B1560
Title: Analysis of multifactorial relative data
Authors: Viktorie Nesrstova - Palacky University, Olomouc (Czech Republic) [presenting]
Paulina Jaskova - Palacky University Olomouc (Czech Republic)
Ivana Pavlu - Palacky University Olomouc (Czech Republic)
Kamila Facevicova - Palacky University Olomouc (Czech Republic)
Karel Hron - Palacky University Olomouc (Czech Republic)
Abstract: Data of a relative nature (also referred to as compositional data) frequently occur in a number of applications, such as geochemistry, metabolomics or time-use epidemiology. Due to their specific nature, which is expressed by their scale invariance property, a careful approach to their statistical processing is required. This is embedded in the framework of the logratio methodology. For the vector case of compositional data, to obtain simple information contained in pairwise logratios, so-called backwards pivot coordinates were introduced in order to set up an orthonormal coordinate system which enables reliable and interpretable statistical processing of compositions. This approach was already applied in principal components analysis and regression analysis. However, there is still a lack of suitable methods for data consisting of several factors (i.e. multifactorial data). Our aim is to extend the framework of backwards coordinates to the case of compositional tables, two-factorial compositions. For these structures, the elemental information lies in simple log odds ratios and pairwise row and column balances. The performance of this approach is demonstrated in data from time-use epidemiology depicting the relative structure of movement behaviour.
