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

[Yuhang Hu]

Thank you very much, Wolfgang. Regarding my second (unclear) follow-up, I
might have a conceptual misunderstanding that I hope to clear up.

When we use a "categorical" moderator (with struct="UN") to the left of |
(e.g., ~outcome | trial_id), conceptually it means that in each unique
trial_id, we fit "effect_size ~ outcome+0", and obtain the Mean for each
outcome category (say two categories). Then in the rma.mv() output, we get
the variation in means of each category as well as the correlation between
the means of the two categories across all unique trial_ids.

Is my conceptual understanding correct?

Thanks,
Yuhang

On Wed, May 3, 2023 at 1:59 PM Viechtbauer, Wolfgang (NP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Please see below for responses.
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: Yuhang Hu [mailto:yh342 using nau.edu]
> >Sent: Wednesday, 03 May, 2023 22:48
> >To: Viechtbauer, Wolfgang (NP)
> >Cc: R Special Interest Group for Meta-Analysis
> >Subject: Re: [R-meta] Plotting the correlation among true/random effects
> across
> >categories
> >
> >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)
>
> Correct.
>
> >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?
>
> Not entirely sure what you mean by this question. The help file explains
> what the different structures do:
>
>
> https://wviechtb.github.io/metafor/reference/rma.mv.html#specifying-random-effects
>
> >Thank you for your time.
> >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
>

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