The consequences of modeling autocorrelation when synthesizing single-case studies using a three-level model.

Results from single-case studies are being synthesized using three-level models in which repeated observations are nested in participants, which in turn are nested in studies. We examined the performance of these models under conditions in which the errors associated with the repeated observations (the Level-1 errors) were assumed to be first-order autoregressive. Monte Carlo methods were used to examine conditions in which the first-order autoregressive assumption was accurate, conditions in which it represented an overspecification because the errors were actually independent, and conditions in which it represented a misspecification because the errors were generated on the basis of a moving-average model.

The use of multilevel analysis for integrating single-case experimental design results within a study and across studies.

The use of multilevel models as a method for synthesising single-case experimental design results is receiving increased consideration. In this article we discuss the potential advantages and limitations of the multilevel modelling approach. We present a basic two-level model where observations are nested within cases, and then discuss extensions of the basic model to accommodate trends, moderators of the intervention effect, non-continuous outcomes, heterogeneity, autocorrelation, the nesting of cases within studies, and more complex single-case design types.

Multilevel models for multiple-baseline data: modeling across-participant variation in autocorrelation and residual variance.

Multilevel models (MLM) have been used as a method for analyzing multiple-baseline single-case data. However, some concerns can be raised because the models that have been used assume that the Level-1 error covariance matrix is the same for all participants. The purpose of this study was to extend the application of MLM of single-case data in order to accommodate across-participant variation in the Level-1 residual variance and autocorrelation.