area models are considered.We focus on three models in common use; the Fay-Herriot model, the nested-error regression model, and the mixed-logistic regression model.We propose two tests that are designed to detect functional form misspecification of the mean function of the Fay-Herriot model and the nested-error regression model.Further, we investigate the use of the classical score, likelihood ratio and Wald tests for testing the need for random effects in the three models.Testing misspecification of these types is of utmost importance in small area estimation in order to produce reliable predictions of various domain characteristics (e.g.means, proportions, etc.) when the sizes of the available domains are very small.The proposed functional form misspecification tests are of the non-constructive type in the sense that they do not lead to determination of an alternative model when the working model is rejected.Artificial data are used in the simulation studies to assess the performance of the new as well as the reviwed tests where the new tests are shown to perform very well.In addition, a real data application is conducted in correspondence to each of the three models under consideration.i