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Title: Principal component analysis of compositional tables using classical and robust methods Authors:  Julie Rendlova - Palacky University (Czech Republic) [presenting]
Kamila Facevicova - Palacky University Olomouc (Czech Republic)
Karel Hron - Palacky University (Czech Republic)
Peter Filzmoser - Vienna University of Technology (Austria)
Abstract: Many practical examples contain relative information about the distribution according to two factors which leads to a $(I \times J)$-dimensional extension of compositional data carrying information about a relationship between these factors. Such a structure, called a compositional table $\boldsymbol{x}$, can be decomposed orthogonally into its independent and interactive parts within the logratio methodology in order to provide a better insight to the original data structure. One of the primary tasks in multivariate statistics is to reduce the dimensionality of the data at hand, done using principal component analysis. To weaken the influence of outliers in PCA, the covariance matrix for robust PCA might be estimated by the Minimum Covariance Determinant estimator. Since popular clr coefficients lead to singularity and are generally not appropriate for robust methods, loadings and scores for PCA need to be computed from pivot coordinates of the interaction and independence tables and then transformed back to clr coefficients for better interpretation of the resulting compositional biplot. Accordingly, the aim is to propose a robust approach to principal component analysis of compositional tables and to illustrate the theoretical background on a real data set from OECD Statistics.