Title: Robust correspondence analysis
Authors: Marco Riani - University of Parma (Italy) [presenting]
Anthony Atkinson - London School of Economics (United Kingdom)
Aldo Corbellini - Faculty of Economics - University of Parma (Italy)
Francesca Torti - European Commission (Italy)
Abstract: Correspondence analysis is a method for displaying information from two-way tables of count data. Typically, the rows are subjects (in our first example the 28 countries of the European Union) and the columns are response categories (in that case the cost range of clothes). The main result is a two-dimensional plot showing the structure of the data. The theory and practice of correspondence analysis are presented in several books by Greenacre. Little attention seems to have been given to the effect of outliers on correspondence analysis nor to the desirability and practice of robust estimation. We introduce a robust form of correspondence analysis based on minimum covariance determinant estimation. This leads to the systematic deletion of outlying rows of the table and to plots of greatly increased informativeness. Our examples are trade flows of clothes and consumer evaluations of the perceived properties of cars. The robust method requires that a specified proportion of the data be used in fitting. To accommodate this requirement we provide an algorithm that uses a subset of complete rows and one row partially, both sets of rows being chosen robustly. We prove the convergence of this algorithm.