[R-meta] min sample size for three random variables in meta-analysis

[Jose Valdebenito]

Hi,

I am conducting a (multi-level) meta-analysis with some sample sizes that
are a bit small.

I was wondering if there is a kind of rule of thumb regarding minimum
sample size number, and the maximum number of random variables I can add to
the models.

I would like to add 3 (as suggested in Cinar et al. Methods Ecol Evol.
2022;13:383–95), but I am afraid that might incur in overparameterization
if I have, say k=10?

These are the random variables:
-Phylogenetic relatedness
-Study ID
-Species ID

Also, would it be any different in a meta-regression?

Here I paste the model and dataset so you can see:

m2 <- rma.mv(L_d, L_v,
                        data = df,
                         random = list(~1|species_2,
                                               ~1|study.ID,
                                               ~1|spp),
                          R = list(species_2 = vcv), digits = 3)


> head(df, 10)
species_2                                 spp
           study.ID         L_d         L_v
Grus_americana                       Grus_americana
p.b.4             0.000       0.135
Loxia_leucoptera                      Loxia_leucoptera
p.b.15          1.057        0.068
Centrocercus_urophasianus    Centrocercus_urophasianus   p.b.60
0.384        0.021
Pica_nuttalli                              Pica_nuttalli
        p.b.8            -2.042      0.037
Acrocephalus_paludicola          Acrocephalus_paludicola       17
    0.000      0.068
Acrocephalus_paludicola          Acrocephalus_paludicola       17
      -4.978      0.334
Lepidothrix_coronata                Lepidothrix_coronata              20
             -2.043     0.088
Erithacus_rubecula                   Erithacus_rubecula                35
              -1.723      0.401
Fringilla_coelebs                       Fringilla_coelebs
 35                 -2.697      0.111
Parus_caeruleus                       Parus_caeruleus                    35
               4.862      0.559


Thanks in advance,
Joe

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