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Interest in considering nonlinear structural equation models is well documented in the behavioral and social sciences as well as in the education and marketing literature. This article considers estimation of polynomial structural models. An existing method is shown to have a limitation that the produced estimator is inconsistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estimator is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are discussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Application of the new procedure in a substance abuse prevention study is also reported.

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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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The desire to fit structural equation models containing an interaction term has received much methodological attention in the social science literature. This paper presents a technique for the cross-product structural model that utilizes factor score estimates and results in closed-form moments-type estimators. The technique, which does not require normality for the underlying factors, was originally introduced in a very general form by Wall and Amemiya (2000) for any polynomial structural model. In this paper, the practical implementation of this method, including standard error estimation, is presented specifically for the cross-product model. The procedure is applied to an example from social/behavioural epidemiology where the flexibility of the cross-product model provides a useful description of the underlying theory. A simulation study is also presented comparing the method of moments for the cross-product model with three other procedures.