Parsimonious item response theory modeling with the negative log-log link: The role of inflection point shift

Shim, Hye-jin; Bonifay, Wes; Wiedermann, Wolfgang

doi:10.3758/s13428-023-02189-z

Cited by 2 publications

(1 citation statement)

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“…Notably, (9) defines a general class of IRT models that share the invariant item-ordering property [44,45]. Alternative link functions to the logistic one, such as the loglog or cloglog link functions [46], can be chosen in (9) (see [47,48]). However, it must be emphasized that the sum score is no longer a sufficient statistic for θ in the general one-parameter IRT model defined in (9).…”

Section: Generalized Logistic Item Response Modelmentioning

confidence: 99%

Relating the One-Parameter Logistic Diagnostic Classification Model to the Rasch Model and One-Parameter Logistic Mixed, Partial, and Probabilistic Membership Diagnostic Classification Models

Robitzsch

2023

Foundations

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Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one skill and shares desirable measurement properties with the Rasch model. This article shows that the 1PLDCM is indeed a latent class Rasch model. Furthermore, the relationship of the 1PLDCM to extensions of the DCM to mixed, partial, and probabilistic memberships is treated. It is argued that the partial and probabilistic membership models are also equivalent to the Rasch model. The fit of the different models was empirically investigated using six datasets. It turned out for these datasets that the 1PLDCM always had a worse fit than the Rasch model and mixed and partial membership extensions of the DCM.

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