Nonlinear sem: Comparison between endogenous and exogenous interaction

In many fields of research to study particular phenomena the analysis of model with interaction is very important. The interaction occurs when the effect of a variable on another variable varies with the varying of a third variable and vice versa. In the SEM analysis the interaction can create problems if the two cause-variables are endogenous, i.e. linked causally to other variables. In literature, only few authors examined the model with the interaction between endogenous variables but without a true analysis of the causal effects. Consequently to analyze this particular model I propose two methods which link the causal theory to the mathematical relations used in the estimation process. The two methods use different causal theories then they consider the interaction in different way, the first as an exogenous variable and the second as an endogenous. To compare them, I analyze 4 groups of simulated datasets and , finding that the two methods give substantially the same results, for the simplicity I advise the use of the exogenous method.