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Modeling missing data in knowledge space theory.

Debora de Chiusole1, Luca Stefanutti1, Pasquale Anselmi1

  • 1Department of Philosophy, Sociology, Pedagogy, and Applied Psychology (FISPPA), University of Padua.

Psychological Methods
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This study introduces two methods, IMBLIM and MissBLIM, to handle missing data in knowledge space theory. Both models effectively address missing data, with the choice depending on whether missingness is random or not.

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Area of Science:

  • Statistical Inference
  • Knowledge Space Theory
  • Psychometrics

Background:

  • Missing data is a common challenge in statistical analysis.
  • Handling missing responses is crucial for accurate inference.
  • Existing models may not adequately address missing data patterns.

Purpose of the Study:

  • To analyze missing data within knowledge space theory.
  • To propose and evaluate extensions of the basic local independence model (BLIM) for missing data.
  • To compare the performance of different models based on missing data mechanisms.

Main Methods:

  • Developed two extensions of the basic local independence model (BLIM): ignorable missing BLIM (IMBLIM) and missing BLIM (MissBLIM).
  • IMBLIM assumes missing data are missing completely at random (MCAR).
  • MissBLIM models dependencies between missing data and knowledge states, assuming missing not at random (MNAR).
  • Evaluated models using a simulation study and an empirical application.

Main Results:

  • Both IMBLIM and MissBLIM demonstrated satisfactory modeling of missing data.
  • When data are missing completely at random, both models provide adequate fit.
  • When missingness depends on unobservable data features (MNAR), only a correctly specified missingness model ensures adequate fit.

Conclusions:

  • The choice between IMBLIM and MissBLIM depends on the underlying missing data-generating process.
  • Accurate modeling of missing data mechanisms is essential for reliable statistical inference.
  • MissBLIM offers a more robust approach when missing data patterns are not completely random.