Graphics Reference
In-Depth Information
Wewilldenote the oddsratio correspondingtothe setof cells
m ij , m i + ,j , m i, j + ,
m i + ,j +
as θ ij , i.e.,
m ij m i + ,j +
m i + , m i, j +
θ ij
=
for all
i
I
,
j
J
.
he differences in the highlighted heights, d , d and d , are approximately linear in
the log odds ratio of the corresponding cells:
log m i m ( i +)
ċ
d i
log θ i
=
m ( i +) m i for i
=
, , .
hefactthat these differences donot change muchindicates alinear relationship (on
alogscale) between the percentage of highparental encouragement andthe IQlevel.
Obviously the two variables X and Y are independent if log θ ij
foralli and j.
Byvisualizing low-dimensional relationships betweenvariables, mosaicplots provide
us with a way to find models graphically and to check the fits of existing models.
Earlier approaches by Friendly ( ) and heus and Lauer ( ) established the
linkbetweenloglinearmodelsandmosaicplotsbydisplayingfittedvaluesofloglinear
models together with their residuals.
=
Variants
13.3
By default, the sizes, shapes and locations of tiles in a mosaicplot are determined by
the mosaic's hierarchical construction process. However, it is of course possible to
vary these features, and this is a very useful technique for exploring the data, as each
of them tends to emphasize different aspects of the data. We are going to discuss two
different groups of variations: doubledecker plots are, as mentioned earlier, a variant
of the default structure of a mosaicplot. All other variations discussed here refer to
the layout of the plot.
Doubledecker Plots
13.3.1
Doubledecker plots were introduced in Hofmann et al. ( ) as a way of visualiz-
ing an association rule within the framework of the whole contingency table. Dou-
bledeckerplotsareaspecialcaseofstandard mosaicplots. Insteadofsplitting thebins
alternately in horizontal and vertical directions as in a default mosaicplot, all of the
bins are split horizontally in a doubledecker plot. All of the bins in a doubledecker
plotarethe same height and aredrawnsidebyside.Doubledecker plots of p variables
X ,...,X p therefore have the structure X , X ,...,X p , X
p ,whereX p is usually the
highlighting variable. hus, highlighting the heights in a p-dimensional mosaicplot
illustrates the conditional probabilities P
. One thing that distin-
guishes doubledecker plots from standard mosaicplots is that they are easy to label.
hisisdone by drawing a striped bar below the graphic for each of the variables. he
stripes show different shades of gray, with each shade representing one category of
(
X p
X ,...,X p
)
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