Contextual Effects in Modeling for Small Domains

During last two decades, different Small Area Estimation (SAE) methods have been proposed to overcome the challenge of finding reliable small area estimates. This happens a lot that the required data for various research purposes are available at different levels. Based on availability of data, individual-level or aggregated-level models are implied in SAE. However, the estimated values for model parameters obtained from individual-level analysis can be different from the one obtained based on analysis of aggregate data. Generally, this is referred to as the ecological fallacy. This happens due to some substantial contextual or area-level effects in the covariates. To have a good interpretation of available data, possible contextual effects must be carefully included, measured, and accounted for in statistical models for calculating reliable estimates. Ignoring these effects leads to misleading results. The main advantage of contextual models is to help statisticians in studying aggregated-level data without concerning about the issue of ecological fallacy. In this paper, synthetic estimators and Empirical Best Linear Unbiased Predictors (EBLUPs) are studied based on different levels of linear mixed models. Using a numerical simulation study, the key role of contextual area-level effects is examined for model selection in SAE.