IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v133y2015icp136-139.html
   My bibliography  Save this article

A test for using the sum score to obtain a stochastic ordering of subjects

Author

Listed:
  • Ligtvoet, R.

Abstract

For many psychological test applications, the simple sum score across the items is used to make inferences about subjects. However, most of the item response theory models for psychological test data do not support such usage of the sum score. A simple test is proposed to assess whether the sum score can be used to obtain a stochastic ordering of subjects. This test is based on general (nonparametric) conditions and requires only the estimation of the unconstrained proportions.

Suggested Citation

  • Ligtvoet, R., 2015. "A test for using the sum score to obtain a stochastic ordering of subjects," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 136-139.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:136-139
    DOI: 10.1016/j.jmva.2014.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002000
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.09.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Rudy Ligtvoet, 2012. "An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 479-494, July.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. Fumiko Samejima, 1995. "Acceleration model in the heterogeneous case of the general graded response model," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 549-572, December.
    4. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 499-516, December.
    5. Bas Hemker & Klaas Sijtsma & Ivo Molenaar & Brian Junker, 1996. "Polytomous IRT models and monotone likelihood ratio of the total score," Psychometrika, Springer;The Psychometric Society, vol. 61(4), pages 679-693, December.
    6. Hartmann Scheiblechner, 1995. "Isotonic ordinal probabilistic models (ISOP)," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 281-304, June.
    7. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    8. Bas Hemker & Klaas Sijtsma & Ivo Molenaar & Brian Junker, 1997. "Stochastic ordering using the latent trait and the sum score in polytomous IRT models," Psychometrika, Springer;The Psychometric Society, vol. 62(3), pages 331-347, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Elina Robeva & Bernd Sturmfels & Ngoc Tran & Caroline Uhler, 2021. "Maximum likelihood estimation for totally positive log‐concave densities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 817-844, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    2. Rudy Ligtvoet, 2012. "An Isotonic Partial Credit Model for Ordering Subjects on the Basis of Their Sum Scores," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 479-494, July.
    3. Rudy Ligtvoet, 2022. "Incomplete Tests of Conditional Association for the Assessment of Model Assumptions," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1214-1237, December.
    4. Jesper Tijmstra & Maria Bolsinova, 2019. "Bayes Factors for Evaluating Latent Monotonicity in Polytomous Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 846-869, September.
    5. van der Ark, L.A., 1999. "A reference card for the relationships between IRT models for ordered polytomous items and some relevant properties," WORC Paper 99.10.02, Tilburg University, Work and Organization Research Centre.
    6. Rudy Ligtvoet, 2015. "Remarks and a Correction of Ligtvoet’s Treatment of the Isotonic Partial Credit Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 514-515, June.
    7. Rudy Ligtvoet & L. Ark & Wicher Bergsma & Klaas Sijtsma, 2011. "Polytomous Latent Scales for the Investigation of the Ordering of Items," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 200-216, April.
    8. Fumiko Samejima, 1997. "Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 471-493, December.
    9. Daphna Harel & Russell J. Steele, 2018. "An Information Matrix Test for the Collapsing of Categories Under the Partial Credit Model," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 721-750, December.
    10. L. Ark & Wicher Bergsma, 2010. "A Note on Stochastic Ordering of the Latent Trait Using the Sum of Polytomous Item Scores," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 272-279, June.
    11. Klaas Sijtsma & Bas Hemker, 1998. "Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models," Psychometrika, Springer;The Psychometric Society, vol. 63(2), pages 183-200, June.
    12. Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    13. Nowak, Piotr Bolesław, 2016. "The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 49-54.
    14. Chi, Chang Koo & Murto, Pauli & Valimaki, Juuso, 2017. "All-Pay Auctions with Affiliated Values," MPRA Paper 80799, University Library of Munich, Germany.
    15. Vikram Krishnamurthy & Udit Pareek, 2015. "Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results," Operations Research, INFORMS, vol. 63(2), pages 428-434, April.
    16. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    17. Prokopovych, Pavlo & Yannelis, Nicholas C., 2019. "On monotone approximate and exact equilibria of an asymmetric first-price auction with affiliated private information," Journal of Economic Theory, Elsevier, vol. 184(C).
    18. Patricio S. Dalton & Sayantan Ghosal & Anandi Mani, 2016. "Poverty and Aspirations Failure," Economic Journal, Royal Economic Society, vol. 126(590), pages 165-188, February.
    19. Bhattacharya, Bhaskar, 2012. "Covariance selection and multivariate dependence," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 212-228.
    20. Klaas Sijtsma & Rob Meijer, 2001. "The person response function as a tool in person-fit research," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 191-207, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:136-139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.