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Structural equation models (SEM) quantify causal relationships proposed by theory or from the study of counterfactuals. Small area estimation (SAE) is geared toward estimating survey parameters in small domains under the constraints of 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.
SEMs with error components have been developed in the context of econometric panel data models. These methods use ANOVA-like variance 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 variance components that yields consistent and asymptotically normal estimators even with unbalanced datasets. We show under normality, that a REML based method lacks the indeterminacy of ANOVA, while also performing well in moderate sized unbalanced datasets. The performance of the estimator is demonstrated with simulated datasets and a significant reduction in standard errors of estimates is observed.
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