How robust are Structural Equation Models to model miss-specification? A simulation study
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Structural Equation Models (SEMs) are routinely used in the analysis of empirical data by researchers spanning different scientific fields such as psychologists or econometricians. In some fields, such as in ecology, SEMs have only started recently to attract attention and thanks to dedicated software packages the use of SEMs have steadily increased. Yet, common analysis practices in such fields that might be transposed from other statistical techniques such as model acceptance or rejection based on p value screening might be poorly fitted for SEMs. In this simulation study, SEMs were fitted via two commonly used R packages: lavaan and piecewiseSEM. Datasets were simulated under different modelling scenarios to test the impact of sample size and model complexity on various global and local model fitness indices. The results showed that not one single model indices should be used to decide on model fitness but rather a combination of different model fitness indices is needed. The global chi square test for lavaan or the Fisher C statistic are, in isolation, poor indicators of model fitness. Combining the different metrics explored here provided little safeguards against model overfitting, this emphasizes the need to cautiously interpret the inferred (causal) relations from fitted SEMs. Researchers in scientific fields with little experience in SEMs, such as in ecology, should consider and accept these limitations.
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