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A Multidimensional Item Response Theory Model for Continuous and Graded Responses With Error in Persons and Items

  • Identification data

    Identifier: imarina:9173275
    Authors:
    Ferrando, Pere JNavarro-Gonzalez, David
    Abstract:
    © The Author(s) 2021. Item response theory “dual” models (DMs) in which both items and individuals are viewed as sources of differential measurement error so far have been proposed only for unidimensional measures. This article proposes two multidimensional extensions of existing DMs: the M-DTCRM (dual Thurstonian continuous response model), intended for (approximately) continuous responses, and the M-DTGRM (dual Thurstonian graded response model), intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the item response theory parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The simulation results suggest that the proposal is quite feasible, and an illustrative example based on personality data is also provided. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates if the existing unidimensional DMs were fitted on a separate-scale basis.
  • Others:

    Author, as appears in the article.: Ferrando, Pere J; Navarro-Gonzalez, David
    Department: Psicologia
    e-ISSN: 1552-3888
    URV's Author/s: Ferrando Piera, Pere Joan / Navarro González, David
    Keywords: Personality measurement Person fluctuation Multidimensional location Multidimensional item response theory Item discrimination Factor analysis
    Abstract: © The Author(s) 2021. Item response theory “dual” models (DMs) in which both items and individuals are viewed as sources of differential measurement error so far have been proposed only for unidimensional measures. This article proposes two multidimensional extensions of existing DMs: the M-DTCRM (dual Thurstonian continuous response model), intended for (approximately) continuous responses, and the M-DTGRM (dual Thurstonian graded response model), intended for ordered-categorical responses (including binary). A rationale for the extension to the multiple-content-dimensions case, which is based on the concept of the multidimensional location index, is first proposed and discussed. Then, the models are described using both the factor-analytic and the item response theory parameterizations. Procedures for (a) calibrating the items, (b) scoring individuals, (c) assessing model appropriateness, and (d) assessing measurement precision are finally discussed. The simulation results suggest that the proposal is quite feasible, and an illustrative example based on personality data is also provided. The proposals are submitted to be of particular interest for the case of multidimensional questionnaires in which the number of items per scale would not be enough for arriving at stable estimates if the existing unidimensional DMs were fitted on a separate-scale basis.
    Thematic Areas: Psychology, mathematical Psychology, educational Psychology (miscellaneous) Psychology Psicología Pedagogical & educational research Mathematics, miscellaneous Mathematics, interdisciplinary applications Matemática / probabilidade e estatística Interdisciplinar Education Educació Economia Developmental and educational psychology Ciencias sociales Applied psychology Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0013-1644
    Author's mail: perejoan.ferrando@urv.cat
    Author identifier: 0000-0002-3133-5466
    Record's date: 2024-10-12
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://journals.sagepub.com/doi/full/10.1177/0013164421998412
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Educational And Psychological Measurement. 81 (0013164421998412): 1029-1053
    APA: Ferrando, Pere J; Navarro-Gonzalez, David (2021). A Multidimensional Item Response Theory Model for Continuous and Graded Responses With Error in Persons and Items. Educational And Psychological Measurement, 81(0013164421998412), 1029-1053. DOI: 10.1177/0013164421998412
    Article's DOI: 10.1177/0013164421998412
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Applied Psychology,Developmental and Educational Psychology,Education,Mathematics, Interdisciplinary Applications,Mathematics, Miscellaneous,Psychology (Miscellaneous),Psychology, Educational,Psychology, Mathematical
    Personality measurement
    Person fluctuation
    Multidimensional location
    Multidimensional item response theory
    Item discrimination
    Factor analysis
    Psychology, mathematical
    Psychology, educational
    Psychology (miscellaneous)
    Psychology
    Psicología
    Pedagogical & educational research
    Mathematics, miscellaneous
    Mathematics, interdisciplinary applications
    Matemática / probabilidade e estatística
    Interdisciplinar
    Education
    Educació
    Economia
    Developmental and educational psychology
    Ciencias sociales
    Applied psychology
    Applied mathematics
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