[R-meta] A potential addition to metafor random-effect structures
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 at r-project.org> on behalf of James Pustejovsky via R-sig-meta-analysis <r-sig-meta-analysis at r-project.org>
Sent: Monday, 6 February 2023 9:14
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: James Pustejovsky <jepusto at gmail.com>
Subject: Re: [R-meta] A potential addition to metafor random-effect structures
Sent: Monday, 6 February 2023 9:14
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis at r-project.org>
Cc: James Pustejovsky <jepusto at 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 at 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 at 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 at 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 at 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 > > _______________________________________________ > R-sig-meta-analysis mailing list @ R-sig-meta-analysis at r-project.org > To manage your subscription to this mailing list, go to: > https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis _______________________________________________ R-sig-meta-analysis mailing list @ R-sig-meta-analysis at r-project.org To manage your subscription to this mailing list, go to: https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis