[R-meta] How does the rma.mv function handle multiple inferences within a study-level

[Divya Ravichandar]

I apologize for my haste in the previous email. All sigma^2 in the above
matrix are indeed the same (There were some rounding offs I overlooked).
So would a take away here be that since there are two inferences under one
Study, these are additionally weighted by the sigma^2? As opposed to case2
shown below where with 1 inference per Bin-level, a meta-analysis at the
Bin level would simply down weight each inference by Sigma^2+SE^2 only

*Case 2*
case <- data.frame(Study=c("a","b","c","c"),
Bin=c("a","b","c","d"),ES=c(-1.5,-3,1.5,3), SE=c(.2,.4,.2,.4))
res <- rma.mv(ES, SE^2, random = ~ 1 | Bin, data=case)

On Wed, Apr 1, 2020 at 2:00 PM Divya Ravichandar <divya using secondgenome.com>
wrote:

> Thank you for your explanation of how the weight matrix is computed.
>
> A followup question, on the 'sigma^2' only terms in the variance matrix
> [terms in matrix positions (3,4) & (4.3)].
>
> I assume (based on running the example above) the sigma^2 here is
> different from the sigma^2 used along the diagonal. Is this correct? If
> yes, is a sigma^2 estimated based on just the values corresponding to study
> c in the example?
>
> Thank you
>
> On Wed, Apr 1, 2020 at 1:21 PM Viechtbauer, Wolfgang (SP) <
> wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:
>
>> Dear Divya,
>>
>> The model you are using implies the following structure for the marginal
>> var-cov matrix of the estimates:
>>
>> [SE_1^2 + sigma^2                                                   ]
>> [                 SE_2^2 + sigma^2                                  ]
>> [                                  SE_3^2 + sigma^2 sigma^2         ]
>> [                                  sigma^2          SE_4^2 + sigma^2]
>>
>> The weight matrix is the inverse thereof. See:
>>
>> library(metafor)
>>
>> case <- data.frame(Study=c("a","b","c","c"), ES=c(-1.5,-3,1.5,3),
>> SE=c(.2,.4,.2,.4))
>> res <- rma.mv(ES, SE^2, random = ~ 1 | Study, data=case)
>> res
>>
>> vcov(res, type="obs")
>> weights(res, type="matrix")
>>
>> The model estimate is then given by b = (X'WX)^(-1) X'Wy, where X is just
>> a column vector of 1s, W is the weight matrix above, and y is a column
>> vector with the 4 effect sizes.
>>
>> Best,
>> Wolfgang
>>
>> -----Original Message-----
>> From: R-sig-meta-analysis [mailto:
>> r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Divya Ravichandar
>> Sent: Wednesday, 01 April, 2020 21:59
>> To: r-sig-meta-analysis using r-project.org
>> Subject: [R-meta] How does the rma.mv function handle multiple
>> inferences within a study-level
>>
>> My use case is presented in the dataframe below. Studies a,b and c are to
>> be integrated in a meta-analysis using: rma.mv(ES, SE^2, random = ~ 1 |
>> Study, data=case)
>>
>> In this case, studies a & b have one inference each but because of my
>> study
>> design two inferences exist for study c.  I am curious as to how the 2
>> inferences under study c are weighted in the meta-analysis calculation as
>> compared to the inference for studies a &b.
>>
>> case <- data.frame(Study=
>>
>> c("a","b","c","c"),Effect_size=c(-1.5,-3,1.5,3),Standard_error=c(.2,.4,.2,.4))
>>
>> Thanks
>> --
>> *Divya Ravichandar*
>> Scientist
>> Second Genome
>>
>
>
> --
> *Divya Ravichandar*
> Scientist
> Second Genome
>


-- 
*Divya Ravichandar*
Scientist
Second Genome

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