Society of Actuaries (SOA) PA Practice Exam

Which link function is generally used with continuous positive targets to ensure positive predictions?

1. Log

2. Logit

3. Probit

4. Cauchit

The correct answer is: Log

The log link function is widely used for continuous positive targets, particularly in generalized linear models, such as Poisson or gamma regression. This function transforms the predictions such that they remain positive. By applying the natural logarithm to the predicted values, the exponential transformation of these predictions ensures that the output will always be positive, which is crucial when modeling data that cannot take negative values, such as counts or monetary amounts. The nature of the log link function allows for a more straightforward interpretation of the coefficients, as they represent multiplicative changes in the response variable. This is especially useful in fields where percentage changes or multiplicative factors are meaningful. In contrast, the logit, probit, and Cauchit link functions are primarily designed for binary or ordinal outcomes rather than continuous positive targets. The logit and probit link functions utilize transformations suited for probabilities, mapping inputs onto a (0,1) interval, which is not appropriate for predictions that need to remain strictly positive and continuous.