Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts the residual-based M-distance with the quantile of a chi distribution. It allows the researcher to visually identify clusters of potential outliers. The article further studies the effect of the potential outliers on the overall model evaluation when they are removed according to the order of the clusters exhibited in the plot. Suggestions are provided on determining the outlier status of outstanding cases in real data analysis. Recommendations are also made on the choice of robust methods and maximum likelihood following outlier removal.