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The Effects of Probability Threshold Choice on an Adjustment for Guessing using the Rasch Model.

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The Guessing Adjustment strategy effectively reduces bias in Rasch model analyses by treating low-probability correct guesses as missing data. Choosing an appropriate probability threshold is crucial for balancing bias reduction and precision.

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Statistical Modeling

Background:

  • The Rasch model is widely used in educational and psychological assessments.
  • Correct guessing can introduce bias into Rasch model parameter estimates.
  • Existing methods for handling correct guessing are limited.

Purpose of the Study:

  • To introduce and evaluate a novel strategy, the Guessing Adjustment, for accounting for correct guessing in the Rasch model.
  • To investigate the impact of different probability thresholds on the performance of the Guessing Adjustment.
  • To examine how sample size, amount of correct guessing, and item difficulty influence the effectiveness of the strategy.

Main Methods:

  • A simulation study was designed to test the Guessing Adjustment strategy.
  • Person/item responses with a probability of correctness below a set threshold were converted to missing data.
  • The Rasch model was recalibrated with the adjusted data.
  • Bias, standard errors, and root mean squared errors (RMSE) were calculated under various conditions.

Main Results:

  • Larger probability thresholds generally led to reduced bias but increased standard errors.
  • The reduction in bias was often more significant than the loss in precision, as indicated by RMSE.
  • The effectiveness of the Guessing Adjustment varied across different sample sizes, guessing levels, and item difficulties.

Conclusions:

  • The Guessing Adjustment is a viable method for mitigating the effects of correct guessing in Rasch model analyses.
  • The selection of an appropriate probability threshold is a critical factor in optimizing the Guessing Adjustment's performance.
  • Further research should explore optimal threshold selection across diverse assessment contexts.