IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v048i05.html
   My bibliography  Save this article

New Developments in Mokken Scale Analysis in R

Author

Listed:
  • van der Ark, L. Andries

Abstract

Mokken (1971) developed a scaling procedure for both dichotomous and polytomous items that was later coined Mokken scale analysis (MSA). MSA has been developed ever since, and the developments until 2000 have been implemented in the software package MSP (Molenaar and Sijtsma 2000) and the R package mokken (Van der Ark 2007). This paper describes the new developments in MSA since 2000 that have been implemented in mokken since its first release in 2007. These new developments pertain to invariant item ordering, a new automated item selection procedure based on a genetic algorithm, inclusion of reliability coefficients, and the computation of standard errors for the scalability coefficients. We demonstrate all new applications using data obtained with a transitive reasoning test and a personality test.

Suggested Citation

  • van der Ark, L. Andries, 2012. "New Developments in Mokken Scale Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i05).
    • Handle: RePEc:jss:jstsof:v:048:i05
    DOI: http://hdl.handle.net/10.18637/jss.v048.i05
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v048i05/v48i05.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v048i05/mokken_2.7.2.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v048i05/v48i05.R
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v048.i05?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
    ---><---

    References listed on IDEAS

    as
    1. van der Ark, L. Andries, 2007. "Mokken Scale Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i11).
    2. L. Ark, 2005. "Stochastic Ordering Of the Latent Trait by the Sum Score Under Various Polytomous IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 283-304, June.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    4. 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.
    5. J. Straat & L. Ark & Klaas Sijtsma, 2013. "Comparing Optimization Algorithms for Item Selection in Mokken Scale Analysis," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 75-99, April.
    6. Linzer, Drew A., 2011. "Reliable Inference in Highly Stratified Contingency Tables: Using Latent Class Models as Density Estimators," Political Analysis, Cambridge University Press, vol. 19(2), pages 173-187, April.
    7. 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.
    8. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    9. L. Ark & Marcel Croon & Klaas Sijtsma, 2008. "Mokken Scale Analysis for Dichotomous Items Using Marginal Models," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 183-208, June.
    10. D. Grayson, 1988. "Two-group classification in latent trait theory: Scores with monotone likelihood ratio," Psychometrika, Springer;The Psychometric Society, vol. 53(3), pages 383-392, September.
    11. 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)

    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. 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.
    2. 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.
    3. J. Straat & L. Ark & Klaas Sijtsma, 2013. "Comparing Optimization Algorithms for Item Selection in Mokken Scale Analysis," Journal of Classification, Springer;The Classification Society, vol. 30(1), pages 75-99, April.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. L. Ark, 2005. "Stochastic Ordering Of the Latent Trait by the Sum Score Under Various Polytomous IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 283-304, June.
    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. repec:jss:jstsof:20:i11 is not listed on IDEAS
    11. 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.
    12. Jesper Tijmstra & Herbert Hoijtink & Klaas Sijtsma, 2015. "Evaluating Manifest Monotonicity Using Bayes Factors," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 880-896, December.
    13. 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.
    14. Tendeiro, Jorge N. & Meijer, Rob R. & Niessen, A. Susan M., 2016. "PerFit: An R Package for Person-Fit Analysis in IRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i05).
    15. Michael Brusco & Hans-Friedrich Köhn & Douglas Steinley, 2015. "An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 949-967, December.
    16. P. A. Ferrari & S. Salini, 2008. "Measuring Service Quality: The Opinion of Europeans about Utilities," Working Papers 2008.36, Fondazione Eni Enrico Mattei.
    17. Chang, Hsin-Li & Yang, Cheng-Hua, 2008. "Explore airlines’ brand niches through measuring passengers’ repurchase motivation—an application of Rasch measurement," Journal of Air Transport Management, Elsevier, vol. 14(3), pages 105-112.
    18. Ivana Bassi & Matteo Carzedda & Enrico Gori & Luca Iseppi, 2022. "Rasch analysis of consumer attitudes towards the mountain product label," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 10(1), pages 1-25, December.
    19. Samantha Bouwmeester & Klaas Sijtsma, 2004. "Measuring the ability of transitive reasoning, using product and strategy information," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 123-146, March.
    20. Antonio Caronni & Marina Ramella & Pietro Arcuri & Claudia Salatino & Lucia Pigini & Maurizio Saruggia & Chiara Folini & Stefano Scarano & Rosa Maria Converti, 2023. "The Rasch Analysis Shows Poor Construct Validity and Low Reliability of the Quebec User Evaluation of Satisfaction with Assistive Technology 2.0 (QUEST 2.0) Questionnaire," IJERPH, MDPI, vol. 20(2), pages 1-19, January.
    21. Hua-Hua Chang, 1996. "The asymptotic posterior normality of the latent trait for polytomous IRT models," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 445-463, September.

    More about this item

    Statistics

    Access and download statistics

    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:jss:jstsof:v:048:i05. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.