Analyzing Data with Robust Multivariate Methods and Diagnostic Plots

Abstract

Principal Component Analysis, Canonical Correlation Analysis and Factor Analysis (Johnson and Wichern 1998) are three different methods for analyzing multivariate data. Recently robust versions of these methods have been proposed by Croux and Haesbroeck (2000), Croux and Dehon (2001) and Pison et al. (2002) which are able to resist the effect of outliers. Influence functions for these methods are also present. However, there does not yet exist a graphical tool to display the results of the robust data analysis in a fast way. Therefore we now construct such a diagnostic tool based on empirical influence functions. These graphics will not only allow us to detect the influential points for the multivariate statistical method but also classify the observations according to their robust distances. In this way we can identify regular points, good (non-outlying) influential points, influential outliers, and non-influential outliers. We can downweigh the influential outliers in the classical estimation method to obtain reliable and efficient estimates of the model parameters. Some generated data examples will be given to show how these plots can be used in practice.KeywordsDiagnostic plotInfluence functionsRobustnessOutliersRobust DistancesCutoff values