[R-meta] Parameter redundancy

[Viechtbauer, Wolfgang (SP)]

Hi Magnus,

My point was that for certain outcome/effect-size measures, the sampling variance is a function of the size of the outcome/effect. For example:

- for the raw correlation coefficient, the usual large-sample approximation to the sampling variance is (1-r^2)^2 / (n-1), which depends on r

- for the standardized mean difference, the usual large-sample approximation to the sampling variance is 1/n1 + 1/n2 + d^2 / (2*(n1+n2)), which depends on d

For other measures, there can also be such dependencies, although sometimes they are not as obvious.

Hence, if we use a form of the 'regression test' (to check for funnel plot asymmetry) where we use the sampling variance (or some function thereof, such as its square root) as the 'predictor', then this can result in inflated Type I error rates of the regression test. To avoid this problem, we can use the sample size (or some function thereof, such as its reciprocal) as the predictor or use an outcome measure where the sampling variance is not a function of the size of the outcome/effect (e.g., those that are obtained via a variance-stabilizing transformation, such as the r-to-z transformed correlation coefficient or the arcsine square root transformed risk difference).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Magnus Magnusson
Sent: Saturday, 15 June, 2019 20:19
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Parameter redundancy

Dear all,

I am using the metafor package (rma.mv) and is currently evaluating publication bias for a multilevel model by using the Eggers regression test.

I saw in a post answered by the package author, Wolfgang Viechtbauer, at the cross validated forum that for some measures you have to be aware of potential parameter redundancy (between the measure and the variance of the measure) when using the test.

I wonder (1) which measures this refers to and (2) how severe this problem likely is for the judging the outcome of a pub-bias test.

Best wishes,
Magnus Magnusson, postdoc at the Swedish University of Agricultural Sciences based in Umeå

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Magnus Magnusson
Post doc position at
Department of Wildlife, Fish and Environmental Studies
Swedish University of Agricultural Sciences
SE-901 83 Umeå
Sweden
phone: +46(0)90-7868587
e-post: magnus.magnusson using slu.se