[R-meta] A potential addition to metafor random-effect structures

Mon Feb 6 22:22:47 CET 2023

Thank you all for the thoughtful comments. Hopefully, topics like this
will come up more frequently on the list so we can have a bit more
reflection on how to tackle applied challenges occasionally
encountered in meta-analysis.

Kind regards,
Reza

On Sun, Feb 5, 2023 at 4:49 PM Yefeng Yang via R-sig-meta-analysis
<r-sig-meta-analysis using r-project.org> wrote:
>
> Great talk. In my dataset, I often have to simplify var-cov structure. It would be great if this FA structure can be incorporated into metafor. Such low-ranked models are quite interesting. I had a quick search - this kind of mixed model with a factor analytic var-cov structure has been used a lot in the analysis of multi-environment trial (MET) datasets. But no cases in the context of multivariate meta-analysis at the moment.
>
> FYI:
> Smith A B, Ganesalingam A, Kuchel H, et al. Factor analytic mixed models for the provision of grower information from national crop variety testing programs[J]. Theoretical and applied genetics, 2015, 128: 55-72.
>
> Smith A B, Borg L M, Gogel B J, et al. Estimation of factor analytic mixed models for the analysis of multi-treatment multi-environment trial data[J]. Journal of Agricultural, Biological and Environmental Statistics, 2019, 24: 573-588.
>
> Kelly A M, Cullis B R, Gilmour A R, et al. Estimation in a multiplicative mixed model involving a genetic relationship matrix[J]. Genetics Selection Evolution, 2009, 41(1): 1-9.
>
> Smith A, Cullis B, Thompson R. Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend[J]. Biometrics, 2001, 57(4): 1138-1147.
>
> Yefeng
> ________________________________
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> on behalf of James Pustejovsky via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org>
> Sent: Monday, 6 February 2023 9:14
> To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
> Cc: James Pustejovsky <jepusto using gmail.com>
> Subject: Re: [R-meta] A potential addition to metafor random-effect structures
>
> Yes, dissertation-sized project for sure.
>
> James
>
> > On Feb 5, 2023, at 3:56 PM, Viechtbauer, Wolfgang (NP) via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:
> >
> > FA structures are available in proc mixed:
> >
> > https://documentation.sas.com/doc/en/pgmsascdc/v_035/statug/statug_mixed_syntax14.htm#statug.mixed.repeatedstmt_type
> >
> > This really does sound like a nice topic for a dissertation to me.
> >
> > Best,
> > Wolfgang
> >
> >> -----Original Message-----
> >> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
> >> Behalf Of James Pustejovsky via R-sig-meta-analysis
> >> Sent: Sunday, 05 February, 2023 22:19
> >> To: R Special Interest Group for Meta-Analysis
> >> Cc: James Pustejovsky
> >> Subject: Re: [R-meta] A potential addition to metafor random-effect structures
> >>
> >> Interesting question, Reza. I've also wondered about using factor-analytic
> >> vcov structures like this. I think they could be potentially quite useful.
> >>
> >> As Reza noted, one application could be for multivariate meta-analysis
> >> (multivariate in the strict sense
> >> <https://www.jepusto.com/what-does-multivariate-mean/>), where each study
> >> could in principle measure effect sizes on a set of p outcomes, but in
> >> practice not every study reports all outcomes. With complete reporting for
> >> a large number of studies, using unstructured random effects variances
> >> works, but with missingness and/or a limited number of studies, struct =
> >> "UN" can be hard to fit. In my experience, the solutions end up returning
> >> correlations at the boundaries of the parameter space (e.g., r = 0.999 or r
> >> = -0.999 for a bivariate random effects model, which is equivalent to a
> >> one-factor model). For a p-dimensional structure, a d-dimensional factor
