Simultaneous Object and Category Score Estimation in Joint Correspondence Analysis

Joint correspondence analysis (JCA) is a statistical method for obtaining a low-dimensional representation of multivariate categorical data. It was developed as an alternative to multiple correspondence analysis (MCA). Typically, the solution is visualized through a map that projects the data onto a reduced space. A joint map, which shows both object and category scores in the same space, helps users explore inter- and intra-relationships in objects and categories. However, unlike MCA, current JCA estimation methods do not allow the joint representation of objects and categories on the map, which limits the interpretability of JCA results. To overcome this limitation, we propose a simultaneous object and category score estimation method for JCA while addressing the underestimated variance problem that is inherent in MCA. In the proposed method, JCA parameters are estimated by minimizing the discrepancy between the observed categorical data and the JCA data model, rather than relying on the JCA covariance model used in existing estimation methods. Previous research has shown that JCA is comparable to exploratory factor analysis. We also address the factor-analytic interpretation of JCA solutions in addition to geometric interpretation. Two real data analysis examples are also presented to demonstrate the geometric and factor-analytic interpretations of the JCA solutions.