Abstract
The emergence of computer-based assessments has made response times, in addition to response accuracies, available as a source of information about test takers’ latent abilities. The development of substantively meaningful accounts of the cognitive process underlying item responses is critical to establishing the validity of psychometric tests. However, existing substantive theories such as the diffusion model have been slow to gain traction due to their unwieldy functional form and regular violations of model assumptions in psychometric contexts. In the present work, we develop an attention-based diffusion model based on process assumptions that are appropriate for psychometric applications. This model is straightforward to analyse using Gibbs sampling and can be readily extended. We demonstrate our model’s good computational and statistical properties in a comparison with two well-established psychometric models.
Highlights
The emergence of computer-based assessments has made response times, in addition to response accuracies, available as a source of information about test takers’ latent abilities
We propose an attention-based diffusion model, which we derive from cognitive process assumptions that are more appropriate in the psychometric setting of performance tests
Based on cognitive process assumptions that we believe to be appropriate in psychometric contexts, we derived a substantively meaningful model with favourable computational properties
Summary
Our ABDM lends itself naturally to Bayesian analysis due its functional form. If we assume for that the value of c is known, this form of the density suggests a conjugate analysis for the estimation of the remaining parameters. Choosing a multivariate normal distribution as joint prior for the model parameters βi , θp, and αi , and an inverse Wishart prior for the variance–covariance matrix, will yield a multivariate normal posterior distribution for all parameters. Due to the interpretation of the volatility αi as a standard deviation, only positive values are admissible for this parameter and the prior distribution for αi needs to be truncated at zero, which complicates the form of the joint posterior distribution considerably. Our model can be straightforwardly analysed using Gibbs sampling
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