A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839
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| Title: | A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839 |
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| Language: | English |
| Authors: | Cai, Li, Monroe, Scott, National Center for Research on Evaluation, Standards, and Student Testing |
| Source: | National Center for Research on Evaluation, Standards, and Student Testing (CRESST). 2014. |
| Availability: | 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 |
| Peer Reviewed: | N |
| Page Count: | 28 |
| Publication Date: | 2014 |
| Sponsoring Agency: | Institute of Education Sciences (ED) National Institute on Drug Abuse (DHHS/PHS) |
| Contract Number: | R305D100039 R305B080016 R01DA026943 R01DA030466 |
| Document Type: | Reports - Evaluative |
| Descriptors: | Item Response Theory, Models, Goodness of Fit, Probability, Statistical Analysis, Outcome Measures, Measurement Techniques, Measurement, Statistics, Computation, Access to Information, Maximum Likelihood Statistics, Statistical Distributions, Statistical Data, Tests, Error of Measurement, Evidence, Mathematical Applications, Evaluation Methods, Statistical Studies |
| Abstract: | 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. |
| Abstractor: | As Provided |
| Number of References: | 20 |
| IES Funded: | Yes |
| Entry Date: | 2015 |
| Accession Number: | ED555726 |
| Database: | ERIC |
| Abstract: | 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. |
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