[R-meta] Analyzing how response ratios of different outcomes co-vary among study

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Tue Aug 7 12:06:06 CEST 2018

Dear Gabri,

This is something that can be done using a multivariate model. The canonical example I always refer to in this case is:


In this example, each study measured both outcomes, but this is not a requirement.

A major difficulty in this type of analysis is computing the covariances between the sampling errors. Equations for computing the covariances between multiple log response ratios measured on the same objects are provided in:

Lajeunesse, M. J. (2011). On the meta-analysis of response ratios for studies with correlated and multi-group designs. Ecology, 92(11), 2049-2055.

See section "Multivariate RR". The problem in computing those covariances is that you need information about the correlation between the different traits (e.g., how does leaf size correlate with leaf nitrogen concentration or leaf weight?). This information is often not available. Maybe some educated guesses can be made about those unknown correlations.

In general, this issue is a 'frequently asked question' on this mailing list and you should browse through the archives (https://stat.ethz.ch/pipermail/r-sig-meta-analysis/) to find posts that address this issue. You could also try a search on Google for:

multivariate site:https://stat.ethz.ch/pipermail/r-sig-meta-analysis/


-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Gabriele Midolo
Sent: Tuesday, 07 August, 2018 10:22
To: r-sig-meta-analysis using r-project.org
Subject: [R-meta] Analyzing how response ratios of different outcomes co-vary among study

Dear all,

A methodological - rather than practical/coding - question: is there any
meta-analytical technique to quantify the relationship of effect sizes for
studies reporting two or more variable of interest for the meta-analysis?

Some explanation:
I am conducting a meta-analysis of respose ratio (lnRR) measuring the
change of multiple plant leaf traits to altitudinal increase. I use
climatic data and the change in altitude in meta-regression to quantify how
traits are affected by the biogeographical contex. Many studies report data
to measure lnRR for multiple dependent variables: e.g. a study can report
how the leaf size of a species changes compared to a control, and at the
same time report data on changes in leaf nitrogen concentration or the
weight of the leaves.
Thus, I have selected several dependent variables in my meta-analysis, and
I think it might be very interesting to investigate somehow how different
variables (calculated as lnRR) co-vary with each other for studies
reporting data on both variables (e.g. is there a relationship between the
lnRR of leaf size and leaf weight in studies reporting both variables?)

To address this goal, I have so far conducted a ranged major axis (RMA)
analysis of lnRR via the 'lmodel2' package. The authors specifies that
model II regression should be used when the two variables in the regression
equation are random,i.e. not controlled by the researcher. The problem is
that the model does not account for the weight (or inverse of the sampling
variance of lnRR), and thereby provide an unweighted relationship between
effect size? In addition, it does not account for the non-independence of
the lnRR of my data: i.e. there are studies using reporting multiple
'treatment' levels compared to a single control.

I was wondering if there are more suitable tools in meta-analysis to
quantify the relationship of multiple random variables reported by a single


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