Cross-validation by downweighting influential cases in structural equation modelling

In the social and behavioural sciences, structural equation modelling has been widely used to test a substantive theory or causal relationship among latent constructs. Cross-validation (CV) is a valuable tool for selecting the best model among competing structural models. Influential cases or outliers are often present in practical data. Therefore, even the correct model for the majority of the data may not cross-validate well. This paper discusses various drawbacks of CV based on sample covariance matrices, and develops a procedure for using robust covariance matrices in the model calibration and validation stages. Examples illustrate that the CV index based on sample covariance matrices is very sensitive to influential cases, and even a single outlier can cause the CV index to support a wrong model. The CV index based on robust covariance matrices is much less sensitive to influential cases and thus leads to a more valid conclusion about the practical value of a model structure.