# [R-meta] Plotting the correlation among true/random effects across categories

Yuhang Hu yh342 @end|ng |rom n@u@edu
Wed May 3 22:48:14 CEST 2023

```Thank you very much, Wolfgang. Two quick follow-ups:

1) To convert these estimated random deviations to true effects, I should
add the fixed effect estimates (assuming I use 'outcome + 0' in model
formula) for each category of outcome to its relevant column, right?

AL = paired[,1] + model\$b[1,1]
PD = paired[,2] + model\$b[2,1]
plot(PD~AL, pch=21, bg="gray", cex=1.5, lwd=1.2)

2) When using categorical variables (with "UN") to the left of |, I think
we drop the intercept in the random-effects design matrix, so what is
actually allowed to vary across the trials given that eac trial has only
one instance of AL and PD in it?

Yuhang

On Wed, May 3, 2023 at 12:51 AM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> You can extract the BLUPs of the random effects and create a scatterplot
> based on them:
>
> re <- ranef(model)
> re
>
> paired <- do.call(rbind, split(re[[1]]\$intrcpt, dat.berkey1998\$trial))
> paired
>
> plot(paired, pch=21, bg="gray", cex=1.5, lwd=1.2)
>
> And before somebody asks why cor(paired) does not yield 0.7752 (or why the
> values in var(paired) do not match up with the variances as estimated from
> the model), see for example:
>
> https://stats.stackexchange.com/q/69882/1934
>
> Or let me give a more technical explanation based on the standard RE model:
>
> dat <- escalc(measure="RR", ai=tpos, bi=tneg, ci=cpos, di=cneg,
> data=dat.bcg)
> res <- rma(yi, vi, data=dat)
> res\$tau2
> var(ranef(res)\$pred)
>
> You will notice that the latter is smaller than tau^2. By the law of total
> variance:
>
> tau^2 = var(u_i) = E(var(u_i|y_i)) + var(E(u_i|y_i)).
>
> The conditional means of the random effects (which is what ranef()
> provides estimates of) are E(u_i|y_i) and hence their variance is only part
> of the total variance. Therefore, the estimate of tau^2 and the estimated
> variance of the BLUPs of the random effects will not match up.
>
> In more complex models, this then also affects things like the correlation
> between the BLUPs of the random effects.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-sig-meta-analysis [mailto:
> r-sig-meta-analysis-bounces using r-project.org] On
> >Behalf Of Yuhang Hu via R-sig-meta-analysis
> >Sent: Wednesday, 03 May, 2023 1:21
> >To: R meta
> >Cc: Yuhang Hu
> >Subject: [R-meta] Plotting the correlation among true/random effects
> across
> >categories
> >
> >Hello Colleagues,
> >
> >I was wondering if there is a way to scatterplot the correlation between
> >the categories of variable "outcome" (AL and PD) which is estimated to be
> >rho = .7752 in my model below?
> >
> >model <- rma.mv(yi~ outcome, vi, data =  dat.berkey1998,
> >                random = ~ outcome | trial, struct = "UN")
> >
> >    rho.AL  rho.PD    AL  PD
> >AL       1             -   5
> >PD  0.7752       1    no   -
> >
> >Thanks,
> >Yuhang
>

[[alternative HTML version deleted]]

```