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If you use neural network procedures to build predictive models, you may have difficulty quantifying the effect of predictor variables on the output. For example, if you consider the churn rate at a telecommunications company and your model discovers that the number of long distance minutes is the best predictor, it isn’t apparent from the output whether using a lot of long distance minutes will cause people to want to leave the company or want to stay. If you use linear regression, you’ll have an equation which makes it easy to explain the effect of a predictor variable on the outcome. Unfortunately, there’s no equation like this that you can use in SPSS Neural Networks.

However, there are a number of ways to help you understand how a neural network makes its predictions. For example, you can use graphs or means tables to examine the relationship between the predicted outcome and the predictor variables. The drawback is that you are looking at the relationship between the predictions and only one variable at a time.

Applying an alternative machine learning technique, such as rule induction, is a more direct way for you to model the neural network predictions. You can use the SPSS Decision Trees add-on module (formerly called SPSS Classification Trees) to perform rule induction in SPSS Statistics Base. Although SPSS Decision Trees will not give you an equation, this module will help you unravel the reasoning behind the predictions. Use SPSS Neural Network's prediction variable as the outcome and all the other variables that you built the model with as predictors.

Choose the Classification and Regression Tree model in SPSS Decision Trees to begin rule induction:

• Click Analyze…Classify…Tree
• Drag MLP_PredictedValue_B into the Dependent Variable box
• Drag all the predictor variables we used to build the neural network model into the Independent variables box
• Select CRT from the pull-down menu in the Growing Methods box
• Click on the Criteria button
• Click on the Pruning tab
• Select Prune tree to avoid overfitting
• Click Continue
• Click OK

 

Figure 1: The completed SPSS Decision Trees dialog after variable and method selection.

The classification tree diagram from the analysis is shown below:

Figure 2: Tree diagram of neural network predictions

Because this is a multivariate analysis, the tree diagram tells you more about the intricacies of the neural networks’ predictions. The most important nodes to look at are the terminal nodes because they cannot be refined further. When looking at a terminal node, the mode response in a decision tree is the prediction for everyone in that node.

As you can see, the tree splits first on local minutes. Of the customers who used just under five minutes of local calling per month, 92.4% were involuntarily dropped.

Next, you’ll see how local minutes per month relate to churn. The neural network tended to predict that people who didn’t use the phone very much would likely be dropped by the company. Of those who did more local calling, the amount of international calling needs to be taken into account for males, and age should be taken into account for females.

Finally, you’ll notice that the neural network model predicted almost without exception that males who did little if any international calling (less than 1.36 minutes) were extremely likely to remain current customers—of that group, 99% stuck with the company. On the other hand, almost all (92%) males who did more international calling were predicted to leave voluntarily. Among females, older women (over 42.5 years old) were heavily predicted to want to leave (83.3%), while younger women were more likely to stay (68.6%).

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