Multilevel analysis of matching behavior
Stop averaging—use multilevel modeling to see each client’s true matching curve.
01Research in Context
What this study did
Caron (2019) looked at how we crunch matching-law numbers.
The paper says stop averaging every subject together.
Use multilevel modeling instead to keep each person’s data intact.
What they found
Pooling data hides individual curves and can tilt the slope.
Multilevel modeling keeps the real shape and gives cleaner estimates.
How this fits with other research
Kronfli et al. (2021) later tracked parent reinforcement at home.
They kept parent-child pairs separate, letting the matching law show the drop in problem behavior after BST.
Simon et al. (2017) saw the opposite pattern: adults talked more to the partner who talked less—antimatching.
Caron’s method would still fit here; it would simply reveal the negative slope instead of forcing a fake positive one.
Older papers like Pear et al. (1984) set up the matching law rules, but they pooled data.
Caron updates the math without changing the basic law.
Why it matters
Next time you graph choice data, plot each client’s line first.
Run a multilevel model in R or Excel.
You will spot who needs schedule tweaks and who is already balanced, without the fog of averages.
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02At a glance
03Original abstract
Multilevel modeling has been considered a promising statistical tool in the field of the experimental analysis of behavior and may serve as a convenient statistical analysis for matching behavior because it structures data in groups (or levels) to account simultaneously for the within-subject and between-subject variances. Heretofore, researchers have sometimes pooled data erroneously from different subjects in a single analysis by using average ratios, average response and reinforcer rates, aggregation of subjects, etc. Unfortunately, this leads to loss of information and biased estimations, which can severely undermine generalization of the results. Instead, a multilevel approach is advocated to combine several subjects' matching behavior. A reanalysis of previous data on matching behavior is provided to illustrate the method and point out its advantages. It illustrates that multilevel regression leads to better estimations, is more convenient, and offers more behavioral information. We hope this paper will encourage the use of multilevel modeling in the statistical practices of behavior analysts.
Journal of the Experimental Analysis of Behavior, 2019 · doi:10.1002/jeab.510