14.3 A few cautionary notes

• Information criteria a relative measures. In a study it may be more helpful to report the change in the information criteria, or even a ratio (see Burnham and Anderson (2002) for a detailed analysis).
• Information criteria are not cross-comparable across studies. If you are pulling in a model from another study, it is helpful to re-calculate the information criteria.
• An advantage to the \(BIC\) is that it measures tradeoffs between favoring a model that has the fewer number of data needed to estimate parameters. Other information criteria examine the distribution of the likelihood function and parameters.

The upshot: Information criteria are one piece of evidence to help you to evaluate the best approximating model. You should do additional investigation (parameter evaluation, model-data fits, forecast values) in order to help determine the best model.

References

Burnham, Kenneth P., and David R. Anderson, eds. 2002. Model Selection and Multimodel Inference. New York, NY: Springer New York.