Applying the Generalized Logistic Model in Single Case Designs: Modeling Treatment-Induced Shifts
The generalized logistic curve in R can trace slow, S-shaped behavior change and gives you numbers when visual calls feel unclear.
01Research in Context
What this study did
Verboon et al. (2018) wrote a how-to paper, not an intervention study.
They show how to fit a generalized logistic curve to single-case data in R.
The curve can trace slow, S-shaped changes instead of sudden jumps.
What they found
The authors give code in the ‘userfriendlyscience’ package.
One function models gradual treatment effects that speed up, then level off.
They argue this shape fits real therapy data better than straight lines.
How this fits with other research
Jones et al. (1977) first brought time-series tests to behavior labs. Their work only spotted level shifts; Verboon adds the curve itself.
Manolov et al. (2017) and Ruiz et al. (2025) built free R tools for graphs. Verboon fills the gap by giving the same users a statistical model, not just pictures.
Wolfe et al. (2019) give step-by-step visual rules. Verboon does not replace eyes; it gives numbers when change is slow and hard to see.
Why it matters
If your client improves bit by bit, the logistic curve can tell you when the speed-up starts and when it flattens. Run the code, paste your data, and get a plot plus a p-value. Use it alongside visual checks to show parents and payers that small weekly gains add up to a real effect.
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02At a glance
03Original abstract
Many analytical approaches to single-case data assume either linear effects (regression-based methods) or instant effects (mean-based methods). Neither assumption is realistic; therefore, these approaches’ assumptions are often violated. In this article, we propose modeling curvilinear effects to appropriately parametrize the characteristics of singe-case data. Specifically, we introduce the generalized logistic function as adequate function for this situation. The merits of the proposed procedure are demonstrated using data previously used in single case research that represent typical single case data. We provide the function with auxiliary graphical options to demonstrate the model parameters. The function is freely available in the R package “userfriendlyscience.” The proposed procedure is a new way to analyze single case data, which may provide applied single case researchers with a new tool to better understand their data and avoid applying methods with violated assumptions.
Behavior Modification, 2018 · doi:10.1177/0145445518791255