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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 …