Total inertia decomposition in tables with a factorial structure

Abstract

In correspondence analysis the variance in a data set is measured by its total inertia. The decomposition of this inertia into parts per row or per column, per dimension, or per row or column on each dimension, is well known. In this paper we consider various other forms of inertia decomposition, inertia between demographic groups and inertia interactions, inertia of substantive versus non-substantive responses. We also consider the case where comparisons between pre-specified groups can be isolated on particular dimensions of the solution, using correspondence analysis of matched matrices. The idea of hierarchically breaking down the inertia into smaller parts of interest and into contrasts is illustrated using data on decision-making by tourists, collected in a Eurobarometer survey. This application shows patterns between the countries of the EU and gender and age effects and interaction within countries. These effects are also tested for statistical significance using permutation testing.