Regression by Parts: Fitting Visually Interpretable Models with GUIDE - Data Visualization - page 468

Figure . shows the GUIDE tree, which has four leaf nodes and an estimated
prediction deviance (based on tenfold cross-validation) about % lower than that
of a single additive loglinear model. From the sample average claim rates printed
beneath the leaf nodes, we see that bonus classes and tend to yield rates two to
three times as large as the other bonus classes.
heestimated regression coe cients intheleaf nodesaregiven inTable . ,where
the coe cients of the dummy variables corresponding to the first levels of each cat-
egorical variable are set to zero. As may be expected, Mileage has a positive slope
coe cient in all three nodes where it is not constant. he slope for Bonus is, how-
ever, negative wherever it is not constant. hus the higher the Bonus class, the lower
the Claim rate tends to be.
ForMake,thecoe cient forlevel hasalargernegative valuethanthecoe cients
for the other Make levels, uniformly across all the nodes. Hence this level of Make
is likely to reduce claim rate the most. In contrast, the coe cient for level of Make
is positive in all nodes and is larger than the coe cients for all other levels in three
nodes - it is second largest in the remaining node. his level of Make is thus most
likely to increase claim rate. he situation is quite similar for Zone: since all its co-
e cients are negative except for level , which is set to zero, that level is most likely
to increase claim rate, across all four nodes. he Zone level most likely to decrease
claim rate is , which has the largest negative coe cient in three of the nodes and the
second largest negative coe cient in the fourth node. Figure . presents the results
more vividly by showing barplots of the coe cients for Make and Zone by node. he
relative sizes of the coe cients are fairly consistent between nodes.

Table . . Regression estimates for GUIDE model using set-to-zero constraints for the first levels of
Make and Zone

Node Node Node Node

Constant −

.

−

.

−

.

−

.

Mileage Aliased . . .

Bonus − . − . − . aliased

Make= −

.

−

. . .

Make= −

.

−

.

−

.

−

.

Make= − . − . − . − .

Make= . . . .

Make= −

.

−

.

−

.

−

.

Make= −

.

−

.

−

. .

Make= − . − . . − .

Make= − . − . − . .

Zone= −

.

−

.

−

.

−

.

Zone= . . . .

− − − −

Zone= − . − . − . − .

Zone= −

.

−

.

−

.

−

.

Zone= −

.

−

.

−

.

−

.

Zone= − . − . − . − .