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

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Wed Jan 25 09:38:12 CET 2023

```Depends on what you mean by 'variance of the residuals'. With:

rstandard(res)\$se^2

you can obtain the *sampling variance* of the residuals. Note that each residual has its own sampling variance.

If you just want the *sample variance* of the residuals, then

var(resid(res))

would give you that.

Best,
Wolfgang

>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
>>
>> 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

```