Model-free measurement of case influence in structural equation modeling

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Commonly used case influence measures in structural equation modeling (SEM) are model-based.
• Model-based measures are susceptible to errors from model misspecification.
• There is a need for a model-free case influence measure to overcome these limitations.

Purpose of the Study:

• To introduce a novel model-free case influence measure, the Deleted-One-Covariance-Residual (DOCR).
• To evaluate the performance of DOCR against established measures like Mahalanobis distance (MD) and generalized Cook's distance (gCD).

Main Methods:

• Simulated data under varying conditions: sample size, proportion of target to non-target cases, and data-generating model type.
• Comparative analysis of DOCR, MD, and gCD in identifying influential cases.

Main Results:

• DOCR generally demonstrated superior performance in identifying target cases compared to MD and gCD across simulated conditions.
• DOCR's performance was unsatisfactory with small sample sizes, indicating sensitivity to sample size limitations.

Conclusions:

• DOCR is a promising model-free alternative for case influence analysis in SEM.
• Researchers should use DOCR cautiously with sufficiently large sample sizes (ideally not exceeding 600) to ensure reliable results.