A Comparative Review of Interaction and Nonlinear Modeling
A Comparative Review of Interaction and Nonlinear Modeling was written by Edward E. Rigdon, Randall E. Schumacker, and Werner Wothke in 1998. It was published as the first chapter of Interaction and Nonlinear Effects in Structural Equation Modeling (eds. Randall E. Schumacker and George A. Marcoulides).
An interaction effect exists where the relation of A and B depends on the level of C.
A = β1B + β2C + β3(B*C) + e
If the variables are continuous, the 'indicant product' method calls for a structural model as
η1 = β1ε1 + β2ε2 + β3ε3 + ζ1
where the relation between η1 and ε3 is linear, and ε3 is constructed based in the theorized relation. For example, if there is a multiplicative effect between B and C, ε3 = ε1 * ε2. Multicolinearity becomes a challenge however, since ε3 is a function of the other two.
If the variables are discrete, or at least if the continuous variables can be discretely binned, the multisample method calls for partitioning the sample based on the interaction threshold of C. This method proceeds as a test for whether the two samples have equivalent intercepts in the interaction of A and B. The major drawback to this approach is that the sample is split.