Sensitivity and specificity of information criteria

Information criteria (ICs) based on penalized likelihood, such as Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and sample-size-adjusted versions of them, are widely used for model selection in health and biological research. However, different criteria sometimes support different models, leading to discussions about which is the most trustworthy. Some researchers and fields of study habitually use one or the other, often without a clearly stated justification. They may not realize that the criteria may disagree. Others try to compare models using multiple criteria but encounter ambiguity when different criteria lead to substantively different answers, leading to questions about which criterion is best. In this paper we present an alternative perspective on these criteria that can help in interpreting their practical implications. Specifically, in some cases the comparison of two models using ICs can be viewed as equivalent to a likelihood ratio test, with the different criteria representing different alpha levels and BIC being a more conservative test than AIC. This perspective may lead to insights about how to interpret the ICs in more complex situations. For example, AIC or BIC could be preferable, depending on the relative importance one assigns to sensitivity versus specificity. Understanding the differences and similarities among the ICs can make it easier to compare their results and to use them to make informed decisions.