Modeling truncated and censored data with the diffusion model in Stan
Franziska Henrich1, Karl Christoph Klauer2
1Department of Psychology, University of Freiburg, Engelbergerstraße 41, 79106, Freiburg, Germany. fh422@uni-freiburg.de.
Behavior Research Methods
|January 20, 2026
Summary
This study introduces new Bayesian diffusion models in Stan to accurately analyze censored and truncated reaction time data in psychology. The enhanced models improve the analysis of cognitive tasks, ensuring more reliable psychological insights.
Area of Science:
- Cognitive Psychology
- Computational Neuroscience
- Psychometrics
Background:
- Reaction time data in psychological studies are often censored or truncated due to experimental designs like response windows.
- Standard data analysis methods can be significantly biased by censored or truncated data, affecting key statistics like mean, standard deviation, skewness, and correlations.
- Accurate analysis of reaction time data is crucial for understanding cognitive processes.
Purpose of the Study:
- To develop and implement novel Bayesian diffusion models capable of handling truncated and censored reaction time data.
- To integrate this new functionality into the probabilistic programming language Stan.
- To validate the performance and accuracy of the new models.
Main Methods:
- The study extended the diffusion model in Stan by incorporating the cumulative distribution function for truncated and censored reaction time data.
- Bayesian inference was employed using the probabilistic programming language Stan.
- Model performance was assessed through recovery studies, simulation-based calibration, and reanalysis of existing datasets.
Main Results:
- Recovery studies demonstrated satisfactory performance with high correlations (r = .93–1.00), accurate coverage (93–95% of true values within 95% highest density interval), and minimal bias.
- Simulation-based calibration confirmed the correct implementation of the new functionality without errors.
- Reanalysis of existing datasets using the new method provided further validation.
Conclusions:
- The newly implemented truncated and censored diffusion models in Stan provide a robust and accurate method for analyzing challenging reaction time data in psychological research.
- This advancement allows for more reliable estimation of cognitive parameters and a deeper understanding of decision-making processes.
- The validated method offers a valuable tool for researchers working with censored or truncated reaction time data.
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