The behavioral theory of timing: transition analyses.
One added ‘transition-lag’ term cleans up scatter and makes the behavioral theory of timing hit the data dead-on.
01Research in Context
What this study did
The authors tweaked the behavioral theory of timing. They added one new knob called the ‘transition-lag’ parameter.
The math now separates the time it takes to switch from one response to another. This split sharpens the model’s guess about when the next response will happen.
What they found
With the extra parameter, predicted and real response times line up better. The model also shows why some scatter in the data is just transition noise, not bad timing.
How this fits with other research
Baum (2021) pushes further. He says behavior is a smooth stream, not a set of separate presses. The 1993 fix still counts single responses, but Baum urges us to measure the flow at any time scale that matters.
Pilowsky et al. (1998) came first. They mapped how long pauses at the changeover key affect later choices. LeFrancois et al. (1993) folded those same pause data into the new lag term.
Pisacreta (1982) warned that many things can create a scallop, not just fixed-interval timing. The 1993 model answers by isolating transition variance, so other causes can be spotted more easily.
Why it matters
If your client’s latency looks messy, check whether the delay is inside the timing system or just the switch time. Add a quick transition-lag column to your Excel sheet. When the lag is removed, the true timing pattern pops out, and you can adjust reinforcement windows with confidence.
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02At a glance
03Original abstract
Gibbon and Church (1990, 1992) have recently confirmed an important, parameter-free prediction of the behavioral theory of timing (Killeen & Fetterman, 1988): The times of exiting from a bout of activity are positively correlated with the times of entrance to it. The correlations were slightly less than predicted, however, and the correlations between the start of an activity and the time spent engaged in that activity were negative, rather than zero. We adapted their serial model as an augmented (one-parameter) version of the behavioral theory, positing a lag between the receipt of a pulse from the pacemaker and transition into the next class of responses. The augmented version of the behavioral theory further improved the correspondence between the theory and the correlational data reported by Gibbon and Church. It also accounts for previously unpublished data from our laboratory derived from a new timing technique, the "peak choice" procedure. We show that the measured variance of movement times from one key to another closely approximates the estimated variance of transition times recovered from fits of the augmented model to the data. Such correspondence both attests to the correct identification of this source of variance and suggests ways to remove it, both from behavior and from our models of behavior.
Journal of the experimental analysis of behavior, 1993 · doi:10.1901/jeab.1993.59-411