Accessible Cognitive Measurement Models
Easing the application and use of formal models
Cognitive measurement models provide a mathematical formalization of the cognitive processes underlying observed behavior.
Cognitive measurement models (the diffusion model for processing speed is a well-known example) translate verbal theories of cognitive processes into mathematical form. Rather than treating observed behavior as a direct readout of some construct, these models describe response times, accuracy rates, and choice patterns as the joint product of several interacting processes. The parameters of the model correspond to specific cognitive operations — and that correspondence is what makes the model theoretically useful, rather than just descriptive.
The problem
Researchers who develop cognitive measurement models usually provide code, but running it typically requires fluency in JAGS or Stan. That is a real barrier. Researchers who would benefit from these models often cannot use them without weeks of investment in a new programming environment — so they fall back on behavioral summary statistics that are theoretically ambiguous.
The bmm package
Together with Ven Popov, I co-develop the R package bmm (CRAN), which implements these models in a hierarchical Bayesian framework via brms. The package started with models for visual working memory, but it has since grown into a broader collection covering both memory and speeded decision-making.
Visual working memory (continuous reproduction tasks):
- 2-parameter mixture model (Zhang & Luck, 2008)
- 3-parameter mixture model (Bays et al., 2009)
- Interference Measurement Model (Oberauer et al., 2017)
- Signal Discrimination Model (Oberauer, 2023)
Working memory tasks with categorical responses:
- Memory Measurement Model (M3) (Oberauer & Lewandowsky, 2019), with ready-made versions for simple and complex span tasks and a custom version for other categorical decision tasks
Speeded decision-making (new in the upcoming release, already available in the development version):
- Diffusion Decision Model (Ratcliff, 1978)
- EZ-diffusion model (Wagenmakers et al., 2007), estimated hierarchically following Chávez De la Peña & Vandekerckhove (2025)
- Censored Shifted Wald model (Miller et al., 2017), with a censoring version for high-accuracy tasks and a competing-risks version for tasks with balanced accuracy
Each model ships with documentation, default priors, a worked-example vignette, and density and random generation functions for exploring what the model predicts before fitting it.
Teaching these models to PhD students
Making the models accessible in software is only half the job — researchers also need training in how to use them well. I currently pursue this through:
- A 2–3 day workshop for PhD and graduate programs: Analyzing Data on the Level of Cognitive Processes — an Introduction to the R package bmm. The workshop moves from the rationale of measurement models to hands-on model fitting, prior specification, and interpreting parameters with respect to substantive research questions. All materials are openly available. If you want to bring this workshop to your graduate program, get in touch.
- Tutorial papers written as self-study material: the bmm tutorial in Behavior Research Methods and a tutorial on the M3 model walk readers through complete analyses, so PhD students can adopt the models without a course or workshop.
An overview of my other workshops is on the teaching page.
Publications & preprints
Published:
- Frischkorn, G. T., & Popov, V. (2025). A tutorial for estimating Bayesian hierarchical mixture models for visual working memory tasks: Introducing the Bayesian Measurement Modeling (bmm) package for R. Behavior Research Methods, 57(5), 144. https://doi.org/10.3758/s13428-025-02643-0
- Nunez, M. D., Schubert, A.-L., Frischkorn, G. T., & Oberauer, K. (2025). Cognitive models of decision-making with identifiable parameters: Diffusion decision models with within-trial noise. Journal of Mathematical Psychology, 125, 102917. https://doi.org/10.1016/j.jmp.2025.102917
Preprints:
- Frischkorn, G. T., & Li, C. (invited for revision at Advances in Methods & Practices for Psychological Science). Applying the Memory Measurement Model (M3): A tutorial using the bmm R package. https://osf.io/tcuzx_v1
- Li, C., Frischkorn, G. T., & Oberauer, K. (under review at Behavior Research Methods). Measuring individual differences with Bayesian hierarchical cognitive models. https://osf.io/24w3z_v1
- Göttmann, J., Frischkorn, G. T., Oberauer, K., Schaefer, S. B., & Schubert, A.-L. (invited for revision at Journal of Mathematical Psychology). Modeling individual differences in working memory: Subject-level parameter recovery within the Memory Measurement Model framework (M³). https://doi.org/10.31234/osf.io/945d2_v2
- Frischkorn, G. T., Rebmann, R., & Oberauer, K. (under review at Psychological Review). Validity is a theoretical problem: A computational psychometrics perspective on how to measure cognition. https://osf.io/pczua_v3