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ERIC Number: ED555726
Record Type: Non-Journal
Publication Date: 2014-Mar
Pages: 28
Abstractor: As Provided
Reference Count: 20
ISBN: N/A
ISSN: N/A
A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839
Cai, Li; Monroe, Scott
National Center for Research on Evaluation, Standards, and Student Testing (CRESST)
We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen (2013), which collapses the marginal probabilities into means and product moments. Unlike M*[subscript 2], C[subscript 2] may be computed even when the number of items is small and the number of categories is large. It is as well calibrated as the alternatives and can be more powerful than M[subscript 2]. When all items are dichotomous, C[subscript 2] becomes equivalent to M*[subscript 2], which is also equivalent to M[subscript 2]. We analyze empirical data from a patient-reported outcomes measurement development project to illustrate the potential differences in substantive conclusions that one may draw from the use of different statistics for model fit assessment.
National Center for Research on Evaluation, Standards, and Student Testing (CRESST). 300 Charles E Young Drive N, GSE&IS Building 3rd Floor, Mailbox 951522, Los Angeles, CA 90095-1522. Tel: 310-206-1532; Fax: 310-825-3883; Web site: http://www.cresst.org
Publication Type: Reports - Evaluative
Education Level: N/A
Audience: N/A
Language: English
Sponsor: Institute of Education Sciences (ED); National Institute on Drug Abuse (DHHS/PHS)
Authoring Institution: National Center for Research on Evaluation, Standards, and Student Testing
IES Funded: Yes
Grant or Contract Numbers: R305D100039; R305B080016; R01DA026943; R01DA030466