Generalized appended product indicator procedure for nonlinear structural equation analysis

procedure 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 incon-sistent for most practical situations. A new procedure is introduced and defined for a general model using products of observed indicators. The resulting estima-tor is consistent without assuming any distributional form for the underlying factors or errors. Identification assessment and standard error estimation are dis-cussed. A simulation study addresses statistical issues including comparisons of discrepancy functions and the choice of appended product indicators. Applica-tion of the new procedure in a substance abuse prevention study is also reported. Structural equation analysis is one of the most widely used statistical methods in the behavioral and social sciences, marketing, and education. The analysis expresses a model for observed measurements in terms of latent variables repre