Society of Actuaries (SOA) PA Practice Exam

How can one determine the optimal complexity parameter (cp) in decision trees?

1. By selecting any available cp value from the dataset

2. By printing cp values and manually selecting the highest

3. By using the fit$cptable to select the one with the least cross-validated error

4. By comparing the increases in decision tree complexity

The correct answer is: By using the fit$cptable to select the one with the least cross-validated error

Determining the optimal complexity parameter (cp) in decision trees is crucial for controlling the size and performance of the tree. The correct approach involves evaluating different cp values through a methodical process to minimize overfitting while ensuring that the model performs well on unseen data. Using fit$cptable allows you to access a table of cp values along with their associated errors calculated during cross-validation. By selecting the cp with the least cross-validated error, you ensure that you are not just fitting the model to the training data but also preserving its generalizability to new data. This approach provides a comprehensive measure of how well different complexity levels work, thereby ensuring that the chosen model is both parsimonious and effective. Other options, such as selecting any available cp value without a systematic evaluation, or manually selecting the highest from printed cp values, do not consider the model's performance. They risk choosing a cp that may not lead to the best prediction capability due to lack of formal evaluation. Comparing increases in complexity does not provide a complete assessment of performance as it does not incorporate evaluation metrics like cross-validation error which captures how well the model is expected to perform in practice.