Society of Actuaries (SOA) PA Practice Exam

Which of the following equations is used to calculate AIC?

1. AIC = 2*k - 2*ln(L)

2. AIC = k * ln(L) - 2 * ln(L)

3. AIC = -2*ln(L) + k

4. AIC = 2*ln(L) + k

The correct answer is: AIC = 2*k - 2*ln(L)

The correct calculation for Akaike Information Criterion (AIC) is represented as AIC = 2*k - 2*ln(L). In this equation, "k" stands for the number of parameters in the statistical model, and "L" represents the likelihood of the model given the data. AIC is a tool used in model selection and is based on the principle of balancing goodness of fit and model complexity. By incorporating the number of parameters (k), the AIC penalizes model complexity to prevent overfitting. The term -2*ln(L) provides a measure of the fit quality: the higher the likelihood (L), the better the model represents the data, thus lowering the AIC score. Ultimately, the formulation ensures that models with a lower AIC are preferred, as they signify a better trade-off between complexity and goodness of fit. This makes the equation fundamental to model selection in statistics. The other options do not appropriately characterize AIC. They either misrepresent the relationship between parameters and likelihood or incorrectly assign the components within their equations, which would lead to incorrect interpretations when attempting to evaluate model performance.