Bayesian Multilevel Single Case Models using 'Stan'. A new tool to study single cases in Neuropsychology

Single case studies continue to play an important role in neuropsychological research. However, the range of statistical tools specifically designed for single cases is still limited. The current gold standard is the Crawford's t-test, but it is crucial to note that this is limited to simple designs and it is not possible to make inferences relevant to support for the null hypothesis with it. The Bayesian Multilevel Single Case models (BMSC) provide a novel tool that grants the flexibility of linear mixed model designs. BMSC is also able to support both null and alternative hypotheses in complex experimental designs using the Bayesian framework. We compared the BMSC and Crawford's t-test in a simulation study involving a case of no-dissociation and a case of simple dissociation between a single case patient and a series of control groups of different sizes (N=5, 15, or 30). We then showed how BMSC is useful in complex designs by means of an example using real data. The BMSC proved to be more reliable than the Crawford's test, in terms of first-type errors and more precise estimating the parameters. Notably, the BMSC model provides a comprehensive vision of the whole experimental design, interpolating a single model. It follows the recent trend which involves a shift in attention from p-values to other inferential indices and estimates.