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Stochastic ordering using the latent trait and the sum score in polytomous IRT models


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  • Bas Hemker
  • Klaas Sijtsma
  • Ivo Molenaar
  • Brian Junker
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    Bibliographic Info

    Article provided by Springer in its journal Psychometrika.

    Volume (Year): 62 (1997)
    Issue (Month): 3 (September)
    Pages: 331-347

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    Handle: RePEc:spr:psycho:v:62:y:1997:i:3:p:331-347

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    Keywords: monotone likelihood ratio; nonparametric IRT models; parametric IRT models; polytomous IRT models; stochastic ordering;


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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. D. Grayson, 1988. "Two-group classification in latent trait theory: Scores with monotone likelihood ratio," Psychometrika, Springer, vol. 53(3), pages 383-392, September.
    2. Huynh Huynh, 1994. "A new proof for monotone likelihood ratio for the sum of independent bernoulli random variables," Psychometrika, Springer, vol. 59(1), pages 77-79, March.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer, vol. 47(2), pages 149-174, June.
    4. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer, vol. 43(4), pages 561-573, December.
    5. Bas Hemker & Klaas Sijtsma & Ivo Molenaar & Brian Junker, 1996. "Polytomous IRT models and monotone likelihood ratio of the total score," Psychometrika, Springer, vol. 61(4), pages 679-693, December.
    6. William Strout, 1990. "A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation," Psychometrika, Springer, vol. 55(2), pages 293-325, June.
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    Cited by:
    1. Francesco Bartolucci & Antonio Forcina, 2005. "Likelihood inference on the underlying structure of IRT models," Psychometrika, Springer, vol. 70(1), pages 31-43, March.
    2. Johnson, Matthew S., 2007. "Modeling dichotomous item responses with free-knot splines," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4178-4192, May.
    3. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer, vol. 66(4), pages 487-506, December.
    4. Hartmann Scheiblechner, 2007. "A Unified Nonparametric IRT Model for d-Dimensional Psychological Test Data (d-ISOP)," Psychometrika, Springer, vol. 72(1), pages 43-67, March.
    5. Rudy Ligtvoet & L. Ark & Wicher Bergsma & Klaas Sijtsma, 2011. "Polytomous Latent Scales for the Investigation of the Ordering of Items," Psychometrika, Springer, vol. 76(2), pages 200-216, April.
    6. L. Ark, 2005. "Stochastic Ordering Of the Latent Trait by the Sum Score Under Various Polytomous IRT Models," Psychometrika, Springer, vol. 70(2), pages 283-304, June.
    7. Hartman Scheiblechner, 1999. "Additive conjoint isotonic probabilistic models (ADISOP)," Psychometrika, Springer, vol. 64(3), pages 295-316, September.
    8. L. Ark & Wicher Bergsma, 2010. "A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores," Psychometrika, Springer, vol. 75(2), pages 272-279, June.
    9. Klaas Sijtsma & Rob Meijer, 2001. "The person response function as a tool in person-fit research," Psychometrika, Springer, vol. 66(2), pages 191-207, June.
    10. Theo Eggen & Norman Verhelst, 2006. "Loss of Information in Estimating Item Parameters in Incomplete Designs," Psychometrika, Springer, vol. 71(2), pages 303-322, June.
    11. Jesper Tijmstra & David Hessen & Peter Heijden & Klaas Sijtsma, 2013. "Testing Manifest Monotonicity Using Order-Constrained Statistical Inference," Psychometrika, Springer, vol. 78(1), pages 83-97, January.
    12. Samantha Bouwmeester & Klaas Sijtsma, 2004. "Measuring the ability of transitive reasoning, using product and strategy information," Psychometrika, Springer, vol. 69(1), pages 123-146, March.
    13. Rudy Ligtvoet, 2012. "An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores," Psychometrika, Springer, vol. 77(3), pages 479-494, July.
    14. Wim Linden, 1998. "Stochastic order in dichotomous item response models for fixed, adaptive, and multidimensional tests," Psychometrika, Springer, vol. 63(3), pages 211-226, September.


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