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

Cited by Lee Sonogan

Item Response Theory - SAGE Research Methods

Abstract by Pere J. Ferrando, David Navarro-González

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.

Publication: Educational and Psychological Measurement (Peer-Reviewed Journal)

Pub Date: Mar 10, 2021 Doi:

Keywords: personality measurement, person fluctuation, item discrimination, factor analysis, multidimensional location, multidimensional item response theory (Plenty more sections and references in this research article)

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