How Do I Search for Multivariate Outliers in Full Structural Models?

If your model fit is poor and the modification indices are providing no help, you might want to examine the multivariate outliers in your data set. A multivariate outlier is a collection of unusual or “out-of-the-norm” scores across multiple variables. Let’s go back to the full structural model example. If you go into the Analysis Properties function     and go to the “Output” tab, you will see an option on the right-hand side called “Test for normality and outliers”. See Figure 5.39.

After making this selection, cancel out of the window and run the analysis. In the out-put, you need to select the option titled “Observations farthest from the centroid”. The results will give a Mahalanobis d-square result.This statistic represents the squared distance from the centroid of a data set. The bigger the distance, the farther the item is from the mean distribution. AMOS also presents two additional statistics, p1 and p2. The p1 column shows the probability of any observation exceeding the squared Mahalanobis distance of that observation. The p2 column shows the probability that the largest squared distance of any observation would exceed the Mahalanobis distance computed. Arbuckle (2017) provides a heuristic for determining which observations may be outliers stating that small numbers in the p1 column are to be expected. Small numbers in the p2 column, on the other hand, indicate observations that are improbably far from the centroid under the hypothesis of normality. If you have p1 and p2 values that are less than .001, these are cases denoted as outliers. Figure 5.40 shows an example of the output when I ran the outlier analysis for the full structural model.

Figure 5.39 Request a Test for Normality and Outliers in the Analysis Properties Window

Figure 5.40 Test of Outliers Using Mahalanobis Distance

Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.

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