Graphics Reference
In-Depth Information
Figure
.
.
Doubledecker plot for the UCB admissions data
model. he models considered are log-linear models, but residual-based shadings
are also conceivable for other types of models, such as logistic regression. In our ex-
ample, from exploratory analysis, we already suspect that admission and gender are
independent for a given department, except in the case of department A. herefore,
a sensible way of representing the table is to nest admission into department instead
of gender to obtain a stratified view. he corresponding mosaic and association plots
are shown in Figs.
.
and
.
. he shading visualizes a model where admission
and gender are conditionally independent, given the department.
Clearly, there is no gender bias in the departments except for department A: here,
significantlymore femalestudentsareadmittedthenexpectedforindependence.Mo-
saic displaysare already considered tobean excellent visualization tool forlog-linear
models(Friendly,
;heus and Lauer,
;Hofmann,
). Using the flat table
representation, the association plot similarly extends from the simple two-way case
to a structured residual plot applicable to the diagnostics of log-linear models. In
particular, if a mosaic display contains very small or empty cells, the corresponding
association plot could providean easier waytodetect deviation patterns than adding
residual-based shading to the mosaicplot. Yet another approach is to plot a mosaic-
plot of the expected frequencies and to highlight the (relative) residuals in the cells,
using different colors for positive and negative residuals (heus and Lauer,
).
As we have seen, we can use all of the plots to analyze stratified data by first split-
ting based on the conditioning variables. However, this also displays the marginal
distributions of the conditioning variables, which might make it more di
cult to in-
