Comparison of three hypothesis testing approaches for the selection of the appropriate number of clusters of variables

Within the scope of cluster analysis of variables, the selection of the appropriate number of clusters is of paramount interest. The strategy of determination of the appropriate number of clusters adopted herein is based on a hypothesis testing approach. It consists in testing whether the variation of a partition quality criterion between two consecutive partitions is far removed from the expected variation under the null-hypothesis stipulating a lack of structure. Three hypothesis testing strategies are detailed and compared in the scope of clustering of variables: Gap, Weighted Gap and a statistic associated with CLV methodology. Finally, an illustration is presented based on data from a preference study.