Object Oriented Solution for Robust Factor Analysis
Description
Outliers virtually exist in any datasets of any application field.
To avoid the impact of outliers, we need to use robust estimators.
Classical estimators of multivariate mean and covariance matrix are
the sample mean and the sample covariance matrix. Outliers will
affect the sample mean and the sample covariance matrix, and thus
they will affect the classical factor analysis which depends on
the classical estimators (Pison, G., Rousseeuw, P.J., Filzmoser,
P. and Croux, C. (2003) ).
So it is necessary to use the robust estimators of the sample
mean and the sample covariance matrix. There are several robust
estimators in the literature: Minimum Covariance Determinant estimator,
Orthogonalized Gnanadesikan-Kettenring, Minimum Volume Ellipsoid,
M, S, and Stahel-Donoho.
The most direct way to make multivariate analysis more robust is to replace
the sample mean and the sample covariance matrix of the classical estimators
to robust estimators (Maronna, R.A., Martin, D. and Yohai, V. (2006)
) (Todorov, V. and Filzmoser, P. (2009)
), which is our choice of robust factor
analysis. We created an object oriented solution for robust factor
analysis based on new S4 classes.