Society of Actuaries (SOA) PA Practice Exam

What is the primary goal of using BIC in model selection?

1. To minimize the likelihood function

2. To select the model with the lowest complexity

3. To select the model with the highest R-squared value

4. To maximize the number of parameters

The correct answer is: To select the model with the lowest complexity

The goal of using the Bayesian Information Criterion (BIC) in model selection is to select a model that balances fit and complexity. BIC is designed to penalize models for having too many parameters, thus discouraging overfitting. It incorporates a penalty for the number of parameters in the model, which helps to ensure that simpler models are favored unless more complex models provide a significantly better fit to the data. By focusing on this balance between model accuracy and complexity, BIC aids in identifying the most appropriate model from a set of candidates, ultimately contributing to better generalization to new data. The other options do not align with the primary goal of BIC. Minimizing the likelihood function, for instance, could lead to overly complex models as it does not account for the number of parameters. Similarly, selecting the model with the highest R-squared value can also result in overfitting, as high R-squared values can be misleading due to a large number of predictors. Lastly, maximizing the number of parameters contradicts the purpose of BIC, which aims to reduce complexity in model selection.