Bayesian methods applied to the generalized matching law
A free website now draws Bayesian pictures of the matching law, giving you instant parameter estimates and model comparisons without code.
01Research in Context
What this study did
Villarreal and colleagues built a free web tool that fits the generalized matching law with Bayesian statistics. They re-analyzed old pigeon choice data to show how the tool works.
You pick your model, click 'run,' and get pictures of parameter values and model odds. No coding or heavy math needed.
What they found
The Bayesian plots gave clear peaks for sensitivity (a) and bias (log k) values. Model-comparison charts instantly showed which version of the matching law fit best.
Standard errors came along for free, so you see how sure you can be about each estimate.
How this fits with other research
Nakamura et al. (1986) already showed that the generalized matching law explains about 91 % of variance in multiple-schedule pigeon data. Villarreal et al. (2019) revisit those same data types, but now you get the answer in pictures instead of tables.
Jacobs (2019) also dislikes old-school null-hypothesis tests. He pushes randomization tests for single-case work, while Villarreal pushes Bayesian graphics for choice data. Both give you p-value-free options; pick the tool that matches your dataset.
Manolov et al. (2022) give a free web plot for judging replication in single-case designs. Villarreal’s tool does a similar ‘upload-click-get plot’ trick, but for the matching law. Together they show a trend: behavior analysis is moving toward free, visual, web-based stats.
Why it matters
If you run concurrent-schedule sessions with students or clients, you can now skip SPSS and Excel gymnastics. Upload your response counts, check the Bayesian peaks, and decide whether sensitivity is low or bias is pushing choice. The pictures make team meetings easier—everyone sees why one reinforcer beats another.
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02At a glance
03Original abstract
We demonstrate the usefulness of Bayesian methods in developing, evaluating, and using psychological models in the experimental analysis of behavior. We do this through a case study, involving new experimental data that measure the response count and time allocation behavior in pigeons under concurrent random-ratio random-interval schedules of reinforcement. To analyze these data, we implement a series of behavioral models, based on the generalized matching law, as graphical models, and use computational methods to perform fully Bayesian inference. We demonstrate how Bayesian methods, implemented in this way, make inferences about parameters representing psychological variables, how they test the descriptive adequacy of models as accounts of behavior, and how they compare multiple competing models. We also demonstrate how the Bayesian graphical modeling approach allows for more complicated modeling structures, including hierarchical, common cause, and latent mixture structures, to formalize more complicated behavioral models. As part of the case study, we demonstrate how the statistical properties of Bayesian methods allow them to provide more direct and intuitive tests of theories and hypotheses, and how they support the creative and exploratory development of new theories and models.
Journal of the Experimental Analysis of Behavior, 2019 · doi:10.1002/jeab.506