help robumeta

Title robumeta -- Robust variance estimation in meta-regression with dependent effect size estimates


robumeta depvar [indepvars] [if] [in], {variance(variancevar)| uweights(userweights)} [options]

options Description ------------------------------------------------------------------------- Model

study(studyid) use studyid as the study id variable

weighttype(weighting_scheme) use weighting_scheme as the method to calculate weights

variance(variancevar) use variancevar as the sampling variance of the effect size

uweights(userweights) use userweights as weights in a fixed effect model

rho(icc) use icc in calculating variance components in the random effects model


where elements of weighting_scheme may be

random a random effects model weighting scheme that assumes the observed effect size estimates within each study are correlated with one another. In this model, the correlation arises from sampling error which occurs when, for example, multiple outcome measures are collected on the same units. This is the default.

fixed a fixed effects model weighting scheme that can be used when generalizations are limited to those effect sizes in the meta-analysis. This is useful when weights other than inverse-variance weights are used.

hierarchical a hierarchical model weighting scheme that is used when there is an additional level of nesting. This model assumes that the observed effect size estimates are nested within studies which are nested within clusters. For example, studies from the same research group may have something in common with one another.


robumeta provides a robust method for estimating standard errors in meta-regression, particularly when there are dependent effects. Dependent effects occur in two basic models: (1) correlated effects and (2) hierarchical meta-regression. In (1), the dependency arises as a result of correlated estimation errors; for example, a study collects two outcome measures on each participant and then summarizes these as two effect size measures. In (2), the dependency arises as a result of correlated parameters; for example, the same research group may publish several studies and there may be elements of these studies that are similar to one another. Importantly, the robust standard error procedure used here does not require the underlying correlation structure to be known; additionally, it works for any weights and can be used to estimate the mean effect size as well as meta-regression models. Finally, note that the procedure also can be used with independent effects, particularly when distributional assumptions might be violated. For more information on the underlying theory, see the references at the end of this help file.


+-------+ ----+ Model +------------------------------------------------------------

study(studyid) specified that studyid be used as the study-level identifier. If this option is not specified, then the effect sizes are assumed to be independent.

weighttype(weighting_scheme) specifies the weights to be used for combining the effect size estimates. The default is weighttype( fixed).

variance(variancevar) specifies the variable variancevar that is the sampling variance of the effect size estimates. This must be specified for any random effects model. For fixed effects models, variance(variancevar) or uweights(userweights) can be specified instead.

uweights(userweights) specified the user created weights for use with a fixed effects model.

rho(icc) for the correlated effects model, specifies the value of the correlation rho to be used, which must be < 1.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.


. use hedgesexample.dta . robumeta effectsize k1, study(study) variance(vareffsize) weighttype(random) rho(.8) . robumeta effectsize k1, study(study) variance(vareffsize) weighttype(hierarchical)

Saved results

robumeta saves the following in e():

Scalars e(N) number of observations e(N_g) number of studies e(df_r) model degrees of freedom

e(tau2) method-of-moments tau-square estimate e(tau2o) observed tau-square if estimate is negative

e(omega2) method-of-moments omega-square estimate (used in hierarchical model) e(omega2o) observed omega-square if estimate is negative

e(QE) QE used for estimating tau-square e(QR) QR used for estimating omega-square

e(rho) in correlated effects models, use specified ICC

Macros e(cmd) robumeta e(depvar) depvar

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample


Hedges, Larry V., Elizabeth Tipton, and Matthew C. Johnson. 2010. Robust variance estimation in meta-regression with dependent effect size estimates. Research Synthesis Methods. ( DOI: 10.1002/jrsm.5

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