Society of Actuaries (SOA) PA Practice Exam

What is the role of weights in a Generalized Linear Model (GLM)?

1. To standardize the prediction across observations

2. To adjust the relative importance of observations during model fitting

3. To account for the presence of outliers

4. To balance the dimensions of the data

The correct answer is: To adjust the relative importance of observations during model fitting

In a Generalized Linear Model (GLM), weights play a crucial role by allowing the model to adjust the relative importance of different observations during the fitting process. This is particularly useful in situations where the observations vary in their reliability or influence on the outcome of the model. For instance, in cases where certain data points are more precise or have more significance due to larger sample sizes, weights can be applied to elevate the contribution of these observations in the statistical estimation process. When weights are used in a GLM, they modify the likelihood function being maximized. Specifically, each observation contributes to the likelihood in proportion to its assigned weight. By incorporating weights, the model becomes more robust and can provide a more accurate estimation of the parameters, particularly in heterogeneous datasets where not all observations should have equal influence. The other choices highlight different conceptual aspects that do not directly relate to the primary purpose of weights in a GLM. For example, while standardization of predictions and addressing outliers are important considerations in data analysis, they do not specifically capture the role of weights in prioritizing or adjusting contributions of different observations in the fitting of a GLM. Balancing dimensions is also unrelated, as weights are not meant to manipulate the size or shape of the data matrix but