Bayesian unknown change-point models to investigate immediacy in single case designs

Area of Science:

• Behavioral Science
• Statistical Modeling
• Psychology

Background:

• Immediacy is crucial for establishing causality in single-case designs (SCDs).
• Current methods rely on visual analysis, which often uses limited data points.
• A statistical tool for quantifying immediacy in SCDs is lacking.

Purpose of the Study:

• To propose a novel Bayesian unknown change-point model for analyzing immediacy in SCDs.
• To provide a statistical method that utilizes all data points for immediacy assessment.
• To develop a model capable of accommodating delayed treatment effects.

Main Methods:

• A Bayesian unknown change-point model was developed.
• The model was evaluated using Monte Carlo simulations for a 2-phase design.
• The method was illustrated with real-world data.

Main Results:

• The Bayesian model quantifies immediacy by the narrowness of the posterior distribution around the true change-point.
• Simulations demonstrated that posterior standard deviations decrease with larger standardized mean differences and shorter test lengths.
• The model successfully accommodates delayed effects.

Conclusions:

• The proposed Bayesian change-point model offers a statistically rigorous approach to assessing immediacy in SCDs.
• This method enhances the inferential capabilities of SCD analysis by considering all data points.
• The model provides a quantifiable measure of immediacy, improving causal inference in behavioral research.