From a single-level analysis to a multilevel analysis of single-case experimental designs

Multilevel modeling provides one approach to synthesizing single-case experimental design data. In this study, we present the multilevel model (the two-level and the three-level models) for summarizing single-case results over cases, over studies, or both. In addition to the basic multilevel models, we elaborate on several plausible alternative models. We apply the proposed models to real datasets and investigate to what extent the estimated treatment effect is dependent on the modeling specifications and the underlying assumptions. By considering a range of plausible models and assumptions, researchers can determine the degree to which the effect estimates and conclusions are sensitive to the specific assumptions made. If the same conclusions are reached across a range of plausible assumptions, confidence in the conclusions can be enhanced. We advise researchers not to focus on one model but conduct multiple plausible multilevel analyses and investigate whether the results depend on the modeling options.