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

[Gabriele Midolo]

Dear Wolfgang,

Thank you very much for the info and sorry for proposing a 'frequently
asked question'.
When reading at your piece on Berkey et al. (1998), I think the part I am
more interested about is the "Variance component" part of the model output
that provides rho values and gives a correlation among the outcomes. As
indeed the correlation between the different traits is not provided by
primary studies I assume that doing a multivariate approach as described in
Lajeunesse (1998) might be impossible (i.e. I don't have the 'v2i' term of
covariance?)...

For this reason in my research I am firstly looking at the leaf traits as
separate entities, e.g. a separate dataset for each trait, performing a
meta-regression measuring the rate of change depending on climate and
altitduinal change (pharaphs this is good to be mentioned in a manuscript
eventually, motivating why a multivariate approach was not used?). As a
secondary goal of my paper/research I would just like to show/see if
studies  e.g. reporting an increase in leaf mass also report an decrease in
leaf size and vice versa, to observe if there are common patterns among
leaf traits change in studies reporting multiple traits.
Thereby I don't need a precise estimation of their relationship, just
explore if there is a general signal of a relationship. That's why I
adopted in the first instance the ranged major axis (RMA) approach. Maybe a
simple correlation matrix of the lnRR could be enough to achieve this
goal...?

Cheers,
Gabri

On 7 August 2018 at 12:06, Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Gabri,
>
> This is something that can be done using a multivariate model. The
> canonical example I always refer to in this case is:
>
> http://www.metafor-project.org/doku.php/analyses:berkey1998
>
> 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/
>
> Best,
> Wolfgang
>
> -----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
> experiment.
>
> Thanks,
> Gabri
>

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