> >> model has sum(p + 1 - 1:d) parameters. So these structures might be useful
> >> just as an atheoretical model-building tool, which bridges between the
> >> low-dimensional structures like CS (2 parameters) or HCS (p + 1 parameters)
> >> and the totally unconstrained UN structure (p x (p + 1) / 2 parameters).
> >>
> >> I could also see applications where such models have a meaningful
> >> theoretical interpretation. For example, perhaps there are p outcomes,
> >> which vary in their degree of sensitivity to intervention. Studies might
> >> vary along a single latent factor of intervention potency, so strong
> >> interventions have relatively large effect sizes for all outcomes, weak
> >> interventions have relatively small effects for all outcomes. The random
> >> effect for outcome j in study i might then be described by u_ij = L_j X
> >> f_i, where f_i is the latent factor of intervention potency and L_j is the
> >> sensitivity to intervention of outcome j. I could also imagine extending
> >> this further to two or more factors---maybe intervention potency and
> >> population risk level, with u_ij = L_1j X f_1j + L_2j x f_2j?
> >>
> >> James
> >>
> >>
> >>> On Sun, Feb 5, 2023 at 2:31 PM Reza Norouzian via R-sig-meta-analysis <
> >>> r-sig-meta-analysis using r-project.org> wrote:
> >>>
> >>> Hi Wolfgang,
> >>>
> >>> Thank you for your interest. Yes, potentially we can lower G's rank but it
> >>> may no longer be invertible.
> >>>
> >>> I haven't looked at the guts of glmmTMB but obviously they use TMB in the
> >>> back end for higher speed for larger models.
> >>>
> >>> The other thing about rr() in glmmTMB is that my quick search didn't return
> >>> any simulation studies testing how approximate this approximation can be,
> >>> especially given that in practice *d* is pretty much determined by
> >>> consulting the information-criteria-type model fit indices.
> >>>
> >>> But overall, there is some potential for this modification to help users
> >>> test multivariate-multilevel models currently difficult or nearly
> >>> impossible to fit.
> >>>
> >>> I've not been lucky enough to come across a large number of such datasets,
> >>> but in the few cases where this was the case, I had to drop a few of the
> >>> assumptions I had in mind which eventually led me to finding about the
> >>> rank-reduced structure recently added to the glmmTMB package.
> >>>
> >>> I may also be looking to see if I can have such models actually fit using
> >>> glmmTMB, if it allows flexibility in its `dispformula=` and `control=`
> >>> arguments.
> >>>
> >>> Kind regards,
> >>> Reza
> >>>
> >>> On Sun, Feb 5, 2023, 7:29 AM Viechtbauer, Wolfgang (NP) via
> >>> R-sig-meta-analysis <r-sig-meta-analysis using r-project.org> wrote:
> >>>
> >>>> I have been doing a bit more thinking about this (can't help myself).
> >>>>
> >>>> One might consider using one of the various decompositions (e.g., SVD) to
> >>>> accomplish this. In fact:
> >>>>
> >>>> https://en.wikipedia.org/wiki/Low-rank_approximation
> >>>>
> >>>> Something even simpler might be to use the Cholesky decomposition, that
> >>>> is, if G is a p*p symmetric positive-definite var-cov matrix, then
> >>>> t(chol(G)) %*% chol(G) == G. So, we could use t(chol(G[1:r,])) %*%
> >>>> chol(G[1:r,]) as a lower rank approximation to G, with r < p. In fact,
> >>> for
> >>>> struct="UN", rma.mv() uses the Cholesky decomposition anyway for
> >>> ensuring
> >>>> that G is positive-definite. So it might be possible to implement this
> >>>> without too much difficulty. Problems might creep in though since
> >>>> t(chol(G[1:r,])) %*% chol(G[1:r,]) is no longer invertible (since it is
> >>> by
> >>>> construction no longer of full rank), so one might need to use a
> >>>> generalized inverse, but whether this is actually an issue or not depends
> >>>> on whether one needs that inverse.
> >>>>
> >>>> Best,
> >>>> Wolfgang
> >
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