A Model for the Clustering of Variables Taking into Account External Data

Abstract

In this paper, a statistical model for the clustering of variables taking into account external data is proposed. This model is particularly appropriate for preference data in the presence of external information about the products. The clustering of variables around latent components (CLV method) is analysed on the basis of this model. Within the CLV method, there is one option without external data and one option taking into account external data. The criteria of both options can be expressed in function of the parameters of the postulated model. It is shown that the hierarchical algorithm finds the correct partition when the parameters of the model are known, no matter which option of CLV is used. Furthermore, the two options of CLV are compared by means of a simulation study. Both options perform well except for the case of small samples with a very large noise. Moreover, in most cases the performance of both options is equivalent.