[R-meta] A potential addition to metafor random-effect structures
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 at 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 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 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 [[alternative HTML version deleted]] _______________________________________________ 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