Business Intelligence and
Decision Modeling
Week 9
Customer Profiling
Decision Trees (Part 2)
CHAID
CRT
CHAID or CART
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Chi-Square Automatic Interaction
Detector
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Based on Chi-Square
All variables discretecized
Dependent variable: nominal
Classification and Regression Tree
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Variables can be discrete or continuous
Based on GINI or F-Test
Dependent variable: nominal or continuous
Use of Decision Trees
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Classify observations from a target binary
or nominal variable  Segmentation
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Predictive response analysis from a target
numerical variable  Behaviour
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Decision support rules  Processing
Decision Tree
Example:
dmdata.sav
Underlying Theory
 X2
CHAID Algorithm
Selecting Variables
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Example
 Regions (4), Gender (3, including Missing)
Age (6, including Missing)
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For each variable, collapse categories to
maximize chi-square test of independence:
Ex: Region (N, S, E, W,*)  (WSE, N*)
Select most significant variable
Go to next branch … and next level
Stop growing if …estimated X2 < theoretical X2
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CART (Nominal Target)
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Nominal Targets:
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GINI (Impurity Reduction or Entropy)
Squared probability of node membership
Gini=0 when targets are perfectly classified.
Gini Index =1-∑pi2
Example
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Prob: Bus = 0.4, Car = 0.3, Train = 0.3
Gini = 1 –(0.4^2 + 0.3^2 + 0.3^2) = 0.660
CART (Metric Target)
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Continuous Variables:
Variance Reduction (F-test)
Comparative Advantages
(From Wikipedia)
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Simple to understand and interpret
Requires little data preparation
Able to handle both numerical
and categorical data
Uses a white box model easily
explained by Boolean logic.
Possible to validate a model
using statistical tests
Robust