Title stata.com BIC note — Calculating and interpreting BIC Description Remarks and examples Methods and formulas References Also see Description

This entry discusses a statistical issue that arises when using the Bayesian information criterion (BIC) to compare models. Stata calculates BIC, assuming N = e(N)—we will explain—but sometimes it would be better if a different N were used. Commands that calculate BIC have an n() option, allowing you to specify the N to be used. In summary, 1. If you are comparing results estimated by the same estimation command, using the default BIC calculation is probably fine. There is an issue, but most researchers would ignore it. 2. If you are comparing results estimated by different estimation commands, you need to be on your guard. a. If the different estimation commands share the same definitions of observations, independence, and the like, you are back in case 1. b. If they differ in these regards, you need to think about the value of N that should be used. For example, logit and xtlogit differ in that the former assumes independent observations and the latter, independent panels. c. If estimation commands differ in the events being used over which the likelihood function is calculated, the information criteria may not be comparable at all. We say information criteria because this would apply equally to the Akaike information criterion (AIC), as well as to BIC. For instance, streg and stcox produce such incomparable results. The events used by streg are the actual survival times, whereas the events used by stcox are failures within risk pools, conditional on the times at which failures occurred. Remarks and examples stata.com Remarks are presented under the following headings: Background The problem of determining N The problem of conformable likelihoods The first problem does not arise with AIC; the second problem does Calculating BIC correctl