ABSTRACT
D. A. Kenny and C. M. Judd formulated the nonlinear structural equation model. Consider a typical social-science empirical researcher who has a more or less clear or strong theory suggesting an interaction effect and has collected some data to support this theory. If the interaction variable is observed and can be used to form some "natural" groups, the multi-group approach is the simplest and most straightforward. If the interaction variable is latent, the factor scores approach or the TSLS approach are probably the most reasonable to use. K. G. Joreskog and Fan Yang Jonsson showed that one product variable is sufficient to identify all the parameters of the model. The procedures differ with respect to whether the latent and error variables are assumed to be normally distributed, whether observed product variables are used, and between one-step or two-step methods. A further difference between the different approaches is whether they require nonlinear constraints to be imposed.
