Chartered Financial Analyst (CFA) Practice Exam Level 2

Which of the following indicates a better fit in the context of BIC?

1. Higher BIC value

2. Lower BIC value

3. Equal BIC values

4. BIC values that are not comparable

The correct answer is: Lower BIC value

The correct response is based on the understanding of the Bayesian Information Criterion (BIC), which is a criterion used for model selection among a finite set of models. BIC takes into account the goodness of fit of the model and introduces a penalty for the complexity of the model. A lower BIC value suggests a model that better balances fit and complexity. Specifically, BIC is defined as: BIC = -2 * log(likelihood) + k * log(n) where k is the number of parameters in the model and n is the sample size. When comparing multiple models, the one with the lowest BIC indicates that it has achieved a better trade-off between fit and simplicity—the best theoretical performance. Thus, when evaluating models, you should choose the one with the lowest BIC value as it implies that it is more accurate in explaining the data without being unnecessarily complex. The other contexts provided do not reflect the principles of BIC usage. Higher BIC values suggest poorer model fit, equal BIC values do not provide any preference toward a better model, and non-comparable BIC values would not facilitate effective model selection.