[R-meta] Question on Multivariate-Multilevel Meta-Analyis

[Martin Brunner]

Dear Wolfgang, 

thank you very much for your swift reply. Your work around solved my problem.

Best,

Martin




-----Ursprüngliche Nachricht-----
Von: Viechtbauer, Wolfgang (SP) [mailto:wolfgang.viechtbauer using maastrichtuniversity.nl] 
Gesendet: Donnerstag, 29. April 2021 18:44
An: Martin Brunner <mabrunner using uni-potsdam.de>; r-sig-meta-analysis using r-project.org
Betreff: RE: Question on Multivariate-Multilevel Meta-Analyis

Dear Martin,

It is a bit of an annoying limitation that rma.mv() does not allow terms like

random = ~ inner | outer1/outer2

but one can easily work around that. Just use:

res <- rma.mv(yi = yi, V = V, mods = ~ b - 1, random = list(~ b | country, ~ b | interaction(country,cycle)), struct=c("UN","UN"), data=dat, method="REML")

Maybe I will clean up the code in rma.mv() eventually so that 'random = ~ inner | outer1/outer2' is possible, but it's not urgent as far as I am concerned given this easy workaround.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis 
>[mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Martin 
>Brunner
>Sent: Thursday, 29 April, 2021 18:22
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] Question on Multivariate-Multilevel Meta-Analyis
>
>Dear meta-analysis folks,
>
>I would like to meta-analyze the results from a regression model where 
>I explain reading achievement by gender, SES, and the interaction 
>between SES and gender. My data stem from seven cycles of a large-scale 
>assessment program with data from 96 countries, up to seven assessment 
>cycles per country and about 4,500 students per cycle within each 
>country. Of note, each student participated only in one single cycle.
>
>My key effect sizes are three (unstandardized) regression coefficients 
>(b_gender, b_SES, b_interaction). I also computed the 
>variance-covariance matrix of the sampling variances/covariances for 
>these three effect sizes for each cycle within each country. I have a 
>total of 412 effect sizes for each regression coefficient which I would like to meta-analyze.
>
>One possibility to meta-analyze these data is to meta-analyze each 
>regression coefficient separately, for example using the rma.mv 
>function of metafor with b_gender depicting the regression coefficient 
>for gender and v_b_gender depicting the sampling variance of this 
>regression coefficient. The metafor code looked like
>this:
>
>res_b_gender <- rma.mv(yi = b_gender, V = v_b_gender, random = ~ 1 | 
>country/cycle, data = dat, method="REML")
>
>This code works very pretty well.
>
>However, following the literature to summarize regression coefficients 
>(e.g., Becker & Wu, 2007; Gasparrinni et al., 2012) I wondered whether 
>I can also jointly meta-analyze the three regression coefficients by 
>using a multivariate multilevel meta-analytic model. Notably, I would 
>also like to allow each regression coefficient to vary across cycles within countries as well as across countries.
>Using the multivariate model may further improve the precision of 
>estimates when I correctly understood the literature cited above. For 
>the multivariate model, I computed the block diagonal 
>variance-covariance matrix of the sampling variance- covariance matrix 
>for each combination of a certain cycle within a certain country 
>(depicted by variable cnt_cycle) using a data set in a long-format. The 
>variances and covariances were stored in the variables v1i, v2i, and 
>v3i. The estimates of the regression coefficients were stored in the variable yi and the type of independent variable (i.e, gender, SES, interaction) was depicted in the variable b.
>
>V <- bldiag(lapply(split(dat[,c("v1i", "v2i", "v3i")], dat$cnt_cycle), 
>as.matrix))
>
>Using this matrix I tried to apply the rma.va function with the following code:
>
>res <- rma.mv(yi = yi, V = V, mods = ~ b - 1, random = ~ b | 
>country/cycle, struct="UN", data=dat, method="REML")
>
>Unfortunately, the code does not work. I get the following error 
>message: "Error in rma.mv(yi, V, mods = ~b - 1, random = ~b | 
>country/cycle,  :  Cannot use '~ inner | outer1/outer2' type terms in the 'random' argument."
>
>I guess that I am missing something really important here. Any help or 
>suggestions are highly appreciated.
>
>Best wishes,
>
>Martin
>
>Here is also some code to reproduce my problem taken from the metafor 
>site (http://www.metafor-project.org/doku.php/analyses:berkey1998). I 
>duplicated the data to simulate two assessment cycles (e.g., an initial 
>result [cycle = 1] and a replication attempt [cycle = 2]) within each 
>trial (which corresponds to countries in my data).
>
>library(metafor)
>dat1 <- dat.berkey1998
>dat1$cycle <- 1
>
>dat2 <- dat.berkey1998
>dat2$cycle <- 2
>
>#duplicate data
>dat <- rbind(dat1, dat2)
>dat$trial_cycle <- paste(dat$trial,dat$cycle)
>
>V <- bldiag(lapply(split(dat[,c("v1i", "v2i")], dat$trial_cycle), 
>as.matrix))
>
>res <- rma.mv(yi, V, mods = ~ outcome - 1, random = ~ outcome | 
>trial/cycle, struct="UN", data=dat, method="ML")
>
>print(res, digits=3)
>
>References:
>
>Becker, B. J., & Wu, M.-J. (2007). The Synthesis of Regression Slopes 
>in Meta- Analysis. Statistical Science, 22(3), 414-429. 
>https://doi.org/10.1214/07-STS243
>
>Gasparrini, A., Armstrong, B., & Kenward, M. G. (2012). Multivariate 
>meta-analysis for non-linear and other multi-parameter associations. 
>Statistics in Medicine, 31(29), 3821-3839. 
>https://doi.org/10.1002/sim.5471
>
>res <- rma.mv(yi, V, mods = ~ b - 1, random = ~ b | as.factor(cnt2), 
>struct="UN", data=dat, method="REML")
>
>print(res1, digits=3)