A new procedure of regression clustering based on Cook's D

Abstract

Clustering is an extremely important task in a wide variety of application domains especially in management and social science research. Usually, clustering methods work based on some distance metric among the observation or it may use Co-variance and correlation structure among the variables. If all the given variables are depends on a single variable, then the procedure of clustering the observations is said to be regression clustering. In this paper, an iterative procedure of regression clustering method was proposed by using the famous Cook’s D distance. At first, the Cook’s D distance should be calculated for the entire sample, then fix a Cut-off distance proposed by Bollen et al (1990) as .The authors fixed this Cut-off point as structural break in the sample, above the Cut-off are treated as Influential observation which are grouped as Influential cluster and repeat the same procedure for the remaining observation, until there are no influential observations in the last cluster. At each iteration, Chow’s F-test (1960) was used to check the discrimination between the influential cluster and the non-influential cluster. Moreover, control charts also used to graphically visualizes the iterations and the clustering process .Finally Chow’s test of equality of several regression equation helps firmly to establish the cluster discrimination and validity. This paper employed this procedure for clustering 220 customers of a famous four-wheeler in India based on 19 different attributes of the four wheeler and its company.