help robumeta

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

Syntax

     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.

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(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.

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

    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

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