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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
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
FullText Text:
  Availability: 0
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PubType: Report
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  Data: A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839
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  Data: <searchLink fieldCode="SO" term="%22National+Center+for+Research+on+Evaluation%2C+Standards%2C+and+Student+Testing+%28CRESST%29%22"><i>National Center for Research on Evaluation, Standards, and Student Testing (CRESST)</i></searchLink>. 2014.
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  Data: 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
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  Data: 28
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  Data: Institute of Education Sciences (ED)<br />National Institute on Drug Abuse (DHHS/PHS)
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  Data: R305D100039<br />R305B080016<br />R01DA026943<br />R01DA030466
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  Data: <searchLink fieldCode="DE" term="%22Item+Response+Theory%22">Item Response Theory</searchLink><br /><searchLink fieldCode="DE" term="%22Models%22">Models</searchLink><br /><searchLink fieldCode="DE" term="%22Goodness+of+Fit%22">Goodness of Fit</searchLink><br /><searchLink fieldCode="DE" term="%22Probability%22">Probability</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Analysis%22">Statistical Analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Outcome+Measures%22">Outcome Measures</searchLink><br /><searchLink fieldCode="DE" term="%22Measurement+Techniques%22">Measurement Techniques</searchLink><br /><searchLink fieldCode="DE" term="%22Measurement%22">Measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Statistics%22">Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Computation%22">Computation</searchLink><br /><searchLink fieldCode="DE" term="%22Access+to+Information%22">Access to Information</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+Likelihood+Statistics%22">Maximum Likelihood Statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Distributions%22">Statistical Distributions</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Data%22">Statistical Data</searchLink><br /><searchLink fieldCode="DE" term="%22Tests%22">Tests</searchLink><br /><searchLink fieldCode="DE" term="%22Error+of+Measurement%22">Error of Measurement</searchLink><br /><searchLink fieldCode="DE" term="%22Evidence%22">Evidence</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+Applications%22">Mathematical Applications</searchLink><br /><searchLink fieldCode="DE" term="%22Evaluation+Methods%22">Evaluation Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+Studies%22">Statistical Studies</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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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  Label: Abstractor
  Group: Ab
  Data: As Provided
– Name: Ref
  Label: Number of References
  Group: RefInfo
  Data: 20
– Name: CodeSource
  Label: IES Funded
  Group: SrcInfo
  Data: Yes
– Name: DateEntry
  Label: Entry Date
  Group: Date
  Data: 2015
– Name: AN
  Label: Accession Number
  Group: ID
  Data: ED555726
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=ED555726
RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 28
    Subjects:
      – SubjectFull: Item Response Theory
        Type: general
      – SubjectFull: Models
        Type: general
      – SubjectFull: Goodness of Fit
        Type: general
      – SubjectFull: Probability
        Type: general
      – SubjectFull: Statistical Analysis
        Type: general
      – SubjectFull: Outcome Measures
        Type: general
      – SubjectFull: Measurement Techniques
        Type: general
      – SubjectFull: Measurement
        Type: general
      – SubjectFull: Statistics
        Type: general
      – SubjectFull: Computation
        Type: general
      – SubjectFull: Access to Information
        Type: general
      – SubjectFull: Maximum Likelihood Statistics
        Type: general
      – SubjectFull: Statistical Distributions
        Type: general
      – SubjectFull: Statistical Data
        Type: general
      – SubjectFull: Tests
        Type: general
      – SubjectFull: Error of Measurement
        Type: general
      – SubjectFull: Evidence
        Type: general
      – SubjectFull: Mathematical Applications
        Type: general
      – SubjectFull: Evaluation Methods
        Type: general
      – SubjectFull: Statistical Studies
        Type: general
    Titles:
      – TitleFull: A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839
        Type: main
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              Type: published
              Y: 2014
          Titles:
            – TitleFull: National Center for Research on Evaluation, Standards, and Student Testing (CRESST)
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