[R-meta] Equivalence of two models in metafor

[Viechtbauer, Wolfgang (NP)]

Yes, this is due to the smaller sigma estimate of f2. In fact, the ratio of the squared sigma estimates of the two models, namely

sigma(f1)^2 / sigma(f2)^2

is identical to the ratio of the squared SEs of the two contrasts, namely

vcov(con1) / vcov(con2)

Best,
Wolfgang

> -----Original Message-----
> From: Zhouhan Jin <zjin65 using uwo.ca>
> Sent: Tuesday, April 9, 2024 00:34
> To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> project.org>; Viechtbauer, Wolfgang (NP)
> <wolfgang.viechtbauer using maastrichtuniversity.nl>
> Subject: RE: Equivalence of two models in metafor
>
> Sorry, Wolfgang, I missed the `method="FE"` part to control for tau^2
> differences. Speaking of the effect of weights, I actually tried to simply fit
> two `lm()` models and, there again, `con1` and `con2` don't match.
>
> I wonder what explains the difference in SEs etc. here (maybe the difference in
> sigmas)?
>
> f1 <- lm(yi~X+0, data = dat)
> f2 <- lm(yi~Y+0, data = dat)
>
> ( con1 = contrast(ref_grid(f1), list(c(1,-1))) )
> ( con2 = contrast(ref_grid(f2), list(c(1/2,1/2,-1))) )
>
> Thanks in advance!
>
> Best wishes,
>
> Zhouhan
> On Apr 8, 2024 at 18:11 -0400, Viechtbauer, Wolfgang (NP)
> <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
>
> I am not sure which two contrasts you are comparing. As I tried to explain,
> these two are exactly identical:
>
> f1 <- rma(yi~X+0, vi, data = dat, method="FE")
> f2 <- rma(yi~Y+0, vi, data = dat, method="FE")
>
> A = emmprep(f1)
> B = emmprep(f2)
>
> ( con1 = contrast(A, list(c(1,-1))) )
> w <- diag(solve(vcov(f2)))[1:2]
> w <- w / sum(w)
> ( con2 = contrast(B, list(c(w,-1))) )
>
>
> -----Original Message-----
> From: Zhouhan Jin <zjin65 using uwo.ca>
> Sent: Monday, April 8, 2024 23:58
> To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-
> project.org>; Viechtbauer, Wolfgang (NP)
> <wolfgang.viechtbauer using maastrichtuniversity.nl>
> Subject: RE: Equivalence of two models in metafor
>
> Thanks so much, Wolfgang!
>
> It seems that the inferential results (SEs, test statistics, and p-values) are
> still different between `con1` and `con2`.
>
> The contrast for the model with more categories (`con2`) produces smaller values
> for these inferential results compared to that from the contrast for the model
> with less categories (`con1`).
>
> Can I conclude that in a situation like this, f2 model (and thus `con2`)
> subsumes/nests/includes f1 model (and thus `con1`), and hence the latter is
> redundant?
>
> Thanks a lot!
>
> Best wishes,
>
> Zhouhan
> On Apr 8, 2024 at 16:37 -0400, Viechtbauer, Wolfgang (NP)
> <wolfgang.viechtbauer using maastrichtuniversity.nl>, wrote:
>
> Dear Zhouhan,
>
> If you want to compare these two contrasts, you should use:
>
> ( con1 = contrast(A, list(c(1,-1))) )
> ( con2 = contrast(B, list(c(1/2,1/2,-1))) )
>
> You will find they are similar, but still not identical. There are two reasons
> for this. First, the estimates of tau^2 are different in the two models. This
> leads to different weighting schemes. But even if we use a fixed-effects meta-
> regression model with:
>
> f1 <- rma(yi~X+0, vi, data = dat, method="FE")
> f2 <- rma(yi~Y+0, vi, data = dat, method="FE")
>
> you will find that the contrasts are still different. That's because one has to
> use an appropriately weighted average of the estimates of Yb and Yc to get the
> same contrast:
>
> w <- diag(solve(vcov(f2)))[1:2]
> w <- w / sum(w)
> ( con2 = contrast(B, list(c(w,-1))) )
>
> This is now the same as:
>
> ( con1 = contrast(A, list(c(1,-1))) )
>
> Best,
> Wolfgang
>
> -----Original Message-----
> From: R-sig-meta-analysis <r-sig-meta-analysis-bounces using r-project.org> On Behalf
> Of Zhouhan Jin via R-sig-meta-analysis
> Sent: Tuesday, April 2, 2024 17:47
> To: r-sig-meta-analysis using r-project.org
> Cc: Zhouhan Jin <zjin65 using uwo.ca>
> Subject: [R-meta] Equivalence of two models in metafor
>
> Dear Wolfgang,
>
> Below, moderator X is coded "no" whenever moderator Y is coded "b" or "c", and
> moderator X is coded "yes" whenever moderator Y is coded "d".
>
> Thus, I expected that a contrast like "no - yes" (`con1`) to be identical to a
> contrast like "b + c - d" (`con2`).
>
> However, I wonder why `con1` and `con2` aren't identical?
>
> dat <- read.table(header=TRUE, text="
> study X Y yi vi
> 1 no b 1 .1
> 1 no b 2 .2
> 1 no c .9 .1
> 2 no c .7 .3
> 2 yes d .6 .1
> 3 yes d .5 .1")
>
> f1 <- rma(yi~X+0, vi, data = dat)
> f2 <- rma(yi~Y+0, vi, data = dat)
>
> A = emmprep(f1)
> B = emmprep(f2)
>
> ( con1 = contrast(A, list(c(1,-1))) )
> ( con2 = contrast(B, list(c(1,1,-1))) )
>
> Thanks in advance!
>
> Best wishes,
>
> Zhouhan