How robust are Structural Equation Models to model miss-specification? A simulation study

Abstract: Structural Equation Models (SEMs) are routinely used in the analysis of empirical data by researchers from different scientific fields such as psychologists or economists. 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 has 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 especially when these models are used to confirm or reject hypotheses. In this simulation study, SEMs were fitted via two commonly used R packages: lavaan and piecewiseSEM. Five different data-generation scenarios were explored: (i) random, (ii) exact, (iii) shuffled, (iv) underspecified and (v) overspecified. In addition, sample size and model complexity were also varied to explore their impact on various global and local model fitness indices. The results showed that not one single model index 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's C statistic for piecewiseSEM were, in isolation, poor indicators of model fitness. In addition, the simulations showed that to achieve sufficient power to detect individual effects, adequate sample sizes are required. Finally, BIC showed good capacity to select models closer to the truth especially for more complex models. I provide, based on these results, a flowchart indicating how information from different metrics may be combined to reveal model strength and weaknesses. Researchers in scientific fields with little experience in SEMs, such as in ecology, should consider and accept these limitations.