Asymptotically Correct Person Fit z-Statistics For the Rasch Testlet Model

Zhongtian Lin (), Tao Jiang, Frank Rijmen and Paul Wamelen
Additional contact information
Zhongtian Lin: Financial Industry Regulatory Authority
Tao Jiang: Cambium Assessment
Frank Rijmen: Cambium Assessment
Paul Wamelen: Cambium Assessment

Psychometrika, 2024, vol. 89, issue 4, No 8, 1230-1260

Abstract: Abstract A well-known person fit statistic in the item response theory (IRT) literature is the $$l_{z}$$ l z statistic (Drasgow et al. in Br J Math Stat Psychol 38(1):67-86, 1985). Snijders (Psychometrika 66(3):331-342, 2001) derived $$l_{z}^{*}$$ l z ∗ , which is the asymptotically correct version of $$l_{z}$$ l z when the ability parameter is estimated. However, both statistics and other extensions later developed concern either only the unidimensional IRT models or multidimensional models that require a joint estimate of latent traits across all the dimensions. Considering a marginalized maximum likelihood ability estimator, this paper proposes $$l_{zt}$$ l zt and $$l_{zt}^{*}$$ l zt ∗ , which are extensions of $$l_{z}$$ l z and $$l_{z}^{*}$$ l z ∗ , respectively, for the Rasch testlet model. The computation of $$l_{zt}^{*}$$ l zt ∗ relies on several extensions of the Lord-Wingersky algorithm (1984) that are additional contributions of this paper. Simulation results show that $$l_{zt}^{*}$$ l zt ∗ has close-to-nominal Type I error rates and satisfactory power for detecting aberrant responses. For unidimensional models, $$l_{zt}$$ l zt and $$l_{zt}^{*}$$ l zt ∗ reduce to $$l_{z}$$ l z and $$l_{z}^{*}$$ l z ∗ , respectively, and therefore allows for the evaluation of person fit with a wider range of IRT models. A real data application is presented to show the utility of the proposed statistics for a test with an underlying structure that consists of both the traditional unidimensional component and the Rasch testlet component.

Keywords: Person fit; IRT; $$l_{z}$$ l z statistic; Rasch testlet model (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11336-024-09997-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:89:y:2024:i:4:d:10.1007_s11336-024-09997-y

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-024-09997-y

Access Statistics for this article

Psychometrika is currently edited by Irini Moustaki

More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().