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A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items

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  • Alexander Robitzsch

    (IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), Olshausenstraße 62, 24118 Kiel, Germany)

Abstract

The two-parameter normal-ogive (2PNO) model is one of the most popular item response theory (IRT) models for analyzing dichotomous items. Consistent parameter estimation of the 2PNO model using marginal maximum likelihood estimation relies on the local independence assumption. However, the assumption of local independence might be violated in practice. Likelihood-based estimation of the local dependence structure is often computationally demanding. Moreover, many IRT models that model local dependence do not have a marginal interpretation of item parameters. In this article, limited information estimation methods are reviewed that allow the convenient and straightforward handling of local dependence in estimating the 2PNO model. In detail, pairwise likelihood, weighted least squares, and normal-ogive harmonic analysis robust method (NOHARM) estimation are compared with marginal maximum likelihood estimation that ignores local dependence. A simulation study revealed that item parameters can be consistently estimated with limited information methods. At the same time, marginal maximum likelihood estimation resulted in biased item parameter estimates in the presence of local dependence. From a practical perspective, there were only minor differences regarding the statistical quality of item parameter estimates of the different estimation methods. Differences between the estimation methods are also compared for two empirical datasets.

Suggested Citation

  • Alexander Robitzsch, 2024. "A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items," Stats, MDPI, vol. 7(3), pages 1-16, June.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:3:p:35-591:d:1419508
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    References listed on IDEAS

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    1. Mark Wilson & Raymond Adams, 1995. "Rasch models for item bundles," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 181-198, June.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    3. Victoria Savalei, 2006. "Logistic Approximation to the Normal: The KL Rationale," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 763-767, December.
    4. Brian Habing & Louis Roussos, 2003. "On the need for negative local item dependence," Psychometrika, Springer;The Psychometric Society, vol. 68(3), pages 435-451, September.
    5. Steffen Fieuws & Geert Verbeke, 2006. "Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles," Biometrics, The International Biometric Society, vol. 62(2), pages 424-431, June.
    6. Steffen Fieuws & Geert Verbeke & Filip Boen & Christophe Delecluse, 2006. "High dimensional multivariate mixed models for binary questionnaire data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(4), pages 449-460, August.
    7. Katsikatsou, Myrsini & Moustaki, Irini & Yang-Wallentin, Fan & Jöreskog, Karl G., 2012. "Pairwise likelihood estimation for factor analysis models with ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4243-4258.
    8. Johan Braeken, 2011. "A Boundary Mixture Approach to Violations of Conditional Independence," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 57-76, January.
    9. Albert Maydeu-Olivares, 2001. "Multidimensional Item Response Theory Modeling of Binary Data: Large Sample Properties of NOHARM Estimates," Journal of Educational and Behavioral Statistics, , vol. 26(1), pages 51-71, March.
    10. Bengt Muthén & Albert Satorra, 1995. "Technical aspects of Muthén's liscomp approach to estimation of latent variable relations with a comprehensive measurement model," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 489-503, December.
    11. Aristidis Nikoloulopoulos & Harry Joe, 2015. "Factor Copula Models for Item Response Data," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 126-150, March.
    12. Yoshio Takane & Jan Leeuw, 1987. "On the relationship between item response theory and factor analysis of discretized variables," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 393-408, September.
    13. Johan Braeken & Francis Tuerlinckx & Paul Boeck, 2007. "Copula Functions for Residual Dependency," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 393-411, September.
    14. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    15. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    16. Edward Ip, 2001. "Testing for local dependency in dichotomous and polytomous item response models," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 109-132, March.
    17. Anders Christoffersson, 1977. "Two-step weighted least squares factor analysis of dichotomized variables," Psychometrika, Springer;The Psychometric Society, vol. 42(3), pages 433-438, September.
    18. Renard, Didier & Molenberghs, Geert & Geys, Helena, 2004. "A pairwise likelihood approach to estimation in multilevel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 649-667, January.
    19. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 5-32, March.
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