Society of Actuaries (SOA) PA Practice Exam

Which combination of impurity measures is typically compared during decision tree modeling?

1. Entropy, Gini, and Classification Error

2. Mean, Median, and Mode

3. Variance, Standard Deviation, and Entropy

4. Max, Min, and Range

The correct answer is: Entropy, Gini, and Classification Error

In decision tree modeling, the effectiveness of various impurity measures is crucial for determining how to split data at each node. The combination of Entropy, Gini, and Classification Error is relevant as these measures assess the purity of the resulting subsets after a split. Entropy measures the unpredictability or disorder within a dataset; a low entropy value indicates a higher degree of purity. Gini impurity, on the other hand, assesses the likelihood of a randomly chosen element being incorrectly labeled if it was randomly labeled based on the distribution of labels in the subset. Classification Error directly measures the proportion of misclassified instances. Using these impurity measures allows for effective comparisons to determine the most appropriate split at any given node in the decision tree, ultimately leading to improved performance and accuracy of the model. This approach helps construct a decision tree that can generalize well to new data while minimizing errors. The other options concern metrics that are not used for assessing impurity in decision tree modeling. Measures like Mean, Median, and Mode focus on central tendency rather than the distribution of class labels, while Variance and Standard Deviation measure data dispersion rather than classification purity. Max, Min, and Range similarly describe data extremes rather than providing insight into decision-making splits.