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).
robu(
formula,
data,
studynum,
var.eff.size,
userweights,
modelweights = c("CORR", "HIER"),
rho = 0.8,
small = TRUE,
...
)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
.
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.
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 as.data.frame 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.
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
data(hierdat)
# 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
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