[R-meta] rma, sandwich correction and very small data sets

[Valeria Ivaniushina]

Dear colleagues,

I do 3-level meta-analysis with a small number of studies and a small
number of clusters.
1st level - model, 2nd level - study, 3rd level - database.

The effect I am interested in can be specified in different ways. Experts
in the field advised me to make separate meta analyses for each
specification and then combine the results, kind of meta-meta.

I have several questions:

1)  Is this a correct code?
First I do REML:
eff1 <- rma.mv(yi=wb$EFFECT_SIZE_Influence,
V=wb$SE_Influence,random = list(~1 | ID_study, ~1 | ID_database),
tdist=TRUE, data=wb)

Then with this object I use sandwich, to get cluster-robust standard
errors, clustering at the highest level of nesting:
coef_test(eff1, vcov = "CR2",cluster = wb$ID_database)

2)  I am worried that the numbers of clusters are too small -- are the
results reliable?
eff1: 17 models, 12 studies, 5 databases
eff2: 8 models, 5 studies, 5 databases
eff3: 11 models, 9 studies, 7 databases

3) Variance distribution is vastly different between three models - what
does it tell me?
eff1: 1st level 4%, 2nd level 0%, 3rd level 96%
eff2: 1st level 100%, 2nd level 0%, 3rd level 0%
eff3: 1st level 15%, 2nd level 0%, 3rd level 85%

4) How can I combine the results of three meta-analyses?

Best,
Valeria

	[[alternative HTML version deleted]]