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For evidence-based regional policy making, geographically differentiated estimates of socio-economic indicators are the basis. However, national surveys are often conducted under a complex sampling design due to diverse reasons. Often small sample sizes result within regions of interest leading to too inefficient classical design-based estimators for policy making. In this case, the methodology of small area estimation (SAE) is applicable.
Classical SAE relies on the assumption of a multi-level regression model underlying the population data and presumes the sample design to be non-informative. These assumptions are hard to verify in practice. Under an informative sample design, estimated regression parameters are biased and the model-consistency of SAE gets lost. We correct for the sample informativeness in the parameter estimates, and construct design- and model-consistent estimates for regional indicators. Besides the estimation procedure we also propose a MSE estimator.
In a simulation study, we illustrate the necessity of survey weights under the violation of typical SAE assumptions. Furthermore, we show that the proposed method is also applicable to generalized linear mixed model settings, allowing also for non-continuous dependent variables.