[R-meta] AICc or variance components, which one matters more?

[Luke Martinez]

Hello Colleagues,

I've fit two candidate models (g1 and g2).

With g1, I get two non-zero variance components for 'lab' and 'study'.

With g2, I get a zero variance component for 'lab' and a non-zero one
for 'study'.

So, from the perspective of variance components, g1 seems like a better model.

But when I compare the models using AICc, g2 seems like a better model.

I wonder, then, which criterion should I use to choose the model (AICc
or the variance components)?

Thanks,
Luke
For reproducibility, I'm showing a somewhat similar situation with a
small section of my data below.

m="
      lab study   yi         vi es_id
         1     1 1.04 0.48503768 1
         1     1 0.96 0.51076604 2
         1     2 1.71 0.05767389 3
         2     2 1.52 0.07539841 4
         1     3 1.91 0.31349510 5
         2     4 3.01 0.67910095 6
         2     4 3.62 0.50670360 7
         9     5 0.99 0.18297170 8
         9     5 0.43 0.37225851 9
         9     6 1.68 0.39072390 10
         9     6 1.25 0.02879550 11"
dd <- read.table(text=m,h=T)

(g1=rma.mv(yi, vi, random = ~1|lab/study, data = dd))
                    estim    sqrt  nlvls  fixed     factor
sigma^2.1  0.1245  0.3529      3     no        lab
sigma^2.2  0.2535  0.5035      7     no  lab/study

(g2=rma.mv(yi, vi, random = list(~1|lab, ~1|study), data = dd))
                     estim    sqrt  nlvls  fixed  factor
sigma^2.1  0.0000  0.0000      3     no     lab
sigma^2.2  0.5127  0.7160      6     no   study

fitstats(g1,g2)[5,]
            g1          g2
AICc: 30.85992 29.73897
(for full data, AICc of g2 is more noticeably smaller than that of g1)