The Confidence Ellipses in Multiple Non-Symmetrical Correspondence Analysis for the Evaluation of the Innovative Performance of the manufacturing enterprises in Campania
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Non-Symmetric Correspondence Analysis-NSCA (D’Ambra and Lauro, 1989) is a useful technique for analyzing a two-way contingency table. There are many real-life applications where it is not appropriate to perform classical correspondence analysis because of the obvious asymmetry of the association between the variables. 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 chisquared 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 the present paper, the Multiple non- Symmetric Correspondence Analysis- MNSCA (Gray and Williams, J. S,1975), is used for the evaluation of the innovative performance of the manufacturing enterprises in Campania. Innovation represents a very important element for the competition of the enterprises and economic growth. Only the enterprises which are able to innovate regularly can have at their disposal a range of more and more appealing products for the customers. Moreover, only a constant innovation provides the constant efficiency of the processes and the optimization of the production costs. Finally, the use of the ellipse confidence has allowed to identify a category which is statistically significant.
Keywords: CATANOVA, Confidence Ellipse, Gray-Williams Multiple Tau Index, Multiple Non Symmetrical Correspondence Analysis
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