Investigating immediacy in multiple-phase-change single-case experimental designs using a Bayesian unknown change-points model.

Immediacy is one of the necessary criteria to show strong evidence of treatment effect in single-case experimental designs (SCEDs). However, with the exception of Natesan and Hedges (2017), no inferential statistical tool has been used to demonstrate or quantify it until now. We investigate and quantify immediacy by treating the change points between the baseline and treatment phases as unknown. We extend Natesan and Hedges' work to multiple-phase-change (e.g. ABAB) designs using a variational Bayesian (VB) unknown change-point model. VB was used instead of Markov chain Monte Carlo methods (MCMC), because MCMC cannot be used effectively to determine multiple change points. Combined and individual probabilities of correctly estimating the change points were used as indicators of the algorithm's accuracy. Unlike MCMC in the Natesan and Hedges (2017) study, the VB method was able to recover the change points with high accuracy even for short time series and in only a fraction of the time for all time-series lengths. We illustrate the algorithm with 13 real data sets. Additionally, we discuss the advantages of the unknown change-point approach, and the Bayesian and variational Bayesian estimation for SCEDs.