On the Use of Recursive Residuals for Testing the Goodness of Fit of Small Area Estimation Models

• Activity Number: 445
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Yahia S. El-Horbaty*
• Companies: University of Southampton/Helwan University
• Keywords: Recursive residuals ; small area estimation ; area-level model ; unit-level model ; variance components ; model testing

Abstract

Correct specification of the model used for small area estimation is important in order to obtain valid predictors of the target quantities and of the prediction of the mean squared error. By using recursive residuals, we construct misspecification tests for the two linear mixed models in common use for small area estimation; the area-level model and the unit-level model. We propose simple formulas for the recursive residuals that do not require repeated estimation of the variance components, and use them to form tests with asymptotic t distribution. The proposed tests are most powerful against nonlinear effects of the covariates. Simulation results reveal that under appropriate sorting of the sample observations, the tests possess the correct size under the null hypothesis and good power in detecting misspecification of the linear predictors.