The Marketing Book 5th Edition

228 The Marketing Book

techniques, we present the predictive ability of
classical statistical methods – logit analysis and
MDA – together with two more closely related
non-parametric decision tree methods, RPA
and the Elysee method, which utilizes ordinal
discriminant analysis.

An overview of VPRS

VPRS (as with RST) operates on what may be
described as a decision table or information
system. As is illustrated in Table 9.11, a set of
objectsU(o 1 ,.. ., o 7 ) are contained in the rows of
the table. The columns denote condition attri-
butesC(c 1 ,.. ., c 6 ) of these objects and a related
decision attribute D(d). A value denoting the
nature of an attribute to an object is called a
descriptor. As noted above, a VPRS data require-
ment is that it must be in discrete or categorical
form. Table 9.11 shows that, with this particular
example, the condition attribute descriptors
comprise zeros and ones (for example, denot-
ing yes and no answers), and the decision
attribute values are L and H (for example,
denoting low and high). The table shows that
the objects have been classified into one of these
decision values, which are also referred to as
concepts.
For the condition attributes in this exam-
ple, all of the objects (U) can be placed in five

groups: X 1 = {o 1 ,o 4 ,o 6 },X 2 = {o 2 },X 3 = {o 3 },X 4 =

{o 5 } and X 5 = {o 7 }. The objects within a group are

indiscernible to each other, so that objects o 1 ,o 4

ando 6 inX 1 have the same descriptor values for

each of the condition attributes. These groups

of objects are referred to as equivalence classesor

conditional classesfor the specific attributes. The

equivalence classes for the decision attribute

are: YL= {o 1 ,o 2 ,o 3 } and YH={o 4 ,o 5 ,o 6 ,o 7 }. The

abbreviation of the set of equivalence classes

for the conditional attributes Cis denoted by

E(C) = {X 1 ,X 2 ,X 3 ,X 4 ,X 5 } and for the decision

attribute it is defined E(D) = {YL,YH}.

VPRS measurement is based on ratios of

elements contained in various sets. A case in

point is the conditional probability of a concept

given a particular set of objects (a condition

class). For example:

Pr (YLX 1 )=Pr({o 1 ,o 2 ,o 3 }{o 1 ,o 4 ,o 6 })

=

{o 1 ,o 2 ,o 3 }{o 1 ,o 4 ,o 6 }

{o 1 ,o 4 ,o 6 }

=0.333

It follows that this measures the accuracy of the

allocation of the conditional class X 1 to the

decision class YL. Hence for a given probability

value, the -positive region corresponding to

a concept is delineated as the set of objects with

Table 9.11 Example of a decision table

Objects Condition attributes (C)

c 1 c 2 c 3 c 4 c 5 c 6

Decision

attribute D

d

o 1 101101L

o 2 100000L

o 3 001000L

o 4 101101H

o 5 000011H

o 6 101101H

o 7 000010H