Determine which of the following pairs of distribution and link function is the most appropriate to model if a person is hospitalized or not.

• Normal distribution, identity link function
• Normal distribution, logit link function
• Binomial distribution, linear link function
• Binomial distribution, logit link function
• It cannot be determined from the information given.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Key: D

The intent is to model a binary outcome, thus a classification model is desired. In GLM, this is equivalent to binomial distribution. The link function should be one that restricts values to the range zero to one. Of linear and logit, only logit has this property.