How to Detect Change Points in Single-Case Designs: Further Results

• In Event: Analysis and Meta-Analysis of Single-Case Experimental Data: Methodological Developments

Abstract

Detecting where a time series changes levels can be a difficult task. For cases in which it is assumed that only a single change occurs, a fairly simple model will work well. The model is based on an extension and reparameterization of logistic regression. The extension is first to the case with a floor and ceiling effect (asymptotes above 0 and below 1), then to the case where the dependent variable can be a count or continuous measure, not just a proportion or a binary outcome. Finally a reparameterization from the slope/intercept form to the slope/ halfway-point form allows estimation of where the change occurs. The equation representing the expected value in the model is E(Y) = F + D * (exp(b*(X - H)) / (1 + exp(b*(X - H))). In the equation, X is time, b is the slope, F is the floor, D is the difference between the floor and ceiling, and H is the halfway point (in units of X) between phases.
In the typical single case design (SCD) we know when the phase changes. However, change is not always instantaneous or obvious. Using the unknown changepoint model can test whether our assumptions about the change in phase are consistent with the actual pattern of change. I will illustrate this with example analyses.

Author

• David M. Rindskopf, City University of New York - CUNY