Mosaic Displays for Multi-Way Contingency Tables

Extensions of the mosaic display to highlight patterns of deviations from various models for categorical data are discussed, and the use of color and shading to represent sign and magnitude of standardized residuals from a specified model is introduced.

Abstract

Abstract Mosaic displays represent the counts in a contingency table by tiles whose size is proportional to the cell count. This graphical display for categorical data generalizes readily to multi-way tables. This article discusses extensions of the mosaic display to highlight patterns of deviations from various models for categorical data. First, we introduce the use of color and shading to represent sign and magnitude of standardized residuals from a specified model. For unordered categorical variables, we show how the perception of patterns of association can be enhanced by reordering the categories. Second, we introduce sequential mosaics of marginal subtables, together with sequential models for these tables. For a class of sequential models of joint independence, the individual mosaics provide a graphic representation of a partition of the overall likelihood ratio G2 for complete independence in the full table into portions attributable to hypotheses about the marginal subtables.