Interaction in multidimensional contingency tables: an information theoretic approach

The problem of interaction in multidime nsional co ntin ge ncy tables is inves ti gated from the viewpoint of information th eory as developed by Kullbac k. The hypothesis of no rth-order interaction is defin ed in the sense of an hypothes is of "generalized " ind ependence of classifications with fix ed rth order marginal restraints. For a three way table, with given cell probabilities 7Tijk , the minimum discrimination information for a contin ge ncy table with marginals P jj ., P. jk, and P i ... is given by the se t of cell probabilities P 0 k = a jjbj k e ,,7Ti j k wh ere aij , b j ,., and eik are fun ctions of th e giv e n marginal probabilities, that is, In (p!jJ7T ij") = In a ij + In bj k + In e ,,, representing no second-order interaction.