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