A new approach to simple correspondence analysis with emphasis on the violation of the independence assumption of the levels of categorical variables

Abstract

The main hypothesis of correspondence analysis is given by the independence between the levels of categorical variables. Due to violation of this hypothesis, this study aims to improve the technique of correspondence analysis, providing a new approach for the calculation of the coordinates through the residual incorporation by tables in which categories have different levels of correlation. For this purpose, the simulation was made using Monte Carlo to generate frequencies from the correlated binomial distribution BC (n, π, ρ). It was concluded that in all evaluated scenarios the approach is promising in the sense that the objects were better discriminated against conventional approach. Moreover, the proposed procedure for obtaining the coordinates is likely to be used on real data as shown in the application example.