Author: Abdulhakeem Eideh (Al-Quds University, Palestine)
Two-stage sampling is frequently used in small areas. When the selection probabilities are related to the values of the response variable, even after conditioning on concomitant variables included in the population model, the sample design is defined as informative. This may result in selection bias. In addition to the effect of applying an informative sampling design at both stages, one of the major problems in fitting small area models is non-ignorable nonresponse at the second stage. In this paper, we study, within a modelling framework, the joint treatment of not missing at random response mechanism at the second stage (within areas selected in the first stage) and informative sampling for both stages, by specifying the probability distribution of the observed measurements. This is the most general situation in surveys and other combinations of sampling informativeness and response mechanisms can be considered as special cases. Furthermore, we predict the finite population total and predict the area-specific effects and the small area totals for areas in the sample and for areas not in the sample, under four small area models, namely: nested error unit level regression model, area level random effects model, Fay and Herriot (1979) model, and random effects model.