[R-meta] multilevel and multivariate model

Hi James,

No particular reason -- added to my to-do list (probably will make it an option, like 'sparse=TRUE' as in rma.mv()).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On
Behalf Of James Pustejovsky via R-sig-meta-analysis
Sent: Monday, 26 June, 2023 19:25
To: R Special Interest Group for Meta-Analysis
Cc: James Pustejovsky
Subject: Re: [R-meta] multilevel and multivariate model

Filippo, Your code looks right to me. To double check it for yourself, try
increasing K to something much larger and verify that rma.mv() returns
estimates that are very close to the specified parameter values. (This
might take some time to compute because of the vcalc() call, which returns
a square matrix with the same number of rows as dat. If nrow(dat) is large,
then V can get very big.)

Wolfgang, is there a reason that V returns a dense k x k matrix? As far as
I can see, V should always have block diagonal form since the cluster
argument is required. Given that, would it be feasible for vcalc() to
return a Matrix::bdiag (or the metafor equivalent)?

James

On Mon, Jun 26, 2023 at 10:22?AM Filippo Gambarota via R-sig-meta-analysis <
r-sig-meta-analysis at r-project.org> wrote:

Hi,
I'm working on a meta-analysis with a multilevel (effects within the
same paper with independent groups) and multivariate (effects within
the same paper/experiment measured on the same participants i.e.
different outcomes). I'm not sure if my workflow is at least capturing
the effect size dependency appropriately.

I have some simulated data with the same structure:

```
library(metafor)

seqw <- function(x){
  unlist(sapply(x, function(i) 1:i))
}

set.seed(2023)

K <- 50 # number of papers
J <- sample(1:3, K, replace = TRUE) # number of studies, within each paper
Z <- sample(1:2, sum(J), replace = TRUE) # number of outcomes per
study/paper

dat <- data.frame(paper = rep(rep(1:K, J), Z),
                  exp = rep(seqw(J), Z),
                  effect = seqw(Z))
head(dat)
```
the `paper` variable is the paper, the `exp` is the experiment
(different experiments have different subjects) and `effect` is the
outcome within each experiment (1 and/or 2).

Then I simulate a 4-level model:

```
set.seed(2023)
# residual variance components
tau2 <- 0.3
omega2 <- 0.1
zeta2 <- 0.1

# random effects
b0_i <- rnorm(K, 0, sqrt(tau2))
b0_ij <- rnorm(sum(J), 0, sqrt(omega2))
b0_ijz <- rnorm(nrow(dat), 0, sqrt(zeta2))

# add to dataframe
dat$b0_i <- b0_i[dat$paper]
dat$b0_ij <- rep(b0_ij, Z)
dat$b0_ijz <- b0_ijz
dat$vi <- runif(nrow(dat), 0.05, 0.1)
```
Now I create the block variance-covariance matrix where sampling
errors are correlated within each experiment and independent across
experiments and papers:

```
set.seed(2023)
# create block-matrix
V <- vcalc(vi, cluster = paper, subgroup = exp, obs = effect, rho =
0.7, data = dat)
# sampling errors
e_ij <- MASS::mvrnorm(1, mu = rep(0, nrow(V)), Sigma = V)
```
Finally I add a dummy variable for the outcome 1 or 2 and simulate the
observed effects:

```
b0 <- 0.1
b1 <- 0.1
# moderator
dat$x <- ifelse(dat$effect == 1, 1, 0)

# simulate effect
dat$yi <- with(dat, (b0 + b0_i + b0_ij + b0_ijz) + b1*x + e_ij)
dat$x <- factor(dat$x)
dat$exp <- factor(dat$exp)
```
Finally my model should be written as:

```
fit <- rma.mv(yi, V, mods = ~0 + x, random = ~1|paper/exp/effect, data
= dat, sparse = TRUE)
```
My question regards if the simulated data structure is correctly
captured by the proposed model.
Thank you!

Filippo

--
Filippo Gambarota, PhD
Postdoctoral Researcher - University of Padova
Department of Developmental and Social Psychology
Website: filippogambarota.xyz
Research Groups: Colab   Psicostat