Society of Actuaries (SOA) PA Practice Exam

What distinguishes offsets in a GLM from weights?

1. Offsets adjust the relative importance of each observation

2. Offsets act as known coefficients rather than fitted coefficients

3. Offsets provide higher prediction accuracy

4. Offsets are applied only to the dependent variable

The correct answer is: Offsets act as known coefficients rather than fitted coefficients

Offsets in a Generalized Linear Model (GLM) play a specific role that is distinct from the concept of weights. The correct answer highlights that offsets act as known coefficients rather than fitted coefficients. This means that when incorporating offsets into a model, the values for these variables are fixed and not estimated through the model's fitting process. They are typically included in the linear predictor to adjust for exposure or different scales without being subjected to estimation—essentially, they provide a way to account for varying amounts of exposure or time across observations. In terms of weights, they adjust the contribution of each observation during the fitting process, allowing for observations to have differing levels of influence based on their assigned weight. This dynamic relationship contrasts with the way offsets are treated in the model. The distinction about offsets enhancing prediction accuracy can occur depending on the context, but it is not a defining characteristic like their role as known coefficients. Similarly, offsets do not apply exclusively to the dependent variable; rather, they are integrated into the linear predictor, which can impact the prediction of the dependent variable but do not exclusively target it. Thus, the concept of offsets being known coefficients is fundamental to understanding their application in GLMs.