[R-meta] How to interpret sigma(model)^2 in metafor

[Yuhang Hu]

Thank you so much Wolfgang, for your response.

On the same note, is there a way to extract the variance of the residuals
for the model, say from a fitted model like below?

dat <- dat.konstantopoulos2011
res <- rma.mv(yi ~ I(year-mean(year)), vi, random = ~ 1 |district/study,
data= dat)

Thank you.
Yuhang


On Tue, Jan 24, 2023 at 1:21 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Yuhang,
>
> sigma() is a generic function:
>
> > sigma
>
> function (object, ...)
>
> UseMethod("sigma")
>
> <bytecode: 0x2e1a3c8>
>
> <environment: namespace:stats>
>
> So, when calling sigma() on an object from the metafor package, the 'S3
> dispatch mechanism' will first check if there is a method for the type
> (i.e., class) of object that you are passing to the sigma() function.
>
> > library(metafor)
> > methods(sigma)
> [1] sigma.default* sigma.gls*     sigma.lmList*  sigma.lme*     sigma.mlm*
> see '?methods' for accessing help and source code
>
> Since there is none (there is no sigma.rma() function or anything like
> it), it will call sigma.default(). So let's look at what that does:
>
> > sigma.default
> Error: object 'sigma.default' not found
>
> Hmmm, why can't we look at the code for this function? Note the * after
> sigma.default -- this indicates that the method definition is not exported.
> But we can still look at this with:
>
> > getAnywhere(sigma.default)
> A single object matching 'sigma.default' was found
> It was found in the following places
>   registered S3 method for sigma from namespace stats
>   namespace:stats
> with value
>
> function (object, use.fallback = TRUE, ...)
> sqrt(deviance(object, ...)/(nobs(object, use.fallback = use.fallback) -
>     sum(!is.na(coef(object)))))
> <bytecode: 0x9806a08>
> <environment: namespace:stats>
>
> (or, if you would happen to know that this function comes from the stats
> package, you could use stats:::sigma.default).
>
> So, we can see what is happening. In essence:
>
> dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
> data=dat.bcg)
> res <- rma(yi, vi, data=dat)
> sigma(res)
> sqrt(deviance(res)/(nobs(res) - sum(!is.na(coef(res)))))
>
> This has, as far as I am concerned, no logical meaning for rma objects.
>
> Note that I try to be very explicit in the documentation what kind of
> methods are available (and meaningful) for a given object in the metafor
> package:
>
> https://wviechtb.github.io/metafor/reference/rma.uni.html#methods
>
> sigma() is not listed there. I cannot prevent default methods from being
> called unless I would actually put a sigma.rma() method into the metafor
> package. I have actually considered this, but I don't have a good idea what
> meaningful result this should return.
>
> In any case, I hope this provides you with some idea how you can dig into
> the code (and the mechanisms of how it is being called) in general.
>
> Best,
> Wolfgang
>
> >Hello Colleagues,
> >
> >By habit, I always check the variance of the residuals of my ordinary
> >regression models using: sigma(model)^2, which is also printed in the
> >output.
> >
> >I know that the variance of the residuals in meta-regression is not
> >estimated but rather taken as being known and fixed by virtue of user's
> >supplying the 'vi' or 'V' to functions such as rma.uni() and
> >rma.mv().
> >
> >So, I was wondering what is the interpretation of sigma(rma.uni_model)^2
> >and sigma(rma.mv_model)^2 and how they connect to the user-supplied
> >'vi'.
> >
> >Thank you very much for your time.
> >
> >Best,
> >Yuhang
>

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