Clustered Coefficient Regression Model-Based Estimators in Small Area Estimation

This research project will develop model-based estimators for estimating population parameters in small areas. Small area estimation is an important problem in survey sampling when the sample sizes are not large enough to provide reliable estimates in small areas or domains. Model-based estimators based on auxiliary variables are widely used to increase the precision of estimators in survey sampling. However, if a heterogeneous relationship exists between the variable of interest and auxiliary variables, traditional models based on homogeneity will not accurately describe the relationship. This project will develop new model-based estimators based on more flexible regression models called clustered coefficient regression models. The new estimators will be applied to different national surveys, such as American Community Survey conducted by the U.S. Census Bureau. Results from the project will be used as examples in a course on survey sampling. Both undergraduate and graduate students will be involved in the research project. Publicly available R packages also will be developed. This research project will develop new model-based estimators based on clustered coefficient regression models using penalty functions, which also can borrow spatial or ordering information in different areas. The project will bridge the gap between clustered coefficient regression and model-based estimators. Three types of estimators in small area estimation will be studied. First, the project will develop new generalized regression estimators based on clustered coefficients for both linear regression models and logistic regression models. Second, the project will examine new unit level estimators based on clustered coefficient regression models, including an extension of the current linear model and the development of new estimators for binary data with consideration of random effects. Finally, the project will develop new area level estimators based on clustered coefficients, including an extension to proportions based on beta regression models. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.