Model Modification in Structural Equation Modeling by Imposing Constraints

Two approaches for model modification, or specification search, in structural equation modeling are: releasing constraints (e.g., adding free parameters) and imposing constraints (e.g., deleting free parameters). These two approaches can be considered as "forward search" and "backward search", respectively. The forward search approach, which starts with a more limited model to find a more general model by adding free parameters, is very frequently utilized in practice. However, the success rate of the forward approach in obtaining the correct model is usually low. The forward search also has been found to depend very highly on the initial model selected in the modification process. The farther the initial model differs from the true model, the less likely is the proper modification to occur. This study illustrates the backward search approach, which starts with a more general model and improves the model by imposing constraints, using the z and Wald (W) tests. Assuming a correct measurement model, this study focuses on the model modification of structural relationships among factors. The results showed that with correct specification of the causal order of latent factors the correct model may be located with higher than 60% accuracy, using the incremental univariate Wald test, or the z test. With more cautious, or restricted, search, the success rates are even higher.

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