8 OUTLIERS, LEVERAGE OBSERVATIONS, AND INFLUENTIAL CASES IN FACTOR ANALYSIS: USING ROBUST PROCEDURES TO MINIMIZE THEIR EFFECT

Parallel to the development in regression diagnosis, this paper de-fines good and bad leverage observations in factor analysis. Outliers are observations that deviate from the factor model, not from the center of the data cloud. The effects of each kind of outlying ob-servations on the normal distribution-based maximum likelihood estimator and the associated likelihood ratio statistic are studied through analysis. The distinction between outliers and leverage ob-servations also clarifies the roles of three robust procedures based on different Mahalanobis distances. All the robust procedures are designed to minimize the effect of certain outlying observations. Only the robust procedure with a residual-based distance prop-erly controls the effect of outliers. Empirical results illustrate the strength or weakness of each procedure and support those obtained This research was supported by the National Science Foundation, grant DMS04-37167. We thank Dr. Michael Villano and the editor and two referees for their constructive comments, which have led to a significant improvement of the paper over the previous version. Direct correspondence to Ke-Hai Yuan a