Mosaic Displays for Loglinear Models

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 multiway tables. This paper discusses extensions of the mosaic display as an exploratory tool 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 G² for complete independence in the full table into portions attributable to hypotheses about the marginal subtables. These methods are illustrated for multidimensional tables and for models of quasi-independence and quasi-symmetry in square tables.

Keywords: categorical data; marginal tables, graphical display, contingency tables

@InProceedings{Friendly92b,
  author = {Michael Friendly},
  title = {Mosaic Displays for Loglinear Models},
  year = {1992},
  month = {aug},
  pages = {61–68},
  address = {Alexandria, VA},
  booktitle = {Proceedings of the Statistical Graphics Section},
  publisher = {American Statistical Association},
  url = {http://datavis.ca/papers/asa92.html},
}