Erratum to: Robust variance estimation in meta-regression with dependent effect size estimates (Research Synthesis Methods, (2010), 1, 1, (39-65), 10.1002/jrsm.5)

On pages 47–48, under the heading ‘Dependence Introduced by Study Level Effects’, the estimators of τ² and ω² given are incorrect. The correct estimators are as follows. Assume a covariance matrix of the form Σ=diag(Σ₁, …, Σ_m), where (Figure presented.) where τ² is the random between cluster variance, ω² is the random within cluster between study variance, I_j is a k_j × k_j identity matrix, J_j is a k_j × k_j matrix of 1's, and V_j is the diagonal matrix of study level known variances. We let Q_E be the sum of squares provided in our original paper. That is, (Figure presented.) where W_j=V (Formula presented.). An additional sum of squares can be written (Figure presented.) where. Method of moments estimators of the parameters τ² and ω² can therefore be written, (Figure presented.) and (Figure presented.) where (Figure presented.) and p=rank(X), k_j is the number of studies in cluster j and V=(X′WX)⁻¹. As suggested in the paper, when either or are negative, their estimators are set equal to 0. Finally, please note that the R functions given in Appendix B contain several typesetting errors (which unfortunately we did not catch). We also did not include an R function for estimating the standard errors in a hierarchical model. In order to avoid new typographical errors, we have included correct (and updated) versions of both functions on our website, http://www.northwestern.edu/ipr/qcenter/RVE-meta-analysis.html.