Estimation for Polynomial Structural Equation Models

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Abstract
Structural equation analysis is one of the most widely used statistical methods in social and behavioral science research and has become a popular tool in marketing. Subject matter needs for considering nonlinear structural models have been well documented. But current fitting procedures are available only for a limited class of models. In this article a systematic statistical approach is developed for the general polynomial structural equation model. The new procedure applies a method of moments procedure similar to the one used in errors-in-variables regression to the factor score estimates from the measurement model fit. The asymptotic properties of the estimator are derived, and a modified estimator with better small-sample properties is introduced. Simulation studies are reported to show the usefulness of the procedure and to compare its performance to other methods. An example from a substance abuse prevention study is also discussed.

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