Applied Quantitative Analysis of Behavior: What It Is, and Why We Care-Introduction to the Special Section

R2 should not be used to describe behavioral-economic discounting and demand models

Literature concerning operant behavioral economics shows a strong preference for the coefficient of determination (R2) metric to (a) describe how well an applied model accounts for variance and (b) depict the quality of collected data. Yet R2 is incompatible with nonlinear modeling. In this report, we provide an updated discussion of the concerns with R2. We first review recent articles that have been published in the Journal of the Experimental Analysis of Behavior that employ nonlinear models, noting recent trends in goodness-of-fit reporting, including the continued reliance on R2. We then examine the tendency for these metrics to bias against linear-like patterns via a positive correlation between goodness of fit and the primary outputs of behavioral-economic modeling. Mathematically, R2 is systematically more stringent for lower values for discounting parameters (e.g., k) in discounting studies and lower values for the elasticity parameter (α) in demand analysis. The study results suggest there may be heterogeneity in how this bias emerges in data sets of varied composition and origin. There are limitations when using any goodness-of-fit measure to assess the systematic nature of data in behavioral-economic studies, and to address those we recommend the use of algorithms that test fundamental expectations of the data.

Revisiting an Analysis of Threats to Internal Validity in Multiple Baseline Designs

In our previous article on threats to internal validity of multiple baseline design variations (Slocum et al., 2022), we argued that nonconcurrent multiple baseline designs (NCMB) are capable of rigorously demonstrating experimental control and should be considered equivalent to concurrent multiple baselines (CMB) in terms of internal validity. We were fortunate to receive five excellent commentaries on our article from experts in single-subject research design-four of whom endorsed the conclusion that NCMBs should be considered strong experimental designs capable of demonstrating experimental control. In the current article, we address the most salient points made in the five commentaries by further elaborating and clarifying the logic described in our original article. We address arguments related to classic threats including maturation, testing and session experience, and coincidental events (history). We rebut the notion that although NCMBs are strong, CMBs provide an increment of additional control and discuss the application of probability-based analysis of the likelihood of threats to internal validity. We conclude by emphasizing our agreement with many of the commentaries that selection of single-case experimental designs should be based on the myriad subtleties of research priorities and contextual factors rather than on a decontextualized hierarchy of designs.