Society of Actuaries (SOA) PA Practice Exam

What R function is used to create a model matrix for Ridge Regression?

1. model.matrix

2. lm

3. glmnet

4. predict

The correct answer is: model.matrix

The function used to create a model matrix for Ridge Regression in R is model.matrix. This function is designed to generate a design (model) matrix from a given formula and dataset, which is essential for performing regression analyses, including Ridge Regression. A model matrix is a matrix representation of the data that includes the response variable and predictor variables in a format suitable for regression analysis. In the context of Ridge Regression, the model.matrix function helps ensure that the predictors are correctly represented, particularly when dealing with factors or categorical variables, by encoding them appropriately. This is a crucial step, as Ridge Regression applies a penalty to the coefficients of the regression model to reduce multicollinearity and enhance model interpretability, which requires a properly structured model matrix. Other functions mentioned, such as lm and glmnet, serve different purposes. The lm function is used for fitting linear models but does not directly create a model matrix. Similarly, glmnet is used specifically for fitting generalized linear models and performing penalized regression, but it requires a model matrix generated beforehand. The predict function, on the other hand, is used to make predictions from a fitted model rather than generating a model matrix. Therefore, model.matrix is the appropriate choice for creating the foundational structure needed for Ridge Regression analysis