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Abstract
Structural equation modeling (SEM) is a method of quantifying causal relationships proposed either from theory or from the study of counterfactuals. It is an important tool in several social and agricultural sciences. Small area estimation (SAE) is a method of estimating survey parameters in small domains under the constraints of an inadequate sample size. Frequently, these parameters are economic or social summaries for a geographic or demographic domain. This dissertation seeks to explore the prospective role of an SEM in the context of an application to SAE. This implies the estimation of a structural equation mixed model that performs well in moderate sized datasets that are unbalanced.
SEMs with error components have been developed by several authors in the context of econometric panel data models. These methods use ANOVA-like variance component estimators which are unbiased and of minimum variance in balanced datasets. However, there is an indeterminacy in the choice of estimator in the case of unbalanced datasets. Additionally, coefficient estimators which are based on the use of instrumental variables are consistent, but do not have established small sample properties.
Residual maximum likelihood estimation (REML) is a likelihood-based method of estimating variance components that yields consistent and asymptotically normal estimators when dealing with datasets that are balanced and otherwise. Further, it has been shown that REML estimates being even and translation invariant lead to best linear unbiased predictors. Given that the objective is to build an estimator which may be applied in the context of small area estimation, a method is proposed that lacks the indeterminacy of ANOVA, while also performing well in moderate sized unbalanced datasets. The performance of the estimator is demonstrated with simulated datasets. In the main, we find a significant reduction in standard errors of estimates.
