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A Didactic Presentation of Snijders's 'l[subscript z]*' Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation

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Title: A Didactic Presentation of Snijders's 'l[subscript z]*' Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation
Language: English
Authors: Magis, David, Raiche, Gilles, Beland, Sebastien
Source: Journal of Educational and Behavioral Statistics. Feb 2012 37(1):57-81.
Availability: SAGE Publications. 2455 Teller Road, Thousand Oaks, CA 91320. Tel: 800-818-7243; Tel: 805-499-9774; Fax: 800-583-2665; e-mail: journals@sagepub.com; Web site: http://sagepub.com
Peer Reviewed: Y
Page Count: 25
Publication Date: 2012
Document Type: Journal Articles
Reports - Descriptive
Reports - Research
Descriptors: Goodness of Fit, Item Response Theory, Computation, Ability, Statistical Analysis, Models, Selection, Language Tests, English (Second Language), Foreign Countries
Geographic Terms: Canada
DOI: 10.3102/1076998610396894
ISSN: 1076-9986
Abstract: This paper focuses on two likelihood-based indices of person fit, the index "l[subscript z]" and the Snijders's modified index "l[subscript z]*". The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample ability estimates. The "l[subscript z]*" index is a generalization of "l[subscript z]", which corrects for this sampling variability. Surprisingly, it is not yet popular in the psychometric and educational assessment community. Moreover, there is some ambiguity about which type of item response model and ability estimation method can be used to compute the "l[subscript z]*" index. The purpose of this article is to present the index "l[subscript z]*" in a simple and didactic approach. Starting from the relationship between "l[subscript z]" and "l[subscript z]*", we develop the framework according to the type of logistic item response theory (IRT) model and the likelihood-based estimators of ability. The practical calculation of "l[subscript z]*" is illustrated by analyzing a real data set about language skill assessment. (Contains 2 tables and 2 figures.)
Abstractor: As Provided
Number of References: 52
Entry Date: 2012
Accession Number: EJ955250
Database: ERIC
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  Data: A Didactic Presentation of Snijders's 'l[subscript z]*' Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation
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  Data: This paper focuses on two likelihood-based indices of person fit, the index "l[subscript z]" and the Snijders's modified index "l[subscript z]*". The first one is commonly used in practical assessment of person fit, although its asymptotic standard normal distribution is not valid when true abilities are replaced by sample ability estimates. The "l[subscript z]*" index is a generalization of "l[subscript z]", which corrects for this sampling variability. Surprisingly, it is not yet popular in the psychometric and educational assessment community. Moreover, there is some ambiguity about which type of item response model and ability estimation method can be used to compute the "l[subscript z]*" index. The purpose of this article is to present the index "l[subscript z]*" in a simple and didactic approach. Starting from the relationship between "l[subscript z]" and "l[subscript z]*", we develop the framework according to the type of logistic item response theory (IRT) model and the likelihood-based estimators of ability. The practical calculation of "l[subscript z]*" is illustrated by analyzing a real data set about language skill assessment. (Contains 2 tables and 2 figures.)
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        Value: 10.3102/1076998610396894
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      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 25
        StartPage: 57
    Subjects:
      – SubjectFull: Goodness of Fit
        Type: general
      – SubjectFull: Item Response Theory
        Type: general
      – SubjectFull: Computation
        Type: general
      – SubjectFull: Ability
        Type: general
      – SubjectFull: Statistical Analysis
        Type: general
      – SubjectFull: Models
        Type: general
      – SubjectFull: Selection
        Type: general
      – SubjectFull: Language Tests
        Type: general
      – SubjectFull: English (Second Language)
        Type: general
      – SubjectFull: Foreign Countries
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      – SubjectFull: Canada
        Type: general
    Titles:
      – TitleFull: A Didactic Presentation of Snijders's 'l[subscript z]*' Index of Person Fit with Emphasis on Response Model Selection and Ability Estimation
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            NameFull: Beland, Sebastien
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