Graphical depiction of three-way association in contingency table using higher-order singular value decomposition Tucker3

Abstract

The anaysis of the association between the variables of a three-way table requires a very different approach to the conventional correspondence analysis techniques. The conventional technique involves by collapsing three-way table into two-way table form. By doing so, no information about three-way interaction among variables. To included interaction among three variables at once, we consider higher-order singular value decomposition (HOSVD) Tucker3. Through the HOSVD Tucker3 decomposition, we can derive marginal of row, column, annd tube categories. Using those marginals, we can easily visualize dependence of the three categories. As a case study, Tucker3 is applied to household data which containing information on race, educational attainment and employment status.