Partial Multiple Correspondence Analysis

Abstract

The present paper proposes a method of multiple correspondence analysis (MCA), which we name partial multiple correspondence analysis(PMCA), where effects of an ancillary item are eliminated from the other items. The idea is a natural extension of partial correspondence analysis (PCA) introduced by the first author. While PCA analyses relationship between two items, the proposed method deals with more than two items. We begin by briefly reviewing the derivation of correspondence analysis, PCA, and MCA in terms of orthogonal projection operators. Using these formulations, extension of PCA to the multiple-item case (PNICA) is described. After introducing an expression of PNICA as a special case of constrained MCA, some properties of PMCA are demonstrated by a small numerical example. We will also refer to the relationship between PMCA and another method called conditional forced classification of dual scaling.