help robumeta

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

Syntax

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

optionsDescription ------------------------------------------------------------------------- Model

study(studyid)usestudyidas the study id variable

weighttype(weighting_scheme)useweighting_schemeas the method to calculate weights

variance(variancevar)usevariancevaras the sampling variance of the effect size

uweights(userweights)useuserweightsas weights in a fixed effect model

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

where elements of

weighting_schememay be

randoma 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.

fixeda 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.

hierarchicala 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.

Description

robumetaprovides 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.

Options+-------+ ----+ Model +------------------------------------------------------------

study(studyid)specified thatstudyidbe 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 isweighttype(fixed).

variance(variancevar)specifies the variablevariancevarthat is the sampling variance of the effect size estimates. This must be specified for any random effects model. For fixed effects models,variance(variancevar)oruweights(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.

Examples

. 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

robumetasaves the following ine():Scalars

e(N)number of observationse(N_g)number of studiese(df_r)model degrees of freedom

e(tau2)method-of-moments tau-square estimatee(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-squaree(QR)QR used for estimating omega-square

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

e(cmd)robumetae(depvar)depvarMatrices

e(b)coefficient vectore(V)variance-covariance matrix of the estimatorsFunctions

e(sample)marks estimation sample

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

Website for further information: http://www.northwestern.edu/ipr/qcenter/RVE-meta-analysis.html