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

Seeing red: Relearning to read in a case of Balint’s Syndrome

“…Regarding the alternatives for data analysis, an option for obtaining overall estimates for the immediate intervention effect and change in slope, as well as empirical Bayes individual estimates, would have been to use multilevel models (Moeyaert, Ferron, Beretvas, & Van den Noortgate, 2014). However, we did not perform such an analysis, given that for most of the A 1 -B comparisons the amount of measurements available was smaller than the smallest series length for which evidence on this technique's performance is available (Ferron, Bell, Hess, Rendina-Gobioff, & Hibbard, 2009).…”

Comparing the percentage of non-overlapping data approach and the hierarchical linear modeling approach for synthesizing single-case studies in autism research

“…We refer the reader interested in the details and code for conducting HLM analyses to the work of Van den Noortgate and Onghena (2003aOnghena ( ,b, 2008 and Moeyaert, Ferron, Beretvas, and Van den Noortgate (2014).…”

“…In contrast to the PND approach, advantages of the HLM approach are that it (1) takes into account all baseline data points and is less easily distorted by the presence of outliers in SCED datasets in comparison with PND; (2) is able to deal with trends, by using an extension to the basic HLM approach (Van den Noortgate & Onghena, 2003b;Moeyaert et al, 2014); and (3) generates not only estimates of the overall treatment effect, the average baseline level, and between-case (co)variance and between-study (co)variance of the intervention effect, but also includes statistical significance tests for these parameters. An additional merit of the HLM approach is that it is able to account for the possible dependency that may result from three-level nesting by modeling the variation within participants, between participants of the same study, and between studies included in the meta-analysis (Van den Noortgate & Onghena, 2008).…”

“…The basic HLM approach might already be technically challenging (Moeyaert et al, 2014). When the SCED data require adjustments to the basic HLM procedure, for instance in order to take into account external events (Moeyaert, Ugille, Ferron, Beretvas, & Van den Noortgate, 2013), to take into account different SCED types (Moeyaert et al, in press), or to take into account trend in SCED data (Van den Noortgate & Onghena, 2003b), HLM analyses might become even more challenging in their calculation and interpretation.…”

“…In addition to estimating the average baseline level and the average intervention effect, the HLM approach can be used to estimate measures of between-case (co)variance and betweenstudy (co)variance. From the (co)variance estimates, especially the between-case and between-study variance in the treatment effect can be relevant to the single-case researcher: This measure can be used to determine whether the shift in the dependent behavior associated with the intervention is similar across the included participants and/or studies or whether the intervention is differentially effective over the participants and/or studies (Moeyaert et al, 2014). Nevertheless, single-case synthesis authors using the HLM approach are usually primarily interested in the average treatment effect over the included cases and studies (i.e., the overall effect).…”