Fitting three-level meta-analytic models in R: A step-by-step tutorial

In the citing paper

“As a result, there no information is lost and (moderator) effects can be estimated more precisely and with maximum power in the statistical analyses (Assink and Wibbelink 2016).”

In the citing paper

“As recommended by Assink and Wibbelink (2016), moderation analyses should be conducted if less than 75% of the variance can be attributed to Level 1.”

In the citing paper

“There is no need to know the correlations between outcomes extracted from one study for estimating the covariance matrix of the effect sizes since the second level in the model accounts for sampling covariation ( Assink and Wibbelink, 2016 ).”

In the citing paper

“To deal with this intra-study dependency of prevalence estimates, we opted for the three-level model with random effects for data points obtained within one article to calculate pooled prevalence estimates (29, 30).”

In the citing paper

“we used a multilevel approach to metaanalysis (Assink & Wibbelink, 2016), which is a strong method for dealing with dependency of effect sizes, as it accounts for the hierarchical structure of the data in which effect sizes are nested within studies (Van Den Noortgate & Onghena, 2003).”

In the citing paper

“The Knapp and Hartung method (2003) has the advantage that it reduces Type I‐errors (Assink & Wibbelink, 2016).”

In the citing paper

“A three‐level random effects model was used to account for three levels of variance, including the sampling variance of each effect size (level 1), the variance between effect sizes extracted from the same study (level 2), and the variance between the studies (level 3).”

In the citing paper

“Likelihood‐ratio tests were used to compare the deviance scores of the full model to the deviance of models excluding level 2 or level 3 variance parameters, making it possible to determine whether significant variance is present at the two levels (Assink & Wibbelink, 2016).”

In the citing paper

“This analysis considers three levels of variance components distributed across the model, including variance between effect sizes from the same study and variance between studies; this therefore allows for an examination of how effect sizes vary between participants (Level 1), outcomes (Level 2) and studies (Level 3; Assink & Wibbelink, 2016).”

In the citing paper

“The analyses suggested that there was significant variability ( p = .001) between effect sizes (Level 2) and between studies (Level 3), indicating that moderator analyses should be conducted (Assink & Wibbelink, 2016).”

In the citing paper

“Dependency of effect sizes normally means that effect sizes within studies are correlated (as these are expected to show a certain similarity); this creates an overlap of information and inflates information produced by the analysis, which can result in an overconfidence in its results (Assink & Wibbelink, 2016).”

In the citing paper

“A hierarchical multi-level multivariate meta-analytical approach for data plotting was used to account for statistical dependence in effect sizes from multiple within-study comparison arms (cannabis use frequencies) to a common control group (non-use)”

In the citing paper

“As studies reported more than one effect size (for example, depression and suicidal ideation), we opted for a multilevel meta-analysis with three levels (for example, ref. 47), a random-effect model, which enables modelling the dependent effect sizes from the same study.”

In the citing paper

“For parameter estimation, restricted maximum likelihood estimation was applied, and for standard errors, P values and 95% CIs, Knapp and Hartung’s adjustment47,227 was used.”