[R-meta] funnel plot(mixed-effect model) and the assumption of normality

Angeline Tsui angelinetsui at gmail.com
Sun Nov 26 23:02:55 CET 2017

Dear Wolfgang,

Thank you very much for your prompt reply. I just have a very quick
question about the assumptions behind meta-analysis. If I need to learn
more about that and also want to learn more how to check these assumptions
before running analysis, can you suggest some readings to me? I will be
happy to learn it more.


On Sun, Nov 26, 2017 at 4:23 PM, Viechtbauer Wolfgang (SP) <
wolfgang.viechtbauer at maastrichtuniversity.nl> wrote:

> Dear Angeline,
> 1) I assume you are referring to funnel plots drawn with the funnel()
> function in the metafor package. Take a look at help(funnel.rma). It says:
> "For models involving moderators, the plot shows the residuals on the
> x-axis against their corresponding standard errors. Either the usual or
> deleted residuals can be used for that purpose (set via the type argument).
> See residuals.rma for more details on the different types of residuals."
> 2) The standard meta-analytic models make no assumptions about the
> distribution of the effect sizes across studies. Also, moderators are not
> assumed to be normally distributed (an obvious counterexample is a dummy
> variable). The distributional assumptions of the random/mixed-effects
> models are that the sampling distributions are normal and that the random
> effects are normally distributed.
> As for robustness, take a look at this question and the answers:
> https://stat.ethz.ch/pipermail/r-sig-meta-analysis/
> 2017-November/000353.html
> Best,
> Wolfgang
> -----Original Message-----
> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-
> bounces at r-project.org] On Behalf Of Angeline Tsui
> Sent: Sunday, 26 November, 2017 18:36
> To: r-sig-meta-analysis at r-project.org
> Subject: [R-meta] funnel plot(mixed-effect model) and the assumption of
> normality
> Hello all,
> I have two questions about my meta-analysis and I wonder if you can answer
> the following:
> 1) When plotting a funnel plot, I want to control for predictors that may
> explain the relationship between effect size and standard error and I
> suspect that this relationship can partially be explained by moderators in
> my meta-regression model. So I plotted my funnel plot based on a
> mixed-effect meta-regression model. However, I do not fully understand what
> I was plotting here. When I plot my funnel plot based on mixed-effect
> model, does it mean that I am plotting the relationship between predicted
> effect size of the mixed-effect model and standard error. Or am I plotting
> the relationship between the residual values of the model and the standard
> error.
> 2) For normality assumption, my teacher said that it is important to ensure
> the effect sizes across studies in the meta-analysis and the moderators are
> normally distributed. Is this true? I was wondering if the normality
> assumption is actually restricting the residual of the meta-regression
> model (fixed/random-effect) to be normally distributed, not the effect
> sizes and moderators? Furthermore, is the model (fixed/random-effect)
> robust for mild or moderate violation of the normality assumption? Can
> someone suggest some references for me to read for this specific topic?
> Thank you,
> Angeline
> --
> Best Regards,
> Angeline

Best Regards,

	[[alternative HTML version deleted]]

More information about the R-sig-meta-analysis mailing list