Calibrated Robust Correspondence Analysis

M. Riani

{}^{1}

A.C. Atkinson

{}^{2}

F. Torti

{}^{3}

A. Corbellini

{}^{4}

G. Morelli

{}^{5}

${}^{1}$

Department of Economics and Management, University of Parma, Parma, Italy [mriani@unipr.it]
${}^{2}$

The London School of Economics, London WC2A 2AE, UK [a.c.atkinson@lse.ac.uk]
${}^{3}$

Joint Research Centre, European Commission, Ispra, Italy [francesca.torti@ec.europa.eu]
${}^{4}$

Department of Economics and Management, University of Parma, Parma, Italy [aldo.corbellini@unipr.it]
${}^{5}$

Department of Economics and Management, University of Parma, Parma, Italy [gianluca.morelli@unipr.it]

Keywords: forward search – inertia – outlier detection – simulation envelopes – trade restrictions

Correspondence analysis is a method for the visual display of information from two-way contingency tables. This paper describes two robust methods for the analysis of contingency tables that provide robust correspondence analyses. Emphasis is on a robust procedure which allows calculation of robust $p$ -values for the detection of outlying rows in the table as well as informative plots of departures from the customary assumption of a multiplicative model for cell probabilities. This leads to the systematic deletion of outlying rows of the table and to plots of greatly increased informativeness.

Our major example is export flows from the European union (EU). The underlying problem is whether export sanctions cause flows of exports to switch to non-sanctioned countries.

We simulate tables under departures from the multiplicative model. This procedure leads to a novel method for the detection of outliers using the scaling of simulation envelopes by an appeal to the theory of robust methods. We show that our procedure has good size and power and leads to correspondence analyses of increased informativeness.