Hedges, Tipton and Johnson (2010): fit weighted least squares with
any working weights, then use the cluster-robust sandwich, which
is consistent as the number of STUDIES grows whatever the
within-study correlation is. The working weights affect efficiency,
never validity. With few clusters the sandwich is badly
downward-biased, so Tipton's (2015) small-sample correction is
applied by default with Satterthwaite degrees of freedom; her rule
of thumb that df < 4 is untrustworthy is flagged rather than
left to be discovered.
Usage
morie_psy_ma_rve(yi, X, cluster, w = NULL, small_sample = TRUE)
Arguments
- yi
effect sizes, possibly several per study.
- X
meta-regression design; a constant is added if absent.
- cluster
study identifiers.
- w
working weights; equal when NULL.
- small_sample
apply the HTZ correction.
Value
list: beta, se, t, df, p, vcov, n_clusters, n_effects,
df_warning, method.
References
Hedges, Tipton and Johnson (2010), Research Synthesis
Methods 1:39-65; Tipton (2015), Psychological Methods
20:375-393.
Examples
set.seed(1)
cl <- rep(1:10, each = 3)
x <- stats::rnorm(30)
morie_psy_ma_rve(0.4 + 0.6 * x + stats::rnorm(30), x, cl)$beta
#> [1] 0.5293207 0.6418863
