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

Viechtbauer Wolfgang (SP) wolfgang.viechtbauer at maastrichtuniversity.nl
Sun Nov 26 22:23:00 CET 2017

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:



-----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

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,

Best Regards,

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