CORRECT CLASSIFICATION RATES IN MULTIPLE CORRESPONDENCE ANALYSIS(Theory and Applications)

Multiple correspondence analysis (MCA) is formulated by various approaches, and homogeneity analysis (HA) is a major one among them. However, the HA approach has not yet provided a suitable index of GOF (goodness-of-fit) of multidimensional solutions. In this paper, the use of a correct classification rate (CCR) as the index is considered. We argue that CCR is congruous to the homogeneity assumption underlying HA, to justify the use of CCR in HA. Following this, we perform a simulation study to evaluate CCR by comparing it with eigenvalue-based GOF indices which have been derived from another approach to MCA. In the simulation CCR showed better performance than the eigenvalue-based indices: the former was found useful for evaluating the quality of MCA solutions and choosing solutions of proper dimensionalities. CCR also gave reasonable results in real data examples.