Which criterion is a goodness-of-fit measure similar to AIC but correcting for model complexity and sample size?

Which criterion is a goodness-of-fit measure similar to AIC but correcting for model complexity and sample size?

• A. CAIC (Bozdogan's criterion)
• B. AIC (Akaike information criterion)
• C. BIC (Bayesian information criterion)
• D. SBC (Schwarz Bayesian criterion)

Answer: (A)

Balancing fit with parsimony is what these information criteria do. AIC penalizes each extra parameter with a fixed amount, which works well in small samples but doesn’t account for how much data you have. CAIC (Bozdogan’s criterion) keeps the same likelihood-based foundation but changes the penalty to k times (ln(n) + 1). That means the penalty grows with sample size, adding more penalty for extra parameters as you collect more data. In this way, CAIC remains similar to AIC in using a likelihood plus a penalty for complexity, but it also corrects for sample size, making it more conservative in larger samples. The result is a criterion that tends to guard against overfitting by incorporating both model complexity and how much data you’ve got.

Balancing fit with parsimony is what these information criteria do. AIC penalizes each extra parameter with a fixed amount, which works well in small samples but doesn’t account for how much data you have. CAIC (Bozdogan’s criterion) keeps the same likelihood-based foundation but changes the penalty to k times (ln(n) + 1). That means the penalty grows with sample size, adding more penalty for extra parameters as you collect more data. In this way, CAIC remains similar to AIC in using a likelihood plus a penalty for complexity, but it also corrects for sample size, making it more conservative in larger samples. The result is a criterion that tends to guard against overfitting by incorporating both model complexity and how much data you’ve got.