Testing for non-linear relationship in structural equation modeling
Ab Mooijaart, Albert Satorra · eScholarship (California Digital Library) · 2010
Since the seminal paper of Kenny and Judd (1984) several methods have been proposed for dealing with non-linear latent variable models.In all these methods more information from the data than just means and covariances is required.In this paper we also use more than just first-and second-order moments; however, we restrict ourselves to a selection of third-order moments.The key issue in this paper is a procedure for selection of the third-order moments for estimating the parameters and testing the goodness-of-fit of a model.The procedure we propose is based on the power of the test associated to the different choices of third-order moments, where the power is defined as the probability that a model without nonlinear factors is rejected by the goodness-of-fit model test when there are in fact nonlinear factors.The main conclusion of this paper is that evaluation of power for selection of third-order moments can easily be done by multivariate analysis of thirdorder moments, a moment test, without reference to a structural equation model.A consequence of this result is that in practice the selection of thirdorder moments is conceptually and computationally simple.Examples will illustrate our method.