Society of Actuaries (SOA) PA Practice Exam

What is a key reason to choose the logit link function?

1. It requires fewer observations

2. It fits better in general linear models

3. It is the canonical link function leading to faster convergence

4. It predicts continuous outcomes better

The correct answer is: It is the canonical link function leading to faster convergence

The logit link function is particularly valued in generalized linear models, especially when dealing with binary outcome variables. Its status as the canonical link function plays a crucial role in models like logistic regression. By utilizing the logit link, the model often achieves faster convergence during the estimation process. This is because the logit function inherently suits the underlying distribution of the data in binary outcomes, which allows the iterative methods used for estimation, such as Newton-Raphson, to converge more efficiently. In the context of generalized linear models, the canonical link function aligns specifically with the chosen probability distribution of the response variable, ensuring a more effective and straightforward interpretation of the results. This leads to improved numerical stability and performance compared to other link functions. Consequently, using the logit link for binary outcomes not only streamlines the process but also enhances overall model performance.