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rally and easily as continuous variables. he data are from the Division of Water Sci-
ence,DSIR, NewZealand (Camden,
).heycontain measurements on
horse
mussels taken from five sites in the Marlborough Sounds, New Zealand, in Decem-
ber
. Besides site, each mussel's length, width, depth (all in millimeters), gender
(male, female, or indeterminate), viscera mass, muscle mass, and shell mass (all in
grams) were recorded, as well as the type of peacrab (five categories) found living in
its shell.
Cook (
, p.
) used Muscle as the response variable and Length, Depth, and
Shellaspredictorstoillustratehisapproachtographicalregression.(Note:Cookused
thesymbols L, W,andS todenotelength, depth andshell,respectively.) Withthe aid
of sliced inverse regression (Li,
) and power transformations, he found that the
mean of Muscle could be modeled by the
-D subspace defined by the variable
.
Depth
.
.
Shell
.
.
SIR1
=
.
Length
+
+
(
.
)
Figure
.
shows the banana-shaped plot of Muscle versus SIR
.
he variable Site is not used in Eq. (
.
) because, unlike GUIDE, sliced inverse
regression doesnot easily handle categorical predictorvariables. Figure
.
shows the
resultoffittingaGUIDEpiecewisebestsimplelinearmodeltothedata.hetreesplits
first on Site.If Site is neither
nor
, the tree splits further on Depth. he best simple
linear predictor is Shell at two of the leaf nodes and Width at the third. Figure
.
shows the data and the fitted lines in the leaf nodes of the tree. he plots look quite
linear.
On the right side of Fig.
.
is the piecewise best two-variable GUIDE model. It
splits the data into two pieces, using the same top-level split as the piecewise best
Figure
.
.
Plot of Muscle vs. SIR
(slightly jittered to reduce overplotting)
