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Multidimensional Test Assembly Using Mixed-Integer Linear Programming: An Application of Kullback-Leibler

Dries Debeer1, Peter W van Rijn2, Usama S Ali3,4

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|December 20, 2019
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Summary
This summary is machine-generated.

This study introduces new statistical targets for creating parallel test forms using mixed-integer linear programming (MILP). Kullback-Leibler divergence shows promise for assembling multidimensional tests with minimal item overlap.

Keywords:
Kullback–Leibler informationMIRTautomated test assemblylinear programming

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Computer Science (Optimization)

Background:

  • Educational testing requires parallel test forms with no item overlap but similar statistical properties.
  • Mixed-integer linear programming (MILP) is used for test assembly, with Fisher information (FI) as a common target in unidimensional cases.
  • Multidimensional FI complicates its use as a target for linear test form assembly, and existing multidimensional computerized adaptive testing (MCAT) criteria are not directly applicable.

Purpose of the Study:

  • To derive and evaluate new statistical targets for assembling multidimensional parallel test forms using MILP.
  • To address the limitations of using multidimensional Fisher information (FI) in MILP for linear test assembly.
  • To compare the effectiveness of FI-based and Kullback-Leibler (KL) divergence-based targets.

Main Methods:

  • Derivation of novel statistical targets based on Fisher information (FI) and Kullback-Leibler (KL) divergence for MILP.
  • Application of these targets in MILP models for assembling multidimensional parallel test forms.
  • Evaluation using simulated and empirical item pools.

Main Results:

  • The study successfully derived new statistical targets for multidimensional test assembly.
  • Kullback-Leibler (KL) divergence-based targets demonstrated promising results in assembling parallel test forms.
  • The proposed targets are suitable for MILP models in the context of linear test assembly.

Conclusions:

  • New statistical targets, particularly those based on KL divergence, offer a viable solution for assembling multidimensional parallel test forms.
  • The developed methods improve upon existing approaches for test assembly in educational measurement.
  • Further research can explore the application and refinement of these targets in various testing contexts.