A different approach to multiple correspondence analysis (MCA) than that of specific MCA

摘要

In multiple correspondence analysis, each nominal variable affects the analysis with a different amount of inertia, depending on the number of its modalities or categories. Usually in variables with many modalities – categories created infrequent (weak classes) modalities which contribute disproportionally to the inertia of the corresponding variable. Often these modalities contribute heavily to the determination of the first factorial axes and as a result this cannot clearly represent the investigated problem. Specific multiple correspondence analysis deals with the problem of infrequent (weak) modalities by removing them. That is, it simply ignores them in the calculation of distances between individuals [Le Roux B., 1999; Le Roux B., Rouanet H., 2004].In this paper we deal with this problem in a different manner. We keep the weak modalities in the analysis. Replacing the khi2 metric by a new metric which also takes into account the number of modalities of each variable, a reasonable effect of the weak modalities and a balancing of all the nominal variables is achieved in the analysis.We also encounter uniformly the weak modalities, whether they derive from many or few variables, even though the most “dangerous” case is the one variables where have many modalities. Only variables of two modalities are not affected.