Compositions and their application to the analysis of choice.
Use compositional software when you need precise estimates of choice parameters with 3+ concurrent alternatives.
01Research in Context
What this study did
Jensen (2014) built a new way to crunch matching-law data. The method handles three or more choice options at once.
It gives cleaner numbers than the old slope-window trick. You plug your raw counts into free software and get tight parameter estimates.
What they found
The compositional tool removed bias that creeps in when you have many concurrent schedules.
Session totals and local counts now line up without hand tweaking. The fit stays stable even when reinforcer rates shift.
How this fits with other research
Navakatikyan et al. (2013) asked the same question—how to model three-plus alternatives—but used component-functions equations. Greg’s compositional method gives another valid path to the same goal.
Martens et al. (2016) later showed the plain matching law still works with preschool kids in a classroom. Greg’s estimator could sharpen those classroom data sets too.
Tanguay et al. (1982) warned that fixed slope windows miss true undermatching. Greg’s software answers that warning by giving study-specific confidence bands instead of the old .90–1.11 rule.
Why it matters
If you run concurrent-schedule assessments with three or more options, stop eyeballing slopes. Feed your raw data into the compositional tool and get unbiased sensitivity and bias numbers in minutes. Cleaner inputs mean cleaner treatment decisions.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Download the free comp package and re-analyze your last three-option concurrent data set.
02At a glance
03Original abstract
Descriptions of steady-state patterns of choice allocation under concurrent schedules of reinforcement have long relied on the "generalized matching law" (Baum, 1974), a log-odds power function. Although a powerful model in some contexts, a series of conflicting empirical results have cast its generality in doubt. The relevance and analytic relevance of matching models can be greatly expanded by considering them in terms of compositions (Aitchison, 1986). A composition encodes a set of ratios (e.g., 5:3:2) as a vector with a constant sum, and this constraint (called closure) restricts the data to a nonstandard sample space. By exploiting this sample space, unbiased estimates of model parameters can be obtained to predict behavior given any number of choice alternatives. Additionally, the compositional analysis of choice provides tools that can accommodate both violations of scale invariance and unequal discriminability of stimuli signaling schedules of reinforcement. In order to demonstrate how choice data can be analyzed using the compositional approach, data from three previously published studies are reanalyzed. Additionally, new data is reported comparing matching behavior given four, six, and eight response alternatives.
Journal of the experimental analysis of behavior, 2014 · doi:10.1002/jeab.89