What Are Alternative Models of Full Structural Models, and Why Should I Be Concerned With Them?

In the past, a heavy emphasis was placed on the idea of alternative models, or the abil- ity to show the superiority of your research model compared to other potential rival models. While still a valid procedure, the popularity of requiring alternative models in research has waned. The main reason is that researchers would put up these “straw-man” models that were obviously worse than the original model. This did not really show the superiority of the original model; it just showed that some alternatives were really poor (Edwards 2008). There is a very good discussion about how to form and test alternative models in SEM from the work of MacCallum et al. (1993). The authors detail the process of using the “replacing rule”, under which the predictors and dependent variables may be swapped to see if the relationship is better in reverse than initially predicted. Addition- ally, the authors suggest using trimmed models or models where the relationships are directed to different dependent variables than initially proposed. Lastly, if there are rival explanations to a construct or concept, assessing the competing models will add credence to the findings.

If you are going to propose a viable rival model, the way to assess the superiority of a model is often through the model fit statistics. Looking at the model fit tests, you can see if your original model is a better fit than the “alternative” model. To do this, you can examine the fit indices, or you can look at the chi-square values for each model and perform a difference test based on the degrees of freedom. As stated earlier, you could also use the specification search tool to examine “trimmed” models to see if they have a better fit.The idea of examining potential alternative models is a good idea and adds some validity that your proposed model is capturing the observed covariance matrix. One should use caution that proposing a rival/ alternative model is not just an exercise in trying to find the worst-fitting model because this provides little justification for the superiority of the original model.

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.