Evaluating a Theory-Based Hypothesis Against Its Complement Using an AIC-Type Information Criterion With an Application to Facial Burn Injury

Abstract

An information criterion (IC) like the Akaike IC (AIC), can be used to select the best hypothesis from a set of competing theory-based hypotheses. An IC developed to evaluate theory-based order-restricted hypotheses is the Generalized Order-Restricted Information Criterion (GORIC). Like for any IC, the values themselves are not interpretable but only comparable. To improve the interpretation regarding the strength, GORIC weights and related evidence ratios can be computed. However, if the unconstrained hypothesis (the default) is used as competing hypothesis, the evidence ratio is not affected by sample-size nor effect-size in case the hypothesis of interest is (also) in agreement with the data. In practice, this means that in such a case strong support for the order-restricted hypothesis is not reflected by a high evidence ratio. Therefore, we introduce the evaluation of an order-restricted hypothesis against its complement using the GORIC (weights). We show how to compute the GORIC value for the complement, which cannot be achieved by current methods. In a small simulation study, we show that the evidence ratio for the order-restricted hypothesis versus the complement increases for larger samples and/or effect-sizes, while the evidence ratio for the order-restricted hypothesis versus the unconstrained hypothesis remains bounded. An empirical example about facial burn injury illustrates our method and shows that using the complement as competing hypothesis results in much more support for the hypothesis of interest than using the unconstrained hypothesis as competing hypothesis.