Approaches for Specifying the Level-1 Error Structure When Synthesizing Single-Case Data

Multilevel modeling has been utilized for combining single-case experimental design (SCED) data assuming simple level-1 error structures. The purpose of this study is to compare various multilevel analysis approaches for handling potential complexity in the level-1 error structure within SCED data, including approaches assuming simple and complex error structures (heterogeneous, autocorrelation, and both) and those using fit indices to select between alternative error structures. A Monte Carlo study was conducted to empirically validate the suggested multilevel modeling approaches. Results indicate that each approach leads to fixed effect estimates with little to no bias and that inferences for fixed effects were frequently accurate, particularly when a simple homogeneous level-1 error structure or a first-order autoregressive structure was assumed and the inferences were based on the Kenward-Roger method. Practical implications and recommendations are discussed.