[R-meta] weighting a multilevel model and quality effects model

[Wolfgang Viechtbauer]

Hi Diego,

Not a direct response to your questions, but I would suggest to take a 
look at:

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

The weighting that happens in such models (automatically) is more complex, 
so unless you have a very thorough understanding of this, I would *not* 
recommend to try to use the 'W' argument.

Best,
Wolfgang

--
Wolfgang Viechtbauer, Ph.D., Statistician | Department of Psychiatry and
Neuropsychology | Maastricht University | P.O. Box 616 (VIJV1) | 6200 MD
Maastricht, The Netherlands | +31 (43) 3884170 | https://www.wvbauer.com

On Fri, 30 Jul 2021, Diego Grados Bedoya wrote:

> Dear all,
>
> I am fitting the following multilevel model using the metafor package:
>
> model_0 <- rma.mv(yi = y, V = var.y, mod = ~ mod.y - 1, random = ~ 1 |
> study.id / es.id, data = dat, method = "REML")
>
> I would like to explore the incorporation of weighting factors such as:
>
> model_1 <- rma.mv(yi = y, V = var.y, W = 1 / var.y, mod = ~ mod.y - 1,
> random = ~ 1 | study.id / es.id, data = dat, method = "REML")
> model_2 <- rma.mv(yi = y, V = var.y, W = sample.size.y, mod = ~ mod.y - 1,
> random = ~ 1 | study.id / es.id, data = dat, method = "REML")
>
> Also assessing a quality effect model according to
> http://dx.doi.org/10.1016/j.cct.2015.05.010, which defines a model based on
> a relative quality index for each individual study (quality.y) varying from
> 0-1:
>
> model_3 <- rma.mv(yi = y, V = var.y, W = quality.y / var.y, mod = ~ mod.y -
> 1, random = ~ 1 | study.id / es.id, data = dat, method = "REML")
>
> I have a couple of questions:
>
> 1) What is the rationality of incorporating weighting factors in the
> multilevel model?. For instance, model_1 is giving more weight to more
> precise studies/effect sizes while model_2 is giving more weight to big
> studies/effect sizes ...
> 2) Is the implementation of model_3 correct? Is there any other
> alternative/method to incorporate a quality index?
>
> Any hint or literature is more than welcome,
> Thank you in advance,
>
> Diego