Author:

Keywords:

Science & Technology, Social Sciences, Physical Sciences, Mathematics, Interdisciplinary Applications, Social Sciences, Mathematical Methods, Psychology, Experimental, Statistics & Probability, Mathematics, Mathematical Methods In Social Sciences, Psychology, Single-case experimental design, effect size, multilevel modeling, meta-analysis, individual participant data, BASE-LINE DESIGNS, MONTE-CARLO, EFFECT SIZES, TESTS, MODELS, IPD, Computer Simulation, Humans, Multilevel Analysis, Research Design, 01 Mathematical Sciences, 15 Commerce, Management, Tourism and Services, 17 Psychology and Cognitive Sciences, Social Sciences Methods, 35 Commerce, management, tourism and services, 49 Mathematical sciences, 52 Psychology

Abstract:

To conduct a multilevel meta-analysis of multiple single-case experimental design (SCED) studies, the individual participant data (IPD) can be analyzed in one or two stages. In the one-stage approach, a multilevel model is estimated based on the raw data. In the two-stage approach, an effect size is calculated for each participant and these effect sizes and their sampling variances are subsequently combined to estimate a meta-analytic multilevel model. The multilevel model in the two-stage approach has fewer parameters to estimate, in exchange for the reduction of information of the raw data to effect sizes. In this paper we explore how the one-stage and two-stage IPD approaches can be applied in the context of meta-analysis of single-case designs. Both approaches are compared for several single-case designs of increasing complexity. Through a simulation study we show that the two-stage approach obtains better convergence rates for more complex models, but that model estimation does not necessarily converge at a faster speed. The point estimates of the fixed effects are unbiased for both approaches across all models, as such confirming results from methodological research on IPD meta-analysis of group-comparison designs. In light of these results, we discuss the implementation of both methods in R.