8. Outliers, Leverage Observations, and Influential Cases in Factor Analysis: Using Robust Procedures to Minimize Their Effect

Abstract

Parallel to the development in regression diagnosis, this paper defines 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 observations on the normal distribution-based maximum likelihood estimator and the associated likelihood ratio statistic are studied through analysis. The distinction between outliers and leverage observations 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 properly controls the effect of outliers. Empirical results illustrate the strength or weakness of each procedure and support those obtained

A Poor Person’s Posterior Predictive Checking of Structural Equation Models

“…In the context of SEM, the development of cases-influence diagnostics remains an open area of research. Some caseinfluence diagnostic methods are based on case-level residual estimates (Bollen & Arminger, 1991;Yuan & Hayashi, 2010;Yuan & Zhong, 2008) and others are based on local influence analysis (Lee & Wang, 1996). With PP-PPMC, we show that the approach as outlined for global model fit assessment can be adapted to automate the generation of p values and plots useful for case-influence diagnosis for any appropriately defined test quantity.…”

“…In the context of factor analysis models, Yuan and Zhong (2008) showed that similar classifications of influential cases are possible when the factor analysis model is regarded as a multivariate regression model with the factor scores playing the role of the predictors and the observed variables playing the role of responses. Outliers and leverage points can then be defined using estimates of factor scores and residuals.…”

“…In this paper, we adopt the same classifications of the influential cases as defined and examined in Yuan and Zhong (2008) and Yuan and Hayashi (2010). The Bartlett formula is used for factor score estimation (see Yuan & Hayashi, 2010, p. 337, for some desirable properties of the Bartlett factor score estimates):…”

“…The model has nine indicator variables and 23 df . Following the method developed by Yuan and Zhong (2008), two outliers, two good leverage points, and two bad leverage points are introduced, and the last six cases in the second data set are replaced by those six influential cases. No replacement is made for the first data set, and thus neither outliers nor leverage points are expected to exist.…”

Quantitative Methods in Psychological Aging Research: A Mini-Review

“…Multivariate analyses have also been enriched by robust statistics. Factor analysis [21] , structural equation modeling [22,23] , and linear mixedeffects models, for both hierarchical and crossed structures [24][25][26] , can also be estimated within the robust framework.…”