Bayesian multilevel single case models using 'Stan'. A new tool to study single cases in neuropsychology

Area of Science:

• Neuropsychology
• Statistical modeling
• Cognitive science

Background:

• Single case studies are vital in neuropsychological research.
• Existing statistical tools, like Crawford's t-test, have limitations for complex designs and null hypothesis inference.
• There is a need for advanced statistical methods in single-case research.

Observation:

• Crawford's t-test is limited to simple designs and cannot support the null hypothesis.
• Bayesian Multilevel Single Case (BMSC) models offer flexibility comparable to linear mixed models.
• BMSC models can analyze complex experimental designs and support both null and alternative hypotheses within a Bayesian framework.

Findings:

• A simulation study showed BMSC models are more reliable than Crawford's t-test, with lower Type I errors.
• BMSC models provided more precise parameter estimations in simulations involving single cases and control groups of varying sizes (N=5, 15, 30).
• BMSC models offer a unified approach to analyzing complex experimental designs, integrating various inferential indices.

Implications:

• BMSC models represent a significant advancement for single-case research in neuropsychology.
• The findings support a shift from p-values towards more comprehensive inferential indices and estimates in statistical analysis.
• This novel approach enhances the analytical capabilities for complex neuropsychological research designs.