Detecting Outliers in Factor Analysis Using the Forward Search Algorithm

In this article we extend and implement the forward search algorithm for identifying atypical subjects/observations in factor analysis models. The forward search has been mainly developed for detecting aberrant observations in regression models (Atkinson, 1994 Atkinson, A. C. 1994. Fast very robust methods for the detection of multiple outliers. Journal of the American Statistical Association, 89: 1329–1339. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and in multivariate methods such as cluster and discriminant analysis (Atkinson, Riani, & Cerioli, 2004 Atkinson, A. C., Riani, M. and Cerioli, A. 2004. Exploring multivariate data with the forward search, New York: Springer-Verlag. [Crossref] , [Google Scholar]). Three data sets and a simulation study are used to illustrate the performance of the forward search algorithm in detecting atypical and influential cases in factor analysis models. The first data set has been discussed in the literature for the detection of outliers and influential cases and refers to the grades of students on 5 exams. The second data set is artificially constructed to include a cluster of contaminated observations. The third data set measures car's characteristics and is used to illustrate the performance of the forward search when the wrong model is specified. Finally, a simulation study is conducted to assess various aspects of the forward search algorithm.