A Basic Introduction to CHAID

CHAID, or Chisquare Automatic Interaction Detection,
is a Classification Tree technique that not only evaluates complex interactions among predictors, but also displays
the modeling results in an easytointerpret tree diagram. The "trunk" of the tree represents the total modeling
database. CHAID then creates a first layer of "branches" by displaying values of the strongest predictor of the
dependent variable. CHAID automatically determines how to group the values of this predictor into a manageable
number of categories. (E.g., we may start with ten categories of age, and CHAID might collapse these ten categories
down to only four or five statistically significantly different age groups.)
CHAID then creates additional layers of branches off of each age grouping, using the strongest of the remaining
predictors. It continues this branching procedure until the final branches or "twigs" of the tree have been
generated. If CHAID is being used to generate a predictive market segmentation model, then these terminal branches
are the final market segments.
A typical CHAID model may have a dozen or so terminal segments, but sometimes we will build a model that has
many more segments than that, especially if we want to identify and understand some smaller "niche" segments that
may represent either a significant problem or an unusually good opportunity. The segments are depicted in the tree
diagram as well as ranked in a "gains table." Statistics produced by the gains table make it easy to determine how
"deep" into a file one must go to select prospects representing a given level of aboveaverage performance (dollar
value; response rate; etc.). Financial assumptions can be folded into the predictive CHAID model to generate
various estimates such as ROI.
When the dependent variable we are trying to predict has only two values (e.g., mail responder vs.
nonresponder), we generate a
nominal CHAID model. In such a model, we are able to see what proportion of each market segment
consists of cases in the desired category of the dependent variable (e.g., mail responders). A relative performance
index is generated for each segment, based on the proportion of that segment that falls into the desired category
of the dependent variable.
When the dependent variable is at least ordinal (i.e., the values can be arranged in some meaningful order),
then we generate an
ordinal CHAID model. Customer dollar value is an example of an ordinal dependent variable. In an
ordinal model, each segment is assigned an average value on the dependent variable (e.g., average dollar value),
and this is shown in both the tree diagram and the gains table. As with the nominal CHAID model, the ordinal model
can be supplemented with proprietary financial data to facilitate decisionmaking.
Below is a very simple, hypothetical ordinal CHAID model tree diagram for illustrative purposes only. [The data
are not real.] It begins at the top with a box representing the entire modeling sample of 81,040 households (marked
"Total"), to which a consumer product might be marketed via direct mail. Also included in this first box is the
average profit per household generated by the initial mailing (seventyfive cents). Household size is identified by
CHAID as the best predictor around which to begin segmenting the prospect market.
CHAID Tree Diagram
We can see that a household size of two to four persons returns an average profit of $1.64, which is twice the
profit generated by a oneperson household, and nearly seven times the profit generated by a fivetosixperson
household. CHAID then shows us that if a twotofourperson household has a bank card, the average profit jumps to
$3.58. If they do not have a bank card they return an average profit of only $1.29. However, among this
nonbankcard group, if the head of household's occupation is White Collar, profitability rises to $2.25.
For illustrative purposes, we have colored the aboveaverage segments green, the average segment yellow, and the
belowaverage segments red. Also, the segments are numbered from one to six on the tree diagram. We have used the
same convention on the Gains Table, below, which displays additional useful data for the six segments displayed in
the tree diagram.
CHAID Gains
Table
Segment ID

Segment Count

Percent of
Total

Average $
Value

Segment Index

Cum. Count

Cum. Percent

Cum. $ Value

Cum. Index

3

2,943

3.6

3.58

476

2,943

3.6

3.58

476

4

5,792

7.1

2.25

298

8,735

10.8

2.70

358

2

14,315

17.7

1.17

155

23,050

28.4

1.75

232

5

10,584

13.1

0.76

101

33,634

41.5

1.44

191

1

11,069

13.7

0.37

49

44,703

55.2

1.17

156

6

36,337

44.8

0.24

31

81,040

100.0

0.75

100

The first column of the gains table shows the segment number identifiers from the tree diagram. The second column
gives the segment household counts. The third column shows what percent of the total modeling sample falls into
each segment. The fourth column shows the average profit per household for each segment. The fifth column
represents this profit number as a relative index, with the average for the entire modeling sample set at 100.
Thus, the best segment has an index of 476, which means that it performs at a profit level of 4.76 times the
average for the entire modeling sample, and more than 15 times the profitability of the worst segment.
Columns six through nine are cumulative representations of the data from columns two through five: cumulative
household count, percent of modeling sample, average profit per household, and profit index. Among other things,
the gains table shows us that the best three segments (segments 3, 4 and 2) represent 28.4% of the total sample,
have an average profit of $1.75 per household, and are therefore 2.32 times as profitable as the average sample
household.
The gains table is a handy tool for seeing what levels of expected profitability would result from going
increasingly deeper into a prospect file. This is invaluable for planning direct marketing outreach programs, since
it helps us determine mailing quantities, and gives us information for calculating return on investment.
If instead of dollar value, our dependent variable had simply been a dichotomous variable such as response vs.
nonresponse to a mailing, then we would have generated a nominal CHAID analysis. In that case, instead of showing
dollar values in the tree diagram and the gains table, we would have shown percent response.
CHAID is particularly useful for generating market segmentation models. In addition to its utility as a
predictive modeling technique, the resulting tree diagram provides a valuable "bird's eye view" of the market
structure, showing the combinations of predictors which lead to any given segment. This can be very helpful to
advertising agency creatives and media planners, who want to be able to visualize and define clear market
segments.
Finally, the results of a CHAID model can be used to score a master database in an easy, straightforward manner.
As with other techniques (e.g., regression), new cases added to a file can be scored quickly once the basic scoring
algorithm is set up.
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