A Hierarchical Ordinal Regression Model for Treatment-Reversal Designs with Application to Non-Overlap Effect Sizes

We present a hierarchical ordinal model for analyzing single-case designs (SCDs), with a focus on treatment-reversal designs. SCDs involve systematic measurement of outcomes for individual cases across different conditions or phases, aiming to establish causal relations between interventions and behavioral changes. While visual analysis is a common approach in SCDs, the field is increasingly adopting quantitative effect size metrics, such as non-overlap indices, to supplement visual examination. However, statistical theory supporting the use of these indices remains underdeveloped. To address this gap, we developed a Bayesian hierarchical ordinal model that enables the estimation of case-specific non-overlap indices. Through simulation studies, we demonstrate that these indices are more accurate than those obtained via standard approaches. Moreover, the model can generate parametric indices with greater accuracy than standard methods. To facilitate the adoption of this model, we provide an R package (ssrhom) for model estimation. This contribution aims to enhance the analysis and interpretation of SCDs, ultimately advancing our understanding of the efficacy of interventions and promoting evidence-based decision-making.