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On Fair Person Classification Based on Efficient Factor Score Estimates in the Multidimensional Factor Analysis Model

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  • Pascal Jordan

    (University of Hamburg)

  • Martin Spiess

    (University of Hamburg)

Abstract

Since Hooker, Finkelman and Schwartzman (Psychometrika 74(3): 419–442, 2009) it is known that person parameter estimates from multidimensional latent variable models can induce unfair classifications via paradoxical scoring effects. The open question as to whether there is a fair and at the same time multidimensional scoring scheme with adequate statistical properties is addressed in this paper. We develop a theorem on the existence of a fair, multidimensional classification scheme in the context of the classical linear factor analysis model and show how the computation of the scoring scheme can be embedded in the context of linear programming. The procedure is illustrated in the framework of scoring the Wechsler Adult Intelligence Scale (WAIS-IV).

Suggested Citation

  • Pascal Jordan & Martin Spiess, 2018. "On Fair Person Classification Based on Efficient Factor Score Estimates in the Multidimensional Factor Analysis Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 563-585, September.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:3:d:10.1007_s11336-018-9613-1
    DOI: 10.1007/s11336-018-9613-1
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    References listed on IDEAS

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    1. Giles Hooker & Matthew Finkelman, 2010. "Paradoxical Results and Item Bundles," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 249-271, June.
    2. Wim Krijnen & Theo Dijkstra & Richard Gill, 1998. "Conditions for factor (in)determinacy in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 63(4), pages 359-367, December.
    3. Matthew D. Finkelman & Giles Hooker & Zhen Wang, 2010. "Prevalence and Magnitude of Paradoxical Results in Multidimensional Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 744-761, December.
    4. Pascal Jordan & Martin Spiess, 2012. "Generalizations of Paradoxical Results in Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 127-152, January.
    5. Wim Linden, 2012. "On Compensation in Multidimensional Response Modeling," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 21-30, January.
    6. Giles Hooker, 2010. "On Separable Tests, Correlated Priors, and Paradoxical Results in Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 694-707, December.
    7. James Steiger, 1979. "Factor indeterminacy in the 1930's and the 1970's some interesting parallels," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 157-167, June.
    8. Jules Ellis & Brian Junker, 1997. "Tail-measurability in monotone latent variable models," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 495-523, December.
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