Graphics Reference
In-Depth Information
Figure
.
.
Mosaic plot for the hospital data, using “visit frequency” as first splitting variable
ble entry. We can still see the marginal distribution of LOS and additionally the visit
frequency given the category of LOS. If the two variables were independent, the grid
would be regular. Clearly, compared to a length of stay of
-
years, more patients
get regular visits for stays from
-
years, and conversely, fewer patients get regular
visits for stays of for more than
years. For patients that get no visits, the pattern is
reversed.
Since mosaicplots are asymmetric by construction, the choice of the variable or-
dermatters,asthefirstsplitting variable dominatestheplot.Inourexample,ifweuse
“visit frequency” as the first splitting variable, the impression obtained is very differ-
ent compared to that of the previous mosaic (see Fig.
.
).In this alternative display
(seeFig.
.
),wesee the marginal distribution of“visit frequency” in therows:about
half of the patients get visited regularly. his group is dominated by patients staying
-
years. It seems apparent that the distribution of LOS is similar for monthly and
never visited patients, so these two categories actually represent one homogeneous
group (patients visited only casually). Since the first splitting variable dominates the
plot, it should be chosen to be the explanatory variable.
Sieve Plots
12.2.2
Whenwe try toexplain data, we assumethe validity of acertain modelforthe gener-
ating process. In the case of two-way contingency tables, the two most common and
well-known hypotheses (Agresti,
) are
. independence of the two variables,
. homogeneity of one variable among the strata defined by the second.
