Extending Mosaic Displays: Marginal, Conditional, and Partial Views of Categorical Data

Abstract This article first illustrates the use of mosaic displays for the analysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of partial views of several quantitative variables, conditioned by the v...