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A multidimensional IRT approach for dimensionality assessment of standardised students’ tests in mathematics

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  • Michela Gnaldi

    (University of Perugia)

Abstract

Mathematics proficiency involves several content domains and processes at different levels. This essentially means that mathematics ability is a complex latent variable. In standardised testing, the complex, and unobserved, latent constructs underlying a test are traditionally appraised by expert panels through subjective measures. In the present research, we deal with the issue of dimensionality of the latent structure behind a test measuring the mathematics ability of Italian students from a statistical and objective point of view, within an IRT framework. The data refer to a national standardised test developed and collected by the Italian National Institute for the Evaluation of the Education System (INVALSI), and administered to lower secondary school students (grade 8). The model we apply is based on a class of multidimensional latent class IRT models, which allows us to ascertain the test dimensionality based on an explorative approach, and by concurrently accounting for non-constant item discrimination and a discrete latent variable formulation. Our results show that the latent abilities underlying the INVALSI test mirror the assessment objectives defined at the national level for the mathematics curriculum. We recommend the use of the proposed extended IRT models in the practice of test construction, primarily—but not exclusively—in the educational field, to support the meaningfulness of the inferences made from test scores about students’ abilities.

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  • Michela Gnaldi, 2017. "A multidimensional IRT approach for dimensionality assessment of standardised students’ tests in mathematics," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1167-1182, May.
    • Handle: RePEc:spr:qualqt:v:51:y:2017:i:3:d:10.1007_s11135-016-0323-4
    DOI: 10.1007/s11135-016-0323-4
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    References listed on IDEAS

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    1. Karl Holzinger & Frances Swineford, 1937. "The Bi-factor method," Psychometrika, Springer;The Psychometric Society, vol. 2(1), pages 41-54, March.
    2. William Stout, 1987. "A nonparametric approach for assessing latent trait unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 52(4), pages 589-617, December.
    3. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    4. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    5. Susan Embretson, 1991. "A multidimensional latent trait model for measuring learning and change," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 495-515, September.
    6. Jinming Zhang & William Stout, 1999. "The theoretical detect index of dimensionality and its application to approximate simple structure," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 213-249, June.
    7. Robert Jennrich & Peter Bentler, 2011. "Exploratory Bi-Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 537-549, October.
    8. Robert Jennrich & Peter Bentler, 2012. "Exploratory Bi-factor Analysis: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 442-454, July.
    9. Jinming Zhang & William Stout, 1999. "Conditional covariance structure of generalized compensatory multidimensional items," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 129-152, June.
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    Cited by:

    1. Francesca Fortuna & Fabrizio Maturo, 2019. "K-means clustering of item characteristic curves and item information curves via functional principal component analysis," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2291-2304, September.

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