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Modeling Omitted and Not-Reached Items in IRT Models.

Norman Rose1, Matthias von Davier2, Benjamin Nagengast3

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Summary

Item nonresponse in assessments can be nonignorable, especially for omitted or not-reached items. This study introduces a joint model to appropriately handle both types of missing responses in latent trait models.

Keywords:
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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Statistical Modeling

Background:

  • Item nonresponse is prevalent in educational and psychological assessments.
  • Unobserved variables can influence the probability of missing responses (omitted or not-reached items).
  • Ignoring nonignorable missingness can bias latent trait model results.

Purpose of the Study:

  • To address the distinct statistical properties of omitted versus not-reached items in nonresponse.
  • To develop a joint model capable of handling both types of nonignorable missing responses.
  • To evaluate the performance of the proposed model for latent trait analysis.

Main Methods:

  • Formalizing missingness using response indicators modeled jointly with the target latent trait model.
  • Differentiating statistical properties between omitted and not-reached items.
  • Deriving and applying a joint model for nonignorable missing responses.
  • Conducting a simulation study to assess model performance.

Main Results:

  • Response indicators exhibit different statistical properties for omitted and not-reached items.
  • The proposed joint model effectively accounts for both omitted and not-reached items.
  • Simulation results demonstrate the model's capability in handling nonignorable missing responses.

Conclusions:

  • A novel joint model is presented for nonignorable item nonresponse in latent trait models.
  • The model appropriately distinguishes and handles omitted and not-reached items.
  • This approach improves the accuracy of psychometric and educational assessments with missing data.