Abstract
Within the framework of item response theory, a new and flexible general three-parameter logistic model with response time (G3PLT) is proposed. The advantage of this model is that it can combine time effect, ability, and item difficulty to influence the correct-response probability. In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden's model. In addition, the Metropolis–Hastings within Gibbs sampling algorithm is employed to estimate the model parameters. Based on Markov chain Monte Carlo output, two Bayesian model assessment methods are used to assess the goodness of fit between models. Finally, two simulation studies and a real data analysis are performed to further illustrate the advantages of the new model over the traditional three-parameter logistic model.
Highlights
AND MOTIVATIONComputerized assessment has become a widely accepted method of testing owing to the fact that the results produced by examinees can be quickly and accurately evaluated by virtue of the computational power that is available
In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden’s model
When the number of examinees is held fixed but the number of items increases from 20 to 40, the average mean squared error (MSE), standard deviation (SD), and SE show that the recovery results for the discrimination, difficulty and guessing parameters do not change much, which indicates that the Bayesian algorithm is stable and there is no reduction in accuracy due to an increase in the number of items
Summary
Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China. Within the framework of item response theory, a new and flexible general three-parameter logistic model with response time (G3PLT) is proposed. The advantage of this model is that it can combine time effect, ability, and item difficulty to influence the correct-response probability. In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden’s model. Two simulation studies and a real data analysis are performed to further illustrate the advantages of the new model over the traditional three-parameter logistic model
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