The comparative analysis of dependence for three-way contingency table using Burt matrix and Tucker3 in correspondence analysis

Abstract

In this paper, we confined our attention to compare two methods to obtain a graphical depiction of the association (dependency) between three categorical variables. We shall first describe how to recode a three-way contingency table by discussing the Burt matrix form of the data. This method is known as multiple correspondence analysis (MCA). Another method is to preserve a three-way contingency table form using Tucker3, it's known as a three-way correspondence analysis (CA3). As a case study, we pay attention to analyze the association between race and gender in occupation field that may have contributes to differences in employment opportunity and the continuing increases in women's educational attainment. The results show that CA3 is more simple in computation and provide the graphical depiction of three-way association simultaneously, while MCA's plot can't. Consider to the cumulative inertia on the two-dimensional plot, the percentage inertia of CA3's plot is better than MCA's plot.