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# Effects of parameter prior variation on posterior distribution response times for an Item Response Theory diffusion model

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Abstract

Diffusion based models have been successfully used to model response time distributions in decision making psychological experiments (see Ratcliff et al. (2016) for a review). van der Maas et al. (2011) proposed an item response theory-based extension of the diffusion model (Q-diffusion) designed to incorporate item-specific characteristics. Kang et al. (2022) and van der Maas et al. (2011) successfully used Bayesian posterior sampling methods to estimate Q-diffusion model response time distributions using a mental rotation dataset and demonstrated model convergence even in the presence of non-informative prior distribution. The current study empirically investigated how the posterior distribution of response times in the Q-diffusion model are affected by difference choices of the mean for a person-specific log-normal prior distribution. Both small and large perturbations of the log-normal mean were chosen to represent situations where a baseline posterior mean is either within or outside the high probability zone of the prior distribution representing "Data-Prior conflict" (see Clarke and Gustafson (1998)). Using the Ruggeri and Sivaganesan (2000) relative sensitivity Rπ metric defined as the square of difference between posterior means of the baselined prior and the perturbed prior distributions and then divided by the posterior variance of the perturbed prior distribution. Results for small perturbations found 0.01 < Rπ < 0.02 while for large perturbations: 0.2 < Rπ < 0.5. These results suggest that the posterior distribution of the Q-diffusion model is sensitive to poor choices of the prior distribution but more robust for appropriate prior distribution choices.

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#### Keywords

Diffusion model
Bayesian Inference
Prior Sensitivity
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##### Cite this as:

Malaiya, R. K. (2022, July). Effects of parameter prior variation on posterior distribution response times for an Item Response Theory diffusion model. Paper presented at Virtual MathPsych/ICCM 2022. Via mathpsych.org/presentation/761.