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Modeling Omitted and Not-Reached Items in IRT Models

Author

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  • Norman Rose

    (University of Tübingen)

  • Matthias Davier

    (Educational Testing Service)

  • Benjamin Nagengast

    (University of Tübingen)

Abstract

Item nonresponse is a common problem in educational and psychological assessments. The probability of unplanned missing responses due to omitted and not-reached items may stochastically depend on unobserved variables such as missing responses or latent variables. In such cases, missingness cannot be ignored and needs to be considered in the model. Specifically, multidimensional IRT models, latent regression models, and multiple-group IRT models have been suggested for handling nonignorable missing responses in latent trait models. However, the suitability of the particular models with respect to omitted and not-reached items has rarely been addressed. Missingness is formalized by response indicators that are modeled jointly with the researcher’s target model. We will demonstrate that response indicators have different statistical properties depending on whether the items were omitted or not reached. The implications of these differences are used to derive a joint model for nonignorable missing responses with ability to appropriately account for both omitted and not-reached items. The performance of the model is demonstrated by means of a small simulation study.

Suggested Citation

  • Norman Rose & Matthias Davier & Benjamin Nagengast, 2017. "Modeling Omitted and Not-Reached Items in IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 795-819, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-016-9544-7
    DOI: 10.1007/s11336-016-9544-7
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    Cited by:

    1. Jinxin Guo & Xin Xu & Zhiliang Ying & Susu Zhang, 2022. "Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 835-867, September.
    2. Matthias von Davier & Youngmi Cho & Tianshu Pan, 2019. "Effects of Discontinue Rules on Psychometric Properties of Test Scores," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 147-163, March.
    3. Susu Zhang & Zhi Wang & Jitong Qi & Jingchen Liu & Zhiliang Ying, 2023. "Accurate Assessment via Process Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 76-97, March.
    4. Simon Grund & Oliver Lüdtke & Alexander Robitzsch, 2021. "On the Treatment of Missing Data in Background Questionnaires in Educational Large-Scale Assessments: An Evaluation of Different Procedures," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 430-465, August.
    5. Sandip Sinharay, 2022. "Reporting Proficiency Levels for Examinees With Incomplete Data," Journal of Educational and Behavioral Statistics, , vol. 47(3), pages 263-296, June.
    6. Robitzsch, Alexander, 2020. "About Still Nonignorable Consequences of (Partially) Ignoring Missing Item Responses in Large-scale Assessment," OSF Preprints hmy45, Center for Open Science.

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