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

[Philippe Tadger]

Dear Luke

I will suggest to choose the model that can provide a reliable 
estimation of the variances. Usually a variance estimation equal to zero 
or a correlation estimation  equal to 1 or -1 are potential warning 
signal, your model is in the limit of the parameter space: so you can 
having an underestimation and/or a non-identifiable model. How can you 
be sure? Using the profile() function in each model. In your case model 
g1 is identifiable, but g2 is not identifiable. I'll choose g1.

On 13/11/2021 05:24, Luke Martinez wrote:
> 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)
>
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-- 
Kind regards/Saludos cordiales
*Philippe Tadger*
ORCID <https://orcid.org/0000-0002-1453-4105>, Reseach Gate 
<https://www.researchgate.net/profile/Philippe-Tadger>
Phone/WhatsApp: +32498774742
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