Which statement about AIC is true?

Which statement about AIC is true?

• A. AIC is corrected for model complexity.
• B. AIC always decreases with more parameters.
• C. AIC cannot be compared across models.
• D. AIC measures the maximum likelihood only.

Answer: (A)

AIC balances goodness-of-fit with model simplicity. It combines the likelihood of the data under the model with a penalty that rises with the number of estimated parameters, so adding parameters only lowers AIC if the improvement in fit is large enough to overcome that penalty. The formula shows this clearly: AIC = -2 times the log-likelihood plus 2k, where k is the number of parameters. This means AIC is a relative measure used to compare models fitted to the same data—the model with the smallest AIC is preferred. It’s not just about maximum likelihood, since the penalty prevents overfitting by rewarding simpler models unless the extra parameters genuinely improve fit.

AIC balances goodness-of-fit with model simplicity. It combines the likelihood of the data under the model with a penalty that rises with the number of estimated parameters, so adding parameters only lowers AIC if the improvement in fit is large enough to overcome that penalty. The formula shows this clearly: AIC = -2 times the log-likelihood plus 2k, where k is the number of parameters. This means AIC is a relative measure used to compare models fitted to the same data—the model with the smallest AIC is preferred. It’s not just about maximum likelihood, since the penalty prevents overfitting by rewarding simpler models unless the extra parameters genuinely improve fit.