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 <i>via</i> 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 (<i>ssrhom</i>) 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.