Hi Ju,
Glad to hear that you are making progress. Construction of the V matrix can be a rather tedious process and often requires quite a bit of manual work.
I have little interested in generalizing fsn() for cases where V is not diagonal, because fsn() is more of interest for historical reasons, not something I would generally use in applied work.
However, the 'Egger regression' test can be easily generalized to rma.mv() models. Simply include a measure of the precision (e.g., the standard error) of the estimates in your model as a predictor/moderator and then you have essentially a multilevel/multivariate version thereof (you would then look at the test of the coefficient for the measure of precision, not the intercept).
I also recently heard a talk by Melissa Rodgers and James Pustejovsky (who is a frequent contributor to this mailing list) on some work in this area. Maybe he can chime in here.
Best,
Wolfgang
-----Original Message-----
From: Ju Lee [mailto:juhyung2 at stanford.edu]
Sent: Thursday, 26 September, 2019 8:13
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis at r-project.org
Subject: Re: Covariance-variance matrix when studies share multiple treatment x control comparison
Dear Wolfgang,
I deeply appreciate your time looking into this issue, and this has been immensely helpful.
I was able to incorporate all possible inter-dependence among effect sizes by adding different layers of non-independence to our dataframe.?
I manually calculated hedges'd based on based on Hedges and Olkin (1985), and it generates exactly same value as hedges' g in escalc() "SMD" function. So hopefully I am doing everything right using the equation we've discussed earlier.
I have been also wondering if it is possible to account of this variance-covariance structure that I've constructed when running publication bias analysis, for example, when using fsn() function or modified egger's regression test (looking at intercept term of residual ~ precision meta-regression using rma.mv). I had no luck so far finding information on this, and I would appreciate if you have any suggestions related to this
Thank you for all of your valuable helps!
Best regards,
JU