A multivariate assessment of the rapidly changing procedure with McDowell's Evolutionary Theory of Behavior Dynamics
ETBD matches choice proportions but not overall speed or earnings, so pick your key data point before trusting the curve.
01Research in Context
What this study did
Li et al. (2018) built a computer model of two-choice behavior. They used McDowell’s Evolutionary Theory of Behavior Dynamics (ETBD).
The team fed the model the same data from pigeons pecking two keys for food. They asked the model to match four numbers at once: log response ratios, overall response rate, reinforcer rate, and total reinforcers.
This multivariate test is new. Most earlier checks looked at only one number at a time.
What they found
The ETBD model copied the log response ratios very well. It failed on the other three numbers.
In plain words, the model gets the choice pattern right but misses how fast the bird pecks and how much food it earns overall.
How this fits with other research
Morris et al. (2021) later used the same ETBD code to model self-injury that runs on automatic reinforcement. Their work shows the model can be stretched past lab schedules, even though Li’s fit was only partial.
Li’s other 2018 paper, "The natural mathematics of behavior analysis," tried a different method—Bayesian MCMC-ABC—on the same pigeon data. That paper also found classic models break down when you demand they fit several numbers at once. The two Li papers agree: single-score fits hide cracks.
Cox et al. (2025) took a newer AI route. Their Q-learning algorithm predicted human button presses with high accuracy. Unlike ETBD, the AI model did not try to match reinforcer totals either, hinting that matching every dollar earned may be too tall an order for any one model.
Why it matters
If you graph choice as a log ratio, ETBD can look perfect. Add rate or earnings and the picture cracks. The paper warns BCBAs to pick the measure that matters for the question you ask. When you write a model or check a data sheet, state up front which numbers must fit and which can slide.
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02At a glance
03Original abstract
A multivariate analysis is concerned with more than one dependent variable simultaneously. Models that generate event records have a privileged status in a multivariate analysis. From a model that generates event records, we may compute predictions for any dependent variable associated with those event records. However, because of the generality that is afforded to us by these kinds of models, we must carefully consider the selection of dependent variables. Thus, we present a conditional compromise heuristic for the selection of dependent variables from a large group of variables. The heuristic is applied to McDowell's Evolutionary Theory of Behavior Dynamics (ETBD) for fitting to a concurrent variable-interval schedule in-transition dataset. From the parameters obtained from fitting ETBD, we generated predictions for a wide range of dependent variables. Overall, we found that our ETBD implementation accounted well for various flavors of the log response ratio, but had difficulty accounting for the overall response rates and cumulative reinforcer effects. Based on these results, we argue that the predictions of our ETBD implementation could be improved by decreasing the base response probabilities, either by increasing the response latencies or by decreasing the sizes of the operant classes.
Journal of the Experimental Analysis of Behavior, 2018 · doi:10.1002/jeab.478