A Comparative Review of Interaction and Nonlinear Modeling

Interaction effects are common in the real world. The indicant product interaction model developed by D. A. Kenny and C. M. Judd required the researcher to establish nonlinear constraints among different model parameters. Continuous moderators can be used as parameters in the model so that each case has its own structural equation model. When researchers suspect an interaction relationship, they may be tempted to avoid structural equation modelling altogether, in favour of older techniques such as regression or analysis of variance. If interaction effects are present, then certain parameters should have different values in different samples. The use of polychoric or polyserial correlations leads to complications in assessing the fit of structural equation models, as researchers may be forced to adopt asymptotically distribution free methods. Techniques for representing and testing interaction effects are familiar in the regression and analysis-of-variance methodologies. Under the multisampling approach, researchers investigate interaction effects using chi-square difference tests.