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

[Diego Grados Bedoya]

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

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