*! version 0.7 07jul2010
help robumeta

Title

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

Syntax

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

Model

study(varname:studyid) use studyid as the study id variable

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

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

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

rho(numlist: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.

Description

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.

Options

Model

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

variance(varname: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(varname:variancevar)
or uweights(varname:userweights) can be specified instead.

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

rho(numlist: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.

nosmallsample; Do not employ the new small sample correction.

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

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

e(dfs) Degrees of freedom for effects

Functions

e(sample) marks estimation sample

References

Hedges, 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

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

Websites for further information: http://www.northwestern.edu/ipr/qcenter/RVE-meta-analysis.html
and
http://blogs.cuit.columbia.edu/let2119/