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

Michael Dewey lists at dewey.myzen.co.uk
Mon Nov 27 13:09:53 CET 2017

Dear Angeline

The usual assumptions which apply to regression about normality of the 
residuals also apply to meta-regression. If you do meta-regression the 
assumptions for linear mixed models apply so the random effects should 
be normal too. This is quite a relief really as it means we do not need 
to learn a whole lorry load of extra stuff to do meta-analysis or 


On 26/11/2017 22:02, Angeline Tsui wrote:
> 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.
> Best,
> Angeline
> 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


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