Residual as Linear Sum of Matrix Determinants in Multiway Contingency Tables

Abstract

A Pearson residual is defined as a residual between an observed value and expected one of each cell in a contingency table, which measures the degree of statistical dependence of two attribute-value pairs corresponding to the cell. This paper shows that this residual is decomposed into a linear sum of determinants of 2 × 2 subtables, which means that the geometrical nature of the residuals can be viewed from grasmmanian algebra.