What is the criterion regarding sample size when using BIC as a check?

What is the criterion regarding sample size when using BIC as a check?

• A. BIC greater than zero indicates sufficient sample size.
• B. BIC less than zero indicates sufficient sample size.
• C. BIC is not used for sample size checks.
• D. BIC equals zero indicates sufficient sample size.

Answer: (A)

BIC balances how well the model fits the data with a penalty for complexity that grows with the sample size. The formula is BIC = -2 log L + k log n, where L is the likelihood, k is the number of parameters, and n is the sample size. Because the first term (-2 log L) is nonnegative and the second term (k log n) is also nonnegative, BIC itself is nonnegative. When using BIC as a check for whether the sample is large enough to support the model, a BIC value greater than zero is taken as evidence that there is enough information in the data to justify the model’s complexity given the sample size. A BIC of zero would be a degenerate case, and negative values are not possible with this form. Therefore, the rule of thumb is that BIC exceeding zero indicates sufficient sample size for the check.

BIC balances how well the model fits the data with a penalty for complexity that grows with the sample size. The formula is BIC = -2 log L + k log n, where L is the likelihood, k is the number of parameters, and n is the sample size. Because the first term (-2 log L) is nonnegative and the second term (k log n) is also nonnegative, BIC itself is nonnegative. When using BIC as a check for whether the sample is large enough to support the model, a BIC value greater than zero is taken as evidence that there is enough information in the data to justify the model’s complexity given the sample size. A BIC of zero would be a degenerate case, and negative values are not possible with this form. Therefore, the rule of thumb is that BIC exceeding zero indicates sufficient sample size for the check.