[R-meta] 3-level meta with robust errors

[Valeria Ivaniushina]

Dear list members,

We are conducting several meta-analyses using the metafor package in R
(Viechtbauer 2010) because of 3-level data structure, followed by
sandwich-type estimator with a small-sample adjustment to get cluster
robust standard errors.

There are some things that puzzle me, and I hope to get answers from the
community.

1. We calculate 95% CI for our mean effect size, and p-value is calculated
as a part of the output. While CI always indicate significant mean effect
size, p-values are often > 0.05
- Should I report both CI and p-value?
- How to interpret such discrepancy?

2. When I draw a forest plot for a meta-analysis of 8 models, I can see
that 95% CIs for every coefficient contain zero (for example, -0.40 -
0.84). However, the 95% CI for the mean coefficient is well above zero
(0,28 - 0,45).  How is it possible?

3.  Theoretically, the data has a 3-level structure (model; article;
database). But sometimes I see that there is no variance on one or two of
the levels. Should I repeat the analysis with only 2 or 1 level, according
to the variance distribution?

Best, Valeria

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