Classification Trees

Objective

Predict cheaters using the Affairs data from the AER package, using the classification algorithm from the rpart package.

Data Prep

Created a new binary variable cheater by classifying observations with 0 affairs as 0, and with one or more affairs as 1.
Split the data (601 observations), into training and validation datasets (70%/30% , 425/176)

The Tree

Two Interpretations from the Tree

The most likely cheaters:
- been married more that 2.8 years
- Not very religious (religiousness < 4)
- Educated (education > = 17 years)
- Rates their marriage not so well (rating < 4)
Unlikely cheater
- Newlywed (years married < 2.8 years)

Variable Importance

Interesting how gender is perceived by many as a predictor for cheating. However, the data shows that it is not a good predictor.

Model Accuracy

Using the validation data, it is observed that the model is able to:

Predict correctly 27% of the cheaters
Misclassify faithful people as cheaters 8.6% of the time

## 
##  
##    Cell Contents
## |-------------------------|
## |                       N |
## | Chi-square contribution |
## |           N / Row Total |
## |           N / Col Total |
## |         N / Table Total |
## |-------------------------|
## 
##  
## Total Observations in Table:  176 
## 
##  
##                         | validation_tree$cheater_predicted 
## validation_tree$cheater |         0 |         1 | Row Total | 
## ------------------------|-----------|-----------|-----------|
##                       0 |       117 |        11 |       128 | 
##                         |     0.377 |     2.387 |           | 
##                         |     0.914 |     0.086 |     0.727 | 
##                         |     0.770 |     0.458 |           | 
##                         |     0.665 |     0.062 |           | 
## ------------------------|-----------|-----------|-----------|
##                       1 |        35 |        13 |        48 | 
##                         |     1.005 |     6.365 |           | 
##                         |     0.729 |     0.271 |     0.273 | 
##                         |     0.230 |     0.542 |           | 
##                         |     0.199 |     0.074 |           | 
## ------------------------|-----------|-----------|-----------|
##            Column Total |       152 |        24 |       176 | 
##                         |     0.864 |     0.136 |           | 
## ------------------------|-----------|-----------|-----------|
## 
##  
## Statistics for All Table Factors
## 
## 
## Pearson's Chi-squared test 
## ------------------------------------------------------------
## Chi^2 =  10.13359     d.f. =  1     p =  0.001455916 
## 
## Pearson's Chi-squared test with Yates' continuity correction 
## ------------------------------------------------------------
## Chi^2 =  8.624406     d.f. =  1     p =  0.003316886 
## 
##