[R-meta] robust error is smaller than model-based error

[Yefeng Yang]

Hi James,

Thanks for your reply.

On point 1, what I mean is that if we use the model-based SE to test null-hypothesis of the average effect, we get a null-effect (p > 0.05). But, if we use robust error (which is returned by robust()​), we get a non-zero effect. The result itself is a bit weird.

Regarding your comment on `robust()`, let me use the reproducible example to explain what I mean (`metafor` is amazing - you can find all sorts of data structure you have interest).

# load package and data
library(metafor)
library(clubSandwich)
dat <- dat.lim2014$o_o_unadj

# calculate zr and sampling variances
dat <- escalc(measure="ZCOR", ri=ri, ni=ni, data=dat)

# create effect size id variable
dat$esid <- 1:nrow(dat)

# fit a multilevel model with a non-nested random-effects structure
res <- rma.mv(yi, vi,  random = list(~ 1 | article, ~ 1 | esid, ~ 1 | species), data=dat)

But, we still can use `robust()` to calculate the cluster-robust error with CR1 adjustment as:
# robust error with CR1 adjustment
robust(res, cluster = article, adjust = T)

As expected, the clubsandwich​ cannot be used to calculate robust error for such a model
coef_test(res, vcov = "CR1", cluster = dat$article)

Also, if we use CR2 adjustment, `robust()` is also not working
# robust error with CR2 adjustment
robust(res, cluster = article, clubSandwich = T)

 I might misunderstand something or made mistakes. But I would be grateful if you would you like to explain a bit.

Best,
Yefeng
________________________________
From: James Pustejovsky <jepusto using gmail.com>
Sent: 16 February 2024 15:18
To: R Special Interest Group for Meta-Analysis <r-sig-meta-analysis using r-project.org>
Cc: Yefeng Yang <yefeng.yang1 using unsw.edu.au>
Subject: Re: [R-meta] robust error is smaller than model-based error

Hi Yefeng,

On point 1, I am not sure what your question is. From inspecting the source code of metafor::robust(), the function is not set up to handle models with crossed random effects. I'm not at all sure what it does if you feed it a model with crossed random effects, but I would be very cautious about interpreting the output. Perhaps Wolfgang can comment on whether robust() is meant to accommodate models with crossed random effects.

On point 2, I can verify that clubSandwich does not support CRVE for models with crossed random effects. Cameron, Gelbach, and Miller (2011) describe multi-way clustered standard errors, but only for ordinary least squares models. As far as I am aware, the statistical theory for multi-way clustered standard errors has not been developed for models that have crossed random effects and the extension from Cameron, Gelbach and Miller is not obvious. So if you want to stay on solid ground in terms of statistical theory, I think your best approach might be just to do a good job of developing and checking the model, and then rely on the model-based SEs for inference.

James

On Thu, Feb 15, 2024 at 7:37 PM Yefeng Yang via R-sig-meta-analysis <r-sig-meta-analysis using r-project.org<mailto:r-sig-meta-analysis using r-project.org>> wrote:
Dear community,

I (or, more precisely, my collaborator) am helping with one meta-analysis with dependent effect sizes. We used a multilevel model with effect size ID, study ID, and species ID as random effects.  We also used the RVE to calculate the robust error. I have two questions.


  1.
The test of model coefficient based on RVE indicates a significant effect (p < 0.05), while the test based on model-based error (we call it naive/original error) shows a non-significant effect (p < 0.05). I used `robust` in `metafor`, with `CR1` correction (`clubsandwich` is not working in my case; see below​) . Sorry, I do not have the raw data so there is no reproducible example.
  2.
How to calculate the robust error for models with non-nested random-effects structure? This issue has troubled me for a long time. Precisely, in my case, because effect size ID is nested within the study ID, so it is easy to calculate robust error (either using ​ ​`robust` or ​`clubsandwich` ​). However, I still have species ID as the random effect (it is a kind of crossed random effect). In such a case `clubsandwich` is not working. `robust` is still working, but we only can use `CR1` correction.

Regards,
Yefeng


        [[alternative HTML version deleted]]

_______________________________________________
R-sig-meta-analysis mailing list @ R-sig-meta-analysis using r-project.org<mailto:R-sig-meta-analysis using r-project.org>
To manage your subscription to this mailing list, go to:
https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis

	[[alternative HTML version deleted]]