Sequential Dynamic Bayesian Modeling for Single-Case Experimental Designs: A Novel Approach to Many Labs Research

Abstract Single-case experimental design (SCED) is a quantitative research method widely used across diverse fields including behavioral education, special education, medicine, and applied behavior analysis. SCED methodology establishes external validity through a well-established sequential process: demonstrating strong internal validity within individual studies, followed by direct and systematic replication across varied populations, settings, and conditions. While this replication-based approach has proven highly successful as evidenced by robust intervention literature bases such as functional communication training and behavioral skills training the traditional process of accumulating replications across independent research teams can require years or decades. Inspired by the ManyLabs initiative’s success in coordinating replication efforts, we developed a sequential experimental design using dynamic Bayesian models to accelerate coordinated SCED research across laboratories. Applied to simulated and published multiple-baseline design data, our approach demonstrates how posterior distributions from completed cases can serve as priors for subsequent participants, creating cumulative knowledge building across research sites. Findings show that dynamic models effectively estimate intervention effects even when timing and effect sizes vary randomly. Parameter estimates converged to true effects after 15-25 coordinated cases, with credible intervals narrowing systematically as participants were added sequentially. This ManyLabs-inspired framework offers SCED researchers a pathway to accelerate the coordination of replications while maintaining the individualized focus and rigorous internal validity that make single-case designs valuable for evidence-based practice.