[R-meta] Difference between subset (in a loop) and mods in metafor rma.mv

[Viechtbauer, Wolfgang (NP)]

Dear Brendan,

Both approaches fit multilevel models. The difference arises because of two reasons:

1) When using the full dataset and using 'Predictor' as a moderator, then it is possible for information to be shared/borrowed from both levels of the moderator within studies. 

2) When subsetting based on 'Predictor', you allow the variance components to differ across the two levels of the moderator. This is essentially what is discussed here:

https://www.metafor-project.org/doku.php/tips:comp_two_independent_estimates

but in the context of a simpler model.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Brendan Pearl via R-sig-meta-analysis
>Sent: Friday, 29 September, 2023 12:00
>To: r-sig-meta-analysis using r-project.org
>Cc: Brendan Pearl
>Subject: [R-meta] Difference between subset (in a loop) and mods in metafor
>rma.mv
>
>I am trying to understand the difference using the 'subset' and 'mods' options in
>rma.mv.
>
>I have run two analyses using rma.mv on the same dataset that has a three level
>structure (articles nested within larger studies) and get different results.
>
>In the first example I have given below, is looping over rma.mv and passing a
>different predictor to the subset option a univariate meta-analysis? And in the
>second example, is passing the predictor to the mods option running a
>multivariable meta-analysis?
>
>Study <- c("A","A","B","C","C","D","E","F","F","G")
>Article <- c("1","2","3","4","5","6","7","8","9","10")
>Predictor <- c("x","x","x","y","y","y","x","x","y","y")
>yi <- c(-.2,-.3,-.8,.5,.6,.4,-.1,-.8,.3,.8)
>vi <- c(.01,.01,.01,.01,.01,.01,.01,.01,.01,.01)
>
>dat <- data.frame(Study,Article,Predictor,yi,vi)
>
>#FIRST EXAMPLE#Subset analyses
># gives me
>
>#1   x OR = -0.49 [-0.84, -0.13]
>#2   y    OR = 0.51 [0.31, 0.72]
>
>df_subset <- data.frame(val=as.character(),subset_result=as.character())
>
>for (val in unique(dat$Predictor)){
>
>res_univariate <- rma.mv(yi=yi,
>V=vi,
>data=dat,
>random = ~1 | Study/Article,
>subset = Predictor == val,
>method = "REML"
>)
>
>result <- capture.output(cat(
>"OR = ",
>format(round(res_univariate$beta, 2),nsmall = 2),
>" [",
>format(round(res_univariate$ci.lb, 2),nsmall = 2),
>", ",
>format(round(res_univariate$ci.ub, 2),nsmall = 2),
>"]",
>sep=""
>)
>)
>
>df_subset[nrow(df_subset) +1,] = c(
>val,
>result
>)
>
>}
>
>#SECOND EXAMPLE
>#Mod analysis
>#gives me:
>
>#                      estimate   ci.lb    ci.ub
>
>#factor(Predictor)x   -0.4825    -0.7246  -0.2404
>#factor(Predictor)y    0.5807     0.3386   0.8229
>
>df_mod <- data.frame(val=as.character(),mod_result=as.character())
>
>res_multivariate <- rma.mv(yi=yi,
>V=vi,
>data=dat,
>random = ~1 | Study/Article,
>mods = ~ factor(Predictor)-1,
>method = "REML"
>)
>summary(res_multivariate)