A flexible approach to modelling over‐, under‐ and equidispersed count data in IRT: the Two‐Parameter Conway–Maxwell–Poisson model

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dc.contributor.authorBeisemann, Marie
dc.date.accessioned2024-02-22T12:57:06Z
dc.date.available2024-02-22T12:57:06Z
dc.date.issued2022-06-09
dc.description.abstractSeveral psychometric tests and self-reports generate count data (e.g., divergent thinking tasks). The most prominent count data item response theory model, the Rasch Poisson Counts Model (RPCM), is limited in applicability by two restrictive assumptions: equal item discriminations and equidispersion (conditional mean equal to conditional variance). Violations of these assumptions lead to impaired reliability and standard error estimates. Previous work generalized the RPCM but maintained some limitations. The two-parameter Poisson counts model allows for varying discriminations but retains the equidispersion assumption. The Conway–Maxwell–Poisson Counts Model allows for modelling over- and underdispersion (conditional mean less than and greater than conditional variance, respectively) but still assumes constant discriminations. The present work introduces the Two-Parameter Conway–Maxwell–Poisson (2PCMP) model which generalizes these three models to allow for varying discriminations and dispersions within one model, helping to better accommodate data from count data tests and self-reports. A marginal maximum likelihood method based on the EM algorithm is derived. An implementation of the 2PCMP model in R and C++ is provided. Two simulation studies examine the model's statistical properties and compare the 2PCMP model to established models. Data from divergent thinking tasks are reanalysed with the 2PCMP model to illustrate the model's flexibility and ability to test assumptions of special cases.en
dc.description.abstractCorrection for this article: https://doi.org/10.1111/bmsp.12312en
dc.identifier.urihttp://hdl.handle.net/2003/42348
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-24185
dc.language.isoende
dc.relation.ispartofseriesBritish journal of mathematical and statistical psychology;75(3)
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/de
dc.subjectConway–Maxwell–Poisson distributionen
dc.subjectCount dataen
dc.subjectEM algorithmen
dc.subjectItem response theoryen
dc.subjectOverdispersionen
dc.subjectUnderdispersionen
dc.subject.ddc310
dc.titleA flexible approach to modelling over‐, under‐ and equidispersed count data in IRT: the Two‐Parameter Conway–Maxwell–Poisson modelen
dc.typeTextde
dc.type.publicationtypeArticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationBeisemann, M. (2022), A flexible approach to modelling over-, under- and equidispersed count data in IRT: The Two-Parameter Conway–Maxwell–Poisson Model. Br J Math Stat Psychol, 75: 411-443. https://doi.org/10.1111/bmsp.12273de
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1111/bmsp.12273de

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