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.

In this paper, we first propose a statistical model, called the Coherent Incurred Paid model, to predict future claims, using simultaneously the information contained in incurred and paid claims. This model does not assume log-normality of the levels (or normality of the growth rates) and is semi-parametric since it only specifies the first and the second moments; however, in order to evaluate the impact of the normality assumption, we also propose a benchmark Gaussian version of our model. Correlations between growth rates of incurred and paid claims are allowed and the tail development period is estimated. We also provide methods for computing the Claim Development Results and their Values at Risk in the semi-parametric framework. Moreover, we show how to take into account the updating of the estimation in the computation of the Claim Development Results. An application highlights the practical importance of relaxing the normality assumption and of updating the estimation of the parameters.