[R-meta] Nonlinear meta-regression

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Wed Dec 19 09:47:43 CET 2018

An example of using cubic splines can be found here:


But if you want a 'truly' non-linear model (i.e., non-linear in the parameters), then metafor doesn't do that. Code to fit non-linear models has passed through this list, but it would require adapting/tweaking depending on the model you want to fit (e.g., in this case, it seems you would want something curvilinear for low values of x and an upper asymptote for high values of x).


-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Michael Dewey
Sent: Tuesday, 18 December, 2018 12:47
To: Cesar Terrer Moreno; r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Nonlinear meta-regression

Dear César

I would have to say that based purely on the plot and given the sparsity 
of points for high levels of phosphorus I would not see quite what you 
see. However if on theoretical grounds you are expecting a ceiling then 

If you want to fit a model which is non-linear in the variables then you 
just enter the transformed predictors as moderators. So this would apply 
if you wanted a polynomial or splines ir some form of segmented fit for 
phosphorus. If you want a model which is non-linear in the parameters 
like some form of exponential then that lies outside what I know how to 
do but someone else will doubtless chip in.


On 18/12/2018 08:54, Cesar Terrer Moreno wrote:
> Dear all,
> The studies of my meta-analysis form this relationship, with y as the effect size, x as the main moderator, and the size of points as the inverse of the variance: https://imgur.com/a/ad6Br5y <https://imgur.com/a/ad6Br5y>
> In my opinion, the regression is clearly nonlinear. And in ecological terms, it makes sense that the relationship saturates. Here I’ve just fitted a regular loess function to aid the eye in seeing the pattern I refer to.
> How would you fit a nonelinear mixed-effects meta regression with metafor for a case like this?
> Thanks in advance.
> Best,
> César

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