Which statement correctly contrasts AIC and BIC in model selection?

Which statement correctly contrasts AIC and BIC in model selection?

• A. AIC penalizes complexity more heavily than BIC
• B. AIC and BIC always select identical models
• C. BIC ignores model fit
• D. BIC penalizes complexity more heavily and tends to favor simpler models

Answer: (D)

Both AIC and BIC balance how well a model fits the data with how complex the model is, but they penalize complexity differently. AIC uses a penalty proportional to the number of parameters (2k), while BIC uses a penalty that grows with both the number of parameters and the sample size (k log n). Because log n increases as more data are collected, BIC’s penalty often becomes larger than AIC’s for typical datasets. This makes BIC more inclined to favor simpler models as the sample size grows, compared with AIC. That’s why the statement that BIC penalizes complexity more heavily and tends to favor simpler models is correct. The other options are not accurate: AIC does not penalize more heavily than BIC; AIC and BIC do not always select the same model; and BIC does consider model fit through the -2 log-likelihood component, not ignore it.

Both AIC and BIC balance how well a model fits the data with how complex the model is, but they penalize complexity differently. AIC uses a penalty proportional to the number of parameters (2k), while BIC uses a penalty that grows with both the number of parameters and the sample size (k log n). Because log n increases as more data are collected, BIC’s penalty often becomes larger than AIC’s for typical datasets. This makes BIC more inclined to favor simpler models as the sample size grows, compared with AIC. That’s why the statement that BIC penalizes complexity more heavily and tends to favor simpler models is correct. The other options are not accurate: AIC does not penalize more heavily than BIC; AIC and BIC do not always select the same model; and BIC does consider model fit through the -2 log-likelihood component, not ignore it.