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 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.

Relationship quality in higher education and the interplay with student engagement and loyalty

“…We used GORICA weights (Altinisik et al., 2018 ; Kuiper, 2020 ; Kuiper, Hoijtink, & Silvapulle, 2011 ), an Akaike Information Criterion (AIC; Akaike, 1978 ) type of criterion, which can evaluate order‐restricted, theory‐based hypotheses as in this study. We evaluated each of our hypotheses against its complement, representing all possible orderings (i.e., all other possible hypotheses; Vanbrabant, Van Loey, & Kuiper, 2020 ). The resulting GORICA weights quantify the support for the hypotheses and their complements (cf.…”

How to Evaluate Theory-Based Hypotheses in Meta-Analysis Using an AIC-Type Criterion

“…For instance, if is not weak, one can check the relative support of and via . Using the complement can be more powerful [ 36 ] and acts like another hypothesis of interest. Moreover, when evaluating versus its complement , the interest even lies in .…”

“…If they have the same maximum log likelihood (which leads in this example to equal support because the penalty is also the same in this example), this implies support for the border: . Even though the best hypothesis can be selected, there will be a maximum support based solely on the penalty values of the hypotheses [ 36 ]. Namely, when the sample size is large enough, the maximum log likelihood will be the same for both hypotheses which will remain to be the same for increasing sample size (even thought the maximum log likelihood value itself does change).…”

Evaluation of inequality constrained hypotheses using a generalization of the AIC.

“…Check the number of theories under consideration. If there is only one hypothesis under consideration, it should be evaluated against the complement of the hypothesis of interest representing all possible theories except the hypothesis of interest (Vanbrabant et al, 2020). Alternatively, one can use the unconstrained hypothesis representing all possible theories including the hypothesis of interest.…”