Model-free measurement of case influence in structural equation modeling

Abstract

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In the field of structural equation modeling (SEM), all commonly used case influence measures are model-based measures whose performance are affected by target-model-misspecification-error. This problem casts light on the need to come up with a model-free measure which avoids the misspecification problem. the main purpose of this study is to introduce a model-free case influence measure, the Deleted- One-Covariance-Residual (DOCR), and then evaluating its performance compared to that of Mahalanobis distance (MD) and generalized Cook’s distance (gCD). The data of this study were simulated under three systematically manipulated conditions: the sample size, the proportion of target cases to non-target cases, and the type of model used to generate the data. The findings suggest that the DOCR measure generally performed better than MD and gCD in identifying the target cases across all simulated conditions. However, the performance of the DOCR measure under a small sample size was not satisfactory, and it raised a red flag about the sensitivity of this measure to small sample size. Therefore, researchers and practitioners should only use the DOCR measure with a sufficiently large sample size, but not larger than 600.

Keywords

• influence analysis
• deletion statistics
• Mahalanobis distance
• generalized Cook’s distance
• Deleted-One-Covariance-Residual (DOCR)