Robust multilevel simultaneous component analysis

• We propose a robust version of multilevel simultaneous component analysis (MSCA).
• We define outliers at different levels.
• Outlier maps reveal the outliers visually.

Multilevel simultaneous component analysis (MSCA) is a class of techniques for analyzing multivariate data with more than one level. However, as MSCA uses classical statistics such as the arithmetic mean, the resulting estimates are highly sensitive to outlying measurements. In this paper we propose a robust version of MSCA-P (the least restrictive MSCA variant) which can withstand the effects of outliers, while its associated outlier maps reveal the outliers visually. The technique is applied to data from an eating disorder study as well as to chemical data. We show by simulation that robust MSCA-P succeeds well in detecting outliers. The latter conclusion also holds when the data are generated according to the other MSCA variants.