Evaluation of Inequality Constrained Hypotheses Using a Generalization of the AIC

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dc.authorid, Albertine/0000-0003-3925-3913
dc.authoridAltinisik, Yasin/0000-0001-9375-2276
dc.authoridVan Lissa, Caspar/0000-0002-0808-5024
dc.authoridKuiper, Rebecca/0000-0002-0267-5197
dc.contributor.authorAltinisik, Yasin
dc.contributor.authorVan Lissa, Caspar J.
dc.contributor.authorHoijtink, Herbert
dc.contributor.authorOldehinkel, Albertine J.
dc.contributor.authorKuiper, Rebecca M.
dc.date.accessioned2025-03-23T19:35:47Z
dc.date.available2025-03-23T19:35:47Z
dc.date.issued2021
dc.departmentSinop Üniversitesi
dc.description.abstractIn the social and behavioral sciences, it is often not interesting to evaluate the null hypothesis by means of a p-value. Researchers are often more interested in quantifying the evidence in the data (as opposed to using p-values) with respect to their own expectations represented by equality and/or inequality constrained hypotheses (as opposed to the null hypothesis). This article proposes an Akaike-type information criterion (AIC; Akaike, 1973, 1974) called the generalized order-restricted information criterion approximation (GORICA) that evaluates (in)equality constrained hypotheses under a very broad range of statistical models. The results of five simulation studies provide empirical evidence showing that the performance of the GORICA on selecting the best hypothesis out of a set of (in)equality constrained hypotheses is convincing. To illustrate the use of the GORICA, the expectations of researchers are investigated in a logistic regression, multilevel regression, and structural equation model. Translational Abstract Evaluation of Inequality Constrained Hypotheses Using a Generalization of the AIC: Researchers are interested in evaluating equality and/or inequality constrained hypotheses in the context not only of normal linear models, but also of the families outside of normal linear models using a suitable information criterion. However, the available information criteria in the literature are not capable of evaluating (in) equality constrained hypotheses under such a broad range of statistical models. The main aim of this paper is to close this research gap by proposing a new information criterion named the GORICA which can be utilized to evaluate these hypotheses for generalized linear (mixed) models and structural equation models. The GORICA enables researchers to quantify the evidence in the data for two or more (in) equality constrained hypotheses. Like all the other information criteria, the GORICA has the log likelihood and penalty parts. The superiority of the GORICA over the other information criteria lies behind the use of a simple formula when calculating its log likelihood. We investigated the performance of the GORICA on choosing the true hypothesis out of a set of competing hypotheses using simulation studies for logistic regression, multilevel regression, and structural equation model. The findings in these simulation studies suggest that the GORICA has a convincing performance on choosing the true hypothesis. The use of the GORICA is illustrated for (real) data sets in line with these simulation studies.
dc.description.sponsorshipRepublic of Turkey, Ministry of National Education; Dutch Ministry of Education, Culture, and Science; Netherlands Organization for Scientific Research (NWO) [024.001.003, 451-16-019]
dc.description.sponsorshipThis research was supported by The Republic of Turkey, Ministry of National Education, the Netherlands Organization for Scientific Research (NWO; VENI Grant 451-16-019), and The Consortium on Individual Development (CID) is funded through the Gravitation program of the Dutch Ministry of Education, Culture, and Science and the Netherlands Organization for Scientific Research (NWO Grant 024.001.003). Some ideas in the article were presented at the CID symposium in 2015, the 25th and 26th Interuniversity Graduate School of Psychometrics and Sociometrics (IOPS) conferences in 2015 and 2016, respectively, and International Society for Bayesian Analysis (ISBA) in 2016.
dc.identifier.doi10.1037/met0000406
dc.identifier.endpage621
dc.identifier.issn1082-989X
dc.identifier.issn1939-1463
dc.identifier.issue5
dc.identifier.pmid34855431
dc.identifier.scopus2-s2.0-85121878794
dc.identifier.scopusqualityQ1
dc.identifier.startpage599
dc.identifier.urihttps://doi.org/10.1037/met0000406
dc.identifier.urihttps://hdl.handle.net/11486/5935
dc.identifier.volume26
dc.identifier.wosWOS:000724458100008
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakPubMed
dc.language.isoen
dc.publisherAmer Psychological Assoc
dc.relation.ispartofPsychological Methods
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectAIC
dc.subjectAkaike weights
dc.subjectGORICA
dc.subject(in)equality constrained hypotheses
dc.subjectmodel selection
dc.titleEvaluation of Inequality Constrained Hypotheses Using a Generalization of the AIC
dc.typeArticle

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