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. This more general model was then used in the analysis of single-case data sets to illustrate the method, to estimate the degree to which the autocorrelation and residual variances differed across participants, and to examine whether inferences about treatment effects were sensitive to whether or not the Level-1 error covariance matrix was allowed to vary across participants. The results from the analyses of five published studies showed that when the Level-1 error covariance matrix was allowed to vary across participants, some relatively large differences in autocorrelation estimates and error variance estimates emerged. The changes in modeling the variance structure did not change the conclusions about which fixed effects were statistically significant in most of the studies, but there was one exception. The fit indices did not consistently support selecting either the more complex covariance structure, which allowed the covariance parameters to vary across participants, or the simpler covariance structure. Given the uncertainty in model specification that may arise when modeling single-case data, researchers should consider conducting sensitivity analyses to examine the degree to which their conclusions are sensitive to modeling choices.