Explain the role of AIC and BIC in model selection.

Instruction: Define AIC and BIC and describe how they are used in selecting the best statistical model.

Context: This question tests the candidate's knowledge of model selection criteria and their ability to apply these criteria to choose the most appropriate model.

Updated

Official answer

For a maximized log-likelihood ℓ and parameter count k, AIC = −2ℓ + 2k and BIC = −2ℓ + k log(n). Lower values are preferred within an appropriate comparison set; neither is an absolute goodness-of-fit certificate.

For n=100, model A with ℓ=−100 and k=3 has AIC 206 and BIC about 213.82. Model B with ℓ=−98 and k=4 has AIC 204 and BIC about 214.42. AIC prefers B while BIC prefers A, illustrating different complexity penalties.

Compare fits to the same response observations using compatible likelihood definitions and constants. Different missing-data subsets or unadjusted response transformations can invalidate a comparison. Do not casually compare REML criteria across different fixed-effect structures.

AIC targets a predictive information-loss tradeoff under its assumptions; BIC has a different asymptotic model-evidence motivation. Check diagnostics, sample-size limitations and out-of-sample performance appropriate to the task. The lowest candidate score does not show that the selected model is true.

Reference: R information-criterion documentation.

Related Questions