Which statistic is used to compare different models and is Bozdogan's criterion?

• A. AIC
• B. BIC
• C. CAIC
• D. SBC

Answer: (C)

Model comparison relies on balancing how well a model fits the data with how complex it is. Bozdogan’s criterion, the Consistent Akaike Information Criterion (CAIC), is a specific information criterion designed for this purpose. CAIC adds a penalty for the number of parameters that grows with the sample size, making it more stringent than AIC and slightly more penalizing than BIC in practice. The formula is CAIC = -2 log-likelihood + k (ln(n) + 1). This stronger penalty helps CAIC be consistent in selecting the true model as the sample size increases, provided the true model is among those compared. That’s why this statistic is Bozdogan’s criterion. AIC and BIC (SBC) are related but have different penalty structures, and CAIC specifically bears Bozdogan’s name.