Residual-based shadings for visualizing (conditional) independence

Residual-based shadings for enhancing mosaic and association plots to visualize independence models for contingency tables are extended in two directions: (a) perceptually uniform HCL colors are used and (b) the result of an associated significance test is coded by the appearance of color in the visualization. For obtaining (a), a general strategy for deriving diverging palettes in the perceptually-based HCL space is suggested. As for (b), cut offs that control the appearance of color are computed in a data-driven way based on the conditional permutation distribution of maximum-type test statistics. The shadings are first established for the case of independence in 2-way tables and then extended to more general independence models for multi-way tables, including in particular conditional independence problems.