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Comparing Optimization Algorithms for Item Selection in Mokken Scale Analysis

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  • J. Straat
  • L. Ark
  • Klaas Sijtsma

Abstract

Mokken scale analysis uses an automated bottom-up stepwise item selection procedure that suffers from two problems. First, when selected during the procedure items satisfy the scaling conditions but they may fail to do so after the scale has been completed. Second, the procedure is approximate and thus may not produce the optimal item partitioning. This study investigates a variation on Mokken’s item selection procedure, which alleviates the first problem, and proposes a genetic algorithm, which alleviates both problems. The genetic algorithm is an approximation to checking all possible partitionings. A simulation study shows that the genetic algorithm leads to better scaling results than the other two procedures. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:30:y:2013:i:1:p:75-99
    DOI: 10.1007/s00357-013-9122-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. van der Ark, L. Andries, 2007. "Mokken Scale Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i11).
    4. 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.
    5. Jinming Zhang & William Stout, 1999. "The theoretical detect index of dimensionality and its application to approximate simple structure," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 213-249, June.
    6. Jinming Zhang, 2007. "Conditional Covariance Theory and Detect for Polytomous Items," Psychometrika, Springer;The Psychometric Society, vol. 72(1), pages 69-91, March.
    7. Brian Junker, 1991. "Essential independence and likelihood-based ability estimation for polytomous items," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 255-278, June.
    8. 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.
    9. 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.
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    4. 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).
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    6. 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.
    7. Jules L. Ellis & Klaas Sijtsma, 2023. "A Test to Distinguish Monotone Homogeneity from Monotone Multifactor Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 387-412, June.

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