metaoutliers {altmeta} | R Documentation |
Calculates the standardized residual for each study in meta-analysis using the methods desribed in Hedges and Olkin (1985) Chapter 12 and Viechtbauer and Cheung (2010). A study is considered as an outlier if its standardized residual is greater than 3 in absolute magnitude.
metaoutliers(y, s2, model)
y |
a numeric vector indicating the observed effect sizes in the collected studies; they are assumed to be normally distributed. |
s2 |
a numeric vector indicating the within-study variances. |
model |
a character string specified as either |
Suppose that a meta-analysis collects n studies. The observed effect size in study i is y_i and its within-study variance is s^{2}_{i}. Also, the inverse-variance weight is w_i = 1 / s^{2}_{i}.
Hedges and Olkin (1985) Chapter 12 describes the outlier detection procedure for fixed-effect meta-analysis (model
= "FE"
). Using the studies except study i, the pooled estimate of overall effect size is \bar{μ}_{(-i)} = ∑_{j \neq i} w_j y_j / ∑_{j \neq i} w_j. The residual of study i is e_{i} = y_i - \bar{μ}_{(-i)}. The variance of e_{i} is v_{i} = s_{i}^{2} + (∑_{j \neq i} w_{j})^{-1}, so the standardized residual of study i is ε_{i} = e_{i} / √{v_{i}}.
Viechtbauer and Cheung (2010) describes the outlier detection procedure for random-effects meta-analysis (model
= "RE"
). Using the studies except study i, let the method-of-moments estimate of between-study variance be \hat{τ}_{(-i)}^{2}. The pooled estimate of overall effect size is \bar{μ}_{(-i)} = ∑_{j \neq i} \tilde{w}_{(-i)j} y_j / ∑_{j \neq i} \tilde{w}_{(-i)j}, where \tilde{w}_{(-i)j} = 1/(s_{j}^{2} + \hat{τ}_{(-i)}^{2}). The residual of study i is e_{i} = y_i - \bar{μ}_{(-i)}, and its variance is v_{i} = s_{i}^2 + \hat{τ}_{(-i)}^{2} + (∑_{j \neq i} \tilde{w}_{(-i)j})^{-1}. Then, the standardized residual of study i is ε_{i} = e_{i} / √{v_{i}}.
This functions returns a list which contains standardized residuals and identified outliers. A study is considered as an outlier if its standardized residual is greater than 3 in absolute magnitude.
Hedges LV and Olkin I (1985). Statistical Method for Meta-Analysis. Academic Press, Orlando, FL.
Viechtbauer W and Cheung MWL (2010). "Outlier and influence diagnostics for meta-analaysis." Research Synthesis Methods, 1(2), 112–125.
data("aex") attach(aex) metaoutliers(y, s2, model = "FE") metaoutliers(y, s2, model = "RE") detach(aex) data("hipfrac") attach(hipfrac) metaoutliers(y, s2) detach(hipfrac)