[R-sig-ME] MCMCglmm multivariate meta-analysis with covariance

[Jon Bischof]

Jarrod,

Thanks for your detailed response! Your understanding of my model is
correct: it's just a single grouping metaanalysis in two dimensions:

(y_i,1, y_i,2) ~ Normal ( (theta_i,1, theta_i,2), V_i )
(theta_i,1, theta_i,2) ~ Normal ( (mu_1, mu_2), S )

where V_i is a known covariance matrix of measurement error.

As a new user of mcmcglmm I will need some time to experiment with your
idea to confirm that it works. My understanding, however, was that residual
error was specified in the R matrix and not the G matrix. Do we need to fix
R as well? Will we still be able to estimate S?

Thanks!
Jon

On Tue, Oct 18, 2016 at 11:45 PM, Jarrod Hadfield <j.hadfield at ed.ac.uk>
wrote:

> Hi Jon,
>
> If you have the covariance matrix for your observations, then take its
> inverse and store it in sparse format:
>
> Cinv_sparse<-as(Cinv, "dgCMatrix")
>
> where Cinv is the inverse in dense format. When you say multivariate do
> you mean something like an explicit bivariate response such that the fixed
> formula is of the form cbind(y_1, y_2)~...?  If so you need to organise
> your data in long format and pass a single response vector. You can include
> a variable that denotes whether the observation is y_1 or y_2 and use it
> like "trait", and include a variable that denotes the original row for the
> observation and use it like "units". If we call this second variable "row"
> then having fit "row" as a random effect, and pass the argument
> ginverse=list(row=Cinv_sparse) to MCMCglmm. You will also need to fix the
> "row" variance to one in the prior:
>
> G1=list(V=1, fix=1)
>
> Presumably covariances are only non-zero between observations from the
> same original row? If so make sure the sparse Matrix also represents this:
> numerical issues during inversion may cause zero entries to differ slightly
> from zero and hence not be represented as zero.
>
> Cheers,
>
> Jarrod
>
>
>
>
> Then you can fit the term ~trait:units
>
>
>
>
>
> On 19/10/2016 05:41, Jon Bischof wrote:
>
>> I'm interested in fitting a multivariate meta-analysis model with
>> correlated measurement error. This means fixing the error to a covariance
>> matrix per row.
>>
>> I saw this post
>> <https://stat.ethz.ch/pipermail/r-sig-mixed-models/2013q2/020180.html> on
>> the mailing list about non-correlated outcomes, but the noise correlation
>> is too large to ignore in my use case. Professor Hadfield implies in the
>> post that it is possible but "complicated". Does anyone know how to do it?
>>
>> Thanks!
>> Jon Bischof
>>
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>>
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>
>
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