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A Multidimensional Model to Facilitate Within Person Comparison of Attributes

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Listed:
  • Mark L. Davison

    (University of Minnesota)

  • Seungwon Chung

    (US Food and Drug Administration)

  • Nidhi Kohli

    (University of Minnesota)

  • Ernest C. Davenport

    (University of Minnesota)

Abstract

In psychological research and practice, a person’s scores on two different traits or abilities are often compared. Such within-person comparisons require that measurements have equal units (EU) and/or equal origins: an assumption rarely validated. We describe a multidimensional SEM/IRT model from the literature and, using principles of conjoint measurement, show that its expected response variables satisfy the axioms of additive conjoint measurement for measurement on a common scale. In an application to Quality of Life data, the EU analysis is used as a pre-processing step to derive a simple structure Quality of Life model with three dimensions expressed in equal units. The results are used to address questions that can only be addressed by scores expressed in equal units. When the EU model fits the data, scores in the corresponding simple structure model will have added validity in that they can address questions that cannot otherwise be addressed. Limitations and the need for further research are discussed.

Suggested Citation

  • Mark L. Davison & Seungwon Chung & Nidhi Kohli & Ernest C. Davenport, 2024. "A Multidimensional Model to Facilitate Within Person Comparison of Attributes," Psychometrika, Springer;The Psychometric Society, vol. 89(1), pages 296-316, March.
    • Handle: RePEc:spr:psycho:v:89:y:2024:i:1:d:10.1007_s11336-023-09946-1
    DOI: 10.1007/s11336-023-09946-1
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    References listed on IDEAS

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    1. Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2018. "CFA Models with a General Factor and Multiple Sets of Secondary Factors," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 785-808, December.
    2. Yiu-Fai Yung & David Thissen & Lori McLeod, 1999. "On the relationship between the higher-order factor model and the hierarchical factor model," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 113-128, June.
    3. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    4. Ben Domingue, 2014. "Evaluating the Equal-Interval Hypothesis with Test Score Scales," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 1-19, January.
    5. H. Brogden, 1977. "The rasch model, the law of comparative judgment and additive conjoint measurement," Psychometrika, Springer;The Psychometric Society, vol. 42(4), pages 631-634, December.
    6. Frank Rijmen & Minjeong Jeon & Matthias von Davier & Sophia Rabe-Hesketh, 2014. "A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 235-256, August.
    7. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
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