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

[Jarrod Hadfield]

Hi Jon,

MCMCglmm fits random-effect meta-analysis (I think this is what it is 
caused) which assumes that even after correcting for sampling errors 
there will be some 'real' between-observation variance (and in your case 
covariance). I'm not sure what you are modelling, but at least in the 
types of data I work with I can't really believe there isn't some  
'real' between-observation variance.

Cheers,

Jarrod




On 20/10/2016 19:09, Jon Bischof wrote:
> 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 
> <mailto: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
>         <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
>
>                 [[alternative HTML version deleted]]
>
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>
>
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