The Bayesian Information Criterion (BIC) is a statistical measure that analysts use to compare models and select the one that best balances goodness-of-fit with model simplicity (i.e., a parsimonious model). Like the Akaike Information Criterion (AIC), BIC penalizes models for having more parameters to discourage overfitting. However, BIC applies a stronger penalty for complexity, especially as sample size increases. Consequently, it tends to favor simpler models more strongly than AIC when the sample size is large.
To interpret BIC, analysts compare the BIC values of two or more models fitted to the same data. The model with the lowest BIC is generally preferred. Unlike p-values, BIC doesn’t produce a significance test—it’s a relative measure. A difference of 10 or more between two BIC values is typically considered strong evidence in favor of the model with the lower value. Because it accounts for both fit and parsimony, BIC helps analysts avoid overly complex models that might not generalize well to new data.
For example, a data analyst modeling student performance might compare two regression models: one with only a few key predictors (like study hours and attendance), and another that includes dozens of additional variables. If the simpler model has a lower BIC, it would be preferred—even if the complex model fits slightly better—because the BIC suggests the added complexity isn’t justified by the improvement.