[R-meta] clubSandwich for rma.uni() models

Hi Luke,

cluster-robust variance estimation methods are relevant to rma.uni()
models for a few reasons:
1. If you cluster by row, as in vcovCR(rma_uni_fit, cluster =
dat$es_ID, type = "CR2"), you get heteroskedasticity-robust standard
errors. This can be useful if the sampling variances used in
estimating the random effects model could be systematically
inaccurate/wrong or just because, in practice, the sampling variances
are usually estimated rather than known exactly. Sidik & Jonkman
provide a thorough rationale and description in this paper:
Sidik, K., & Jonkman, J. N. (2006). Robust variance estimation for
random effects meta-analysis. Computational Statistics & Data
Analysis, 50(12), 3681-3701.
2. Perhaps you have a dataset with a little bit of dependency (say,
just a few studies that report multiple effect size estimates) but you
don't want to go to the trouble of modeling it all and you'd rather
just ignore the dependencies. Instead of sticking your fingers in your
ears and going "la la la", you could fit the model with rma.uni
(ignoring the dependencies) but then use cluster-robust standard
errors to acknowledge the possibility that not all of the effect sizes
are independent.
3. Perhaps you have some other reason to fit a univariate (or
"marginal") model to a dataset that has some dependency structure to
it. For instance, multivariate random effects models involve (tacit)
assumptions about independence between random effects and predictors
and independence between random effects and structural features of the
data (such as sampling variances or number of effect sizes per study).
Using a multivariate model when those assumptions are violated can
lead to systematically biased estimates of average effects, and
perhaps there's a situation where using a univariate model would avoid
those assumptions and produce unbiased estimates. In such a situation,
it would make sense to cluster the standard errors to account for
dependence in the effect size estimates.

James

Dear Meta Experts,

(A) My understanding has been that the sandwich estimators are only
relevant to rma.mv() models where the structure of `V=` and/or
`random=` is suspected to be misspecified (hence SE of fixed effects
may be inaccurate).

(B) My understanding has also been that the sandwich estimators use
the highest clustering variable in purely nested models to compute the
dfs needed for fixed effects' p-value calculations.

rma.uni() models may loosely meet the (B) requirement. But it is not
obvious to me how such models may meet the (A) requirement.

Thus, how is clubSandwich:::vcovCR.rma.uni() relevant to rma.uni() models?

Thanks,
Luke

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