A fuzzy approach to discriminant analysis based on polynomial regression model

The dissimilarity among the combined units in common classification techniques leads to consider the opportunity of assigning each of them to more than a single group with different degrees of membership. In this paper, we propose a discriminant analysis structured by regressing such degrees on the classification variables. In particular, we show that even the sum of the estimated degrees of membership equals one for every unit. Polynomial regression models are actually more appropriate than linear ones, as the rate of increase or decrease of each dependent variable can vary depending on the values assumed by the independent variables; the order of the polynomial is to be chosen so as to ensure both the homogeneity within clusters and the parsimony of the entire regression model. The reliability of our proposal is showed in an applicative case, concerning the entrepreneurial propensity of the provinces in Central and Southern Italy.