title: The consequences of modeling autocorrelation when synthesizing single-case studies using a three-level model.
abstract: 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. Conditions also varied the series lengths, the numbers of participants per study, the numbers of studies per meta-analysis, the variances between the participants within studies, and the variances between studies. Fixed effects (e.g., the average treatment effect for the intervention and the average treatment effect for the trend) tended to be unbiased, and confidence intervals for the fixed effects tended to be accurate even when the error covariance model was overspecified or misspecified. The variance components, particularly at Levels 2 and 3, showed substantial bias.
authors.affiliation: University of South Florida, Tampa, FL, USA. mpetitbo@usf.edu.|Department of Educational Measurement and Research, University of South Florida, Tampa, FL, USA. mpetitbo@usf.edu.
authors.forename: Merlande
authors.initials: M
authors.lastname: Petit-Bois
authors.affiliation: University of South Florida, Tampa, FL, USA.
authors.forename: Eun Kyeng
authors.initials: EK
authors.lastname: Baek
authors.affiliation: Katholieke Universiteit Leuven, Leuven, Belgium.
authors.forename: Wim
authors.initials: W
authors.lastname: Van den Noortgate
authors.affiliation: University of Texas, Austin, TX, USA.
authors.forename: S Natasha
authors.initials: SN
authors.lastname: Beretvas
authors.affiliation: University of South Florida, Tampa, FL, USA.
authors.forename: John M
authors.initials: JM
authors.lastname: Ferron
mesh_terms: D000465:Algorithms; D035841:Behavioral Research; D015982:Bias; D003627:Data Interpretation, Statistical; D006801:Humans; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D009010:Monte Carlo Method; D012044:Regression Analysis
keywords: Autocorrelation; Meta-analysis; Multilevel modeling; Single-case designs