Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types

Maxwell Hong, Lizhen Lin and Ying Cheng ()
Additional contact information
Maxwell Hong: University of Notre Dame
Lizhen Lin: University of Notre Dame
Ying Cheng: University of Notre Dame

Psychometrika, 2021, vol. 86, issue 2, No 5, 464-488

Abstract: Abstract Person fit statistics are frequently used to detect aberrant behavior when assuming an item response model generated the data. A common statistic, $$l_z$$ l z , has been shown in previous studies to perform well under a myriad of conditions. However, it is well-known that $$l_z$$ l z does not follow a standard normal distribution when using an estimated latent trait. As a result, corrections of $$l_z$$ l z , called $$l_z^*$$ l z ∗ , have been proposed in the literature for specific item response models. We propose a more general correction that is applicable to many types of data, namely survey or tests with multiple item types and underlying latent constructs, which subsumes previous work done by others. In addition, we provide corrections for multiple estimators of $$\theta $$ θ , the latent trait, including MLE, MAP and WLE. We provide analytical derivations that justifies our proposed correction, as well as simulation studies to examine the performance of the proposed correction with finite test lengths. An applied example is also provided to demonstrate proof of concept. We conclude with recommendations for practitioners when the asymptotic correction works well under different conditions and also future directions.

Keywords: person fit; item response theory; $$l_z$$ l z; Asymptotics; outlier detection; multidimensional; mixed item type (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11336-021-09756-3 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:86:y:2021:i:2:d:10.1007_s11336-021-09756-3

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

DOI: 10.1007/s11336-021-09756-3

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 ().