The Bayesian information criterion (BIC) helps compare models by balancing fit against complexity. Lower BIC is preferred among models being compared. Like AIC, it penalizes complexity, but it applies a heavier penalty, making it useful when simplicity is a priority. A single BIC value does not establish whether a model is good on its own. section 9.1.2
Use BIC as one part of an iterative model check:
- Compare candidate models rather than treating a score as an absolute verdict. Adding predictors may increase complexity without adding useful information. section 9.1.2
- Read it alongside R-squared, adjusted R-squared, and residuals. These measures address different questions about explained variation and model behavior. section 9.4
- Keep the prediction task in view: a model intended for stakeholder decisions needs useful predictions, not just an attractive summary score. section 9.1.2 section 9.3.3
Checking an added housing-price predictor
A housing-price regression initially uses square footage and bedroom count. After adding number of floors, R-squared and adjusted R-squared do not improve, and the new predictor is not statistically significant. BIC offers a further way to weigh that added complexity when comparing the fitted models; the unchanged scores already give a reason to question whether floors belongs in the simpler prediction tool. section 9.1.2
Model revisions can also change BIC without adding predictors. In a rat-sightings regression, removing an erroneous data point lowers AIC and BIC; a later outcome transformation produces still lower reported values. Residual plots remain important: removing the bad record does not resolve the other extreme residuals. Treat BIC as evidence for a comparison, not a substitute for investigating data quality and model assumptions. section 9.2.2
