[R-meta] metafor applicable for non-linear associations?

[Michael Dewey]

Dear Katrin

On 01/02/2018 13:09, Wolf, Katrin wrote:
> Dear Wolfgang,
> 
> Thank you very much for your immediate response!
> I'm not sure if I get the difference between the alternatives you mentioned. We expect a non-linear/quadratic association between two variables (effects of duration in early childcare on social-emotional outcomes) and will include all studies that reported results on that association.

So each study reports a coefficient for a quadratic effect (and its 
standard error)? In that case I think it is your option 2.

  So is it about a (1) non-linear association between two variables 
within each study or (2) non-linear association between some outcome and 
one or more predictor? (I guess the latter)
> 
> Thank you very much for your information on rms and its graphic functions - that is very helpful!
> 
> Best,
> katrin
> 
> 
> 
> ------------------------------
> 
> Message: 4
> Date: Tue, 30 Jan 2018 10:42:49 +0000
> From: "Viechtbauer Wolfgang (SP)"
> 	<wolfgang.viechtbauer at maastrichtuniversity.nl>
> To: "Wolf, Katrin" <katrin.wolf2 at fu-berlin.de>,
> 	"r-sig-meta-analysis at r-project.org"
> 	<r-sig-meta-analysis at r-project.org>
> Subject: Re: [R-meta] metafor applicable for non-linear associations?
> Message-ID: <4d9263e0576645669d4795cc412ae8dc at UM-MAIL3214.unimaas.nl>
> Content-Type: text/plain; charset="utf-8"
> 
> Dear Katrin,
> 
> Do you mean the non-linear association between two variables within each study or do you mean the non-linear association in the context of meta-regression (i.e., between some outcome/effect size and one or more predictor variables)?
> 
> The former would require that some measure of the non-linear association is reported by each study. Those estimates (with corresponding SEs/variances) can then be used as input into rma().
> 
> For the latter, it depends on how you want to model the non-linear association. Polynomials (quadratic, cubic, etc.) can be easily included as predictor/moderator variables. Cubic splines can also be used for this purpose (the 'rms' package provides useful functions for this). Here is an example:
> 
> library(metafor)
> 
> ### load data
> dat <- get(data(dat.raudenbush1985, package="metafor"))
> 
> ### plot data
> with(dat, plot(weeks, yi, pch=19, xlab="Weeks", ylab="Standardized Mean Difference"))
> xs <- seq(0,25,by=1)
> 
> ### linear and quadratic models
> res <- rma(yi ~ weeks, vi, data=dat)
> lines(xs, predict(res, newmods=xs)$pred, lwd=2)
> res <- rma(yi ~ weeks + I(weeks^2), vi, data=dat)
> lines(xs, predict(res, newmods=cbind(xs,xs^2))$pred, col="blue", lwd=2)
> 
> ### model with restricted cubic spline
> library(rms)
> knots <- c(1,2,5,10)
> res <- rma(yi ~ rcs(weeks,knots), vi, data=dat)
> points(dat$weeks, fitted(res))
> lines(xs, predict(res, newmods=rcspline.eval(xs, knots, inclx=TRUE))$pred, col="red", lwd=2)
> 
> ### end example
> 
> If you want a truly non-linear model, then the answer is no, metafor does not provide functionality for that.
> 
> Best,
> Wolfgang
> 
>> -----Original Message-----
>> From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-
>> project.org] On Behalf Of Wolf, Katrin
>> Sent: Tuesday, 30 January, 2018 11:29
>> To: r-sig-meta-analysis at r-project.org
>> Subject: [R-meta] metafor applicable for non-linear associations?
>>
>> Dear all,
>>
>> Is it possible to apply metafor for non-linear associations? Is there any
>> literature on how doing so? I really appreciate any comments,
>> suggestions...
>>
>> Best,
>> katrin
>> -----------------------------------------------------------------
>> Dipl.-Psych. Katrin M. Wolf
>> Freie Universit?t Berlin
>> Fachbereich Erziehungswissenschaft und Psychologie
>> Arbeitsbereich Fr?hkindliche Bildung und Erziehung
>> Habelschwerdter Allee 45
>> 14195 Berlin
>> Telefon: 030 - 838 63922
>> Raum: KL 23/222c
> 
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-- 
Michael
http://www.dewey.myzen.co.uk/home.html