Law of effect models and choice between many alternatives.
Use Navakatikyan’s component-functions model, not classic matching, when you analyze choice across three or more concurrent schedules.
01Research in Context
What this study did
Alexander and colleagues tested two math formulas that describe how pigeons split their time among three or more food levers.
They compared the old generalized-matching equation with Navakatikyan’s newer component-functions model.
Birds pecked on concurrent VI schedules while computers logged every response and stay duration.
What they found
The component-functions equations tracked the birds’ choices and dwell times more closely than the classic formula.
Sensitivity to reward rate also changed as more levers were added, something the older model missed.
How this fits with other research
Jensen (2014) built a free software tool that uses the same component-functions logic, giving you an easy way to run these newer calculations.
Dosen (2007) first showed the component idea worked for two-lever cases; Alexander et al. proved it scales up to three or four.
Beeby et al. (2017) seems to clash: they saw preference flip when they deleted quick switch pecks. The difference is response definition—Alexander counted every peck and stay, Beeby removed changeovers, so both can be true.
Why it matters
If you run concurrent reinforcement programs with more than two options, switch from the old matching slope to Navakatikyan’s component model. It keeps accuracy without extra work, especially when you care about how long clients stay at each activity.
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02At a glance
03Original abstract
Data from five experiments on choice between more than two variable-interval schedules were modeled with different equations for the Law of Effect. Navakatikyan's (2007) component-functions models with three, four and five free parameters were compared with Stevens' (1957), Herrnstein's (1970) and Davison and Hunter's (1976) equations. These latter models are consistent with the generalized-matching principle, whereas Navakatikyan's models are not. Navakatikyan's models performed better or on par with their competitors, especially in predicting residence-time data and generalized-matching sensitivities for time allocation. The models described well an observed decrease, in several of these data sets, in generalized-matching sensitivity between two alternatives when reinforcer rate increased on the other alternatives. Models built on the generalized-matching principle cannot do this. Navakatikyan's models also performed better, though to a lesser extent, than their competitors for data sets that are not obviously inconsistent with generalized matching.
Journal of the experimental analysis of behavior, 2013 · doi:10.1002/jeab.37