Generalized least squares transformation for single-case experimental design: Introducing the R package lmeSCED

Data generated from single-case experimental designs (SCEDs) are repeated observations on one or a few participants, making multilevel models (MLMs) a useful tool. However, there are two features inherent to SCED data: autocorrelation and small sample sizes. These features result in biased standard errors and inflated type I error rates for fixed effects. Existing commercial statistical programs (for example, SAS) can model first-order autoregressive [AR(1)] residuals and apply small-sample corrections such as Satterthwaite's adjustment, but they are costly and offer no principled test of random effects. Widely used R packages, in contrast, implement either small-sample adjustments or AR(1) structures, but not both. This study aims to (1) evaluate a two-step solution that combines a generalized least squares (GLS) transformation to remove AR(1) residual correlation with Satterthwaite's small-sample adjustment for fixed-effects inference, and (2) implement these methods along with a boundary-corrected restricted likelihood-ratio test and parametric bootstrapping for random effects variance components in a user-friendly R package, lmeSCED. Results from the Monte Carlo simulation study show that applying MLMs to GLS-transformed data recovers true parameter values without bias and keeps type I error rates at nominal levels. We then demonstrate the utility of lmeSCED on an empirical dataset to illustrate its use in practice. The limitations and future directions are also discussed.