Which statement about using BIC is correct?

Which statement about using BIC is correct?

• A. Use BIC when the sample size is under 100.
• B. Use BIC when the sample size is 100.
• C. Use BIC when the sample size is between 50 and 150.
• D. Use BIC when the sample size is greater than 200.

Answer: (D)

BIC penalizes model complexity more as the dataset gets larger. Specifically, BIC = -2 log-likelihood + k log(n), so the penalty term grows with the log of the sample size. As n increases, adding parameters becomes more costly under BIC, making the criterion more conservative and tending to favor simpler models. Because of this, BIC is especially appropriate when you have a large amount of data—the asymptotic properties that justify its use (consistency in model selection) become more reliable with bigger samples. A common rule-of-thumb is to use BIC for large samples, such as when the sample size is in the hundreds. That’s why choosing a threshold like greater than 200 aligns with the idea of applying BIC to large datasets, where its stronger penalty helps prevent overfitting and supports identifying a parsimonious model that generalizes well. For smaller samples, the penalty is less dominant and AIC often performs better in terms of predictive accuracy, so BIC isn’t as advantageous there.

BIC penalizes model complexity more as the dataset gets larger. Specifically, BIC = -2 log-likelihood + k log(n), so the penalty term grows with the log of the sample size. As n increases, adding parameters becomes more costly under BIC, making the criterion more conservative and tending to favor simpler models. Because of this, BIC is especially appropriate when you have a large amount of data—the asymptotic properties that justify its use (consistency in model selection) become more reliable with bigger samples.

A common rule-of-thumb is to use BIC for large samples, such as when the sample size is in the hundreds. That’s why choosing a threshold like greater than 200 aligns with the idea of applying BIC to large datasets, where its stronger penalty helps prevent overfitting and supports identifying a parsimonious model that generalizes well.

For smaller samples, the penalty is less dominant and AIC often performs better in terms of predictive accuracy, so BIC isn’t as advantageous there.