## WarningEdit

It may seem odd to begin with a warning, but the popular misuse and misinterpretation of Structural Equation Modeling is so widespread that users of this wiki should be aware of some of the issues involved before they begin. While this warning is overly brief, you can follow-up these issues and more in the Further Reading section of this article. A number of these issues also apply to Confirmatory Factor Analysis. While Structural Equation Modeling has been popular in recent years to test the degree of fit between a proposed structural model and the emergent structure of the data, the perceived superiority of the technique is waning. Aside from the fact that the results of Structural Equation Modeling are often poorly reported, the conclusions drawn do not typically grasp the limitations of the technique. The most obvious, and some ways the most critical issue is that of incorrectly inferring a particular configuration of causal relationships from correlational data. This mistake can be illustrated with the simplest of all structural examples – that of 2 variables (variable A and B). If we ignore the additional complexity of latent structure, the number of possible causal structures is 4. Clearly, the number of possible models grows exponentially as the number of variables grows. In this example, the 4 possible causal models in this example are:

- A causes B;
- B causes A;
- A and B cause each other;
- finally, A and B are unrelated.

If A and B are indeed significantly correlated, it is likely that the first 3 models will be supported by significant fit statistics. If this is the case, what has been proven? Which of the 3 supported models is the correct model? What makes matters worse is that we have not even conclusively ruled out the last model. It is still possible that the correlation between A and B was spurious. To reinforce a maxim that most people know, but fail to apply to Structural Equation Modeling – you can not determine causation from correlation. Yet in most cases, researchers only test one or two models out of all the myriad of potential models, poorly report their results, then proclaim confirmation of their model (implying the exclusion of all other possible models). So what is the value of Structural Equation Modeling? If large correlational datasets are already available, and a large range of plausible models are assessed, the results can be valuable in conceiving an experimental study that can test the proposed causal relationships.

## Further ReadingEdit

- Principles and Practice in Reporting Structural Equation Analyses
- Structural Equation Modelling: Strengths, Limitations, and Misconceptions
- Some Cautions Concerning the Application of Causal Modelling Methods
- Potential Problems with "well fitting" Models
- Applications of Covariance Structure Modelling in Psychology: Cause for Concern?
- Power Analysis and Determination of Sample Size for Covariance Structure Modelling
- Applications of Structural Equation Modelling in Psychological Research