robu: Fitting Robust Variance Meta-Regression Models

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robuR Documentation

Fitting Robust Variance Meta-Regression Models


robu is used to meta-regression models using robust variance estimation (RVE) methods. robu can be used to estimate correlated and hierarchical effects models using the original (Hedges, Tipton and Johnson, 2010) and small-sample corrected (Tipton, 2013) RVE methods. In addition, robu contains options for fitting these models using user-specified weighting schemes (see the Appendix of Tipton (2013) for a discussion of non- efficient weights in RVE).


  modelweights = c("CORR", "HIER"),
  rho = 0.8,
  small = TRUE,



An object of class "formula". A typical meta-regression formula will look similar to y ~ x1 + x2..., where y is a vector of effect sizes and x1 + x2... are (optional) user-specified covariates. An intercept only model can be specified with y ~ 1 and the intercept can be ommitted as follows y ~ -1 +....


A data frame, list or environment or an object coercible by to a data frame.


A vector of study numbers to be used in model fitting. studynum must be a numeric or factor variable that uniquely identifies each study.


A vector of user-calculated effect-size variances.


A vector of user-specified weights if non-efficient weights are of interest. Users interested in non-efficient weights should see the Appendix of Tipton (2013) for a discussion of the role of non-efficient weights in RVE).


User-specified model weighting scheme. The two two avialable options are modelweights = "CORR" and modelweights = "HIER". The default is "CORR". See Hedges, Tipton and Johnson (2010) and Tipton (2013) for extended explanations of each weighting scheme.


User-specified within-study effect-size correlation used to fit correlated (modelweights = "CORR") effects meta-regression models. The value of rho must be between 0 and 1. The default value for rho is 0.8. rho is not specified for hierarchical (modelweights = "HIER") effects models.


small = TRUE is used to fit the meta-regression models with the small- sample corrections for both the residuals and degrees of freedom, as detailed in Tipton (2013). Users wishing to use the original RVE estimator must specify small = FALSE as the corrected estimator is the default option.


Additional arguments to be passed to the fitting function.



A data frame containing some combination of the robust coefficient names and values, standard errors, t-test value, confidence intervals, degrees of freedom and statistical significance.


The number of studies in the sample n



The number of effect sizes in the sample k


k descriptives

the minimum min.k, mean mean.k, median median .k, and maximum max.k number of effect sizes per study.


tau.sq is the between study variance component in the correlated effects meta-regression model and the between-cluster variance component in the hierarchical effects model. tau.sq is calculated using the method-of-moments estimator provided in Hedges, Tipton, and Johnson (2010). For the correlated effects model the method-of-moments estimar depends on the user-specified value of rho.


omega.sq is the between-studies-within-cluster variance component for the hierarchical effects meta-regression model. omega.sq is calculated using the method-of-moments estimator provided in Hedges, Tipton, and Johnson (2010) erratum.


I.2 is a test statistics used to quantify the amount of variability in effect size estimates due to effect size heterogeneity as opposed to random variation.


Hedges, L.V., Tipton, E., Johnson, M.C. (2010) Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods. 1(1): 39–65. Erratum in 1(2): 164–165. DOI: 10.1002/jrsm.5

Tipton, E. (in press) Small sample adjustments for robust variance estimation with meta-regression. Psychological Methods.


# Load data

# Small-Sample Corrections - Hierarchical Dependence Model
HierModSm <-  robu(formula = effectsize ~ binge + followup + sreport
                   + age, data = hierdat, studynum = studyid, 
                   var.eff.size = var, modelweights = "HIER", small = TRUE)

print(HierModSm) # Output results

robumeta documentation built on March 31, 2023, 11:48 p.m.

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