The Confidence Ellipses in Decomposition Multiple Non Symmetric Correspondence Analysis

Abstract

Non Symmetric Correspondence Analysis (NSCA) (D'Ambra and Lauro, 1989) is a useful technique for analyzing a two-way contingency table. The key difference between the symmetrical and non symmetrical versions of correspondence analysis rests on the measure of the association used to quantify the relationship between the variables. For a two-way, or multi-way, contingency table, the Pearson chi-squared statistic is commonly used when it can be assumed that the categorical variables are symmetrically related. However, for a two-way table, it may be that one variable can be treated as a predictor variable and the second variable can be considered as a response variable. Yet, for such a variable structure, the Pearson chi-squared statistic is not an appropriate measure of the association. Instead, one may consider the Goodman-Kruskal tau index. In the case that there are more than two cross-classified variables, multivariate versions of the Goodman-Kruskal tau index can be considered. These include Marcotorchino's index (Marcotorchino, 1985) and Gray-Williams’ index (Gray and Williams, 1975). In this article, the Multiple non Symmetric Correspondence Analysis (MNSCA), along with the decomposition of the TAU by Gray-Williams in main effects and interaction (D'Ambra et al., 2011), is used for the evaluation of the innovative performance of the manufacturing enterprises in Campania. Finally, to identify a category which is statistically significant, the confidence ellipses have been proposed for the Multiple Non Symmetric Correspondence Analysis starting from the ellipses suggested by Beh (2010) for the symmetrical analysis.