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Structural Equation Mixed Models in the context of Small Area Estimation (303503)

Structural equation models (SEM) quantify causal relationships proposed by theory or the study of counterfactuals. Small area estimation (SAE) is geared to estimation of survey parameters in small domains with small sample sizes. This work explores the prospective role of an SEM in the context of SAE. This implies the estimation of a structural equation mixed model that performs well in moderate sized unbalanced datasets. Methods to estimate SEMs with error components have been developed in the context of econometric panel data models. They employ ANOVA-like error component estimators which suffer from indeterminacy in the choice of estimator with unbalanced datasets. Residual maximum likelihood estimation (REML) is a likelihood-based method of estimating error components that yields consistent and asymptotically normal estimators even with unbalanced datasets. We show under normality, that a REML based method while lacking the indeterminacy of ANOVA, also performs well in moderate sized unbalanced datasets. The performance of the estimator is demonstrated on simulated datasets.