<div dir="ltr">Gabriele,<div><br></div><div>I see what you mean. Your explanation suggests that there would be high variance in the outcome from study to study, due to examining different species or other aspects of the study's design. I don't think that this precludes using the raw means as effect sizes---it just means that there would be a large between-study variance component. I think this approach would still make it easier to model how the ES might depend on covariates that have variation within a given study (such as altitude level).</div><div><br></div><div>The difficulty with using the ROM effect size is that when you compare multiple conditions to a single control condition, there is correlation in the effect size estimates. In the notation of your original email, you would have </div><div>cov(yi1, yi2) != 0</div><div>cov(yi1, yi3) != 0</div><div>cov(yi2, yi3) != 0</div><div>In fact, there would be very strong dependence because yi3 = yi2 - yi1. So if you use this approach, it would be critical to account for the sampling covariance between the effect sizes. Lajeunesse (2011) gives formulas for the covariances that you'd need.</div><div><br></div><div>James</div><div><br></div><div>Lajeunesse, M. J. (2011). On the meta-analysis of resposne ratios for studies with correlated and multi-design groups. Ecology, 92(11), 2049–2055.<br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Tue, Apr 10, 2018 at 10:22 AM, Gabriele Midolo <span dir="ltr"><<a href="mailto:gabriele.midolo@gmail.com" target="_blank">gabriele.midolo@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>
<div>Dear James (all),<br><br></div><span class="">Thanks for your ideas, very appreciated.<br>I
understand what you mean, but SLA can be calculated on different
species which are likely to report very different magnitude depending on
the species. Plus I think the ratios calculated with "ROM" should
provide a standardized measure of how much a single species' SLA changes
in response to altitudinal shift, that is what I think might be
interesting to measure in the context of my study.<br>I am not unkeen to
use your option of course, I am just wondering if a three-level
meta-analysis could deal with a type of independency described above, or
it can work with data that share multiple treatment "doses" compated to
a single control...
<br><br></span></div><span class="HOEnZb"><font color="#888888">Gabriele<br></font></span></div><div class="gmail_extra"><br><div class="gmail_quote"><span class="">On 10 April 2018 at 16:21, James Pustejovsky <span dir="ltr"><<a href="mailto:jepusto@gmail.com" target="_blank">jepusto@gmail.com</a>></span> wrote:<br></span><div><div class="h5"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Gabriele,<div><br></div><div>If all of the studies use SLA as the outcome measure, would it make sense to model the mean levels directly (instead of calculating proportionate changes)? In other words, use the mean SLA level as the effect size. If it makes sense conceptually, I think this would be a good way to go because then the effect size estimates at each altitude level would be independent of each other, conditional on the true mean levels for that study, and a three-level meta-analysis model would be a natural fit.</div><span class="m_-6276785066066874975HOEnZb"><font color="#888888"><div><br></div><div>James</div></font></span></div><div class="gmail_extra"><br><div class="gmail_quote"><div><div class="m_-6276785066066874975h5">On Sun, Apr 8, 2018 at 11:12 AM, Gabriele Midolo <span dir="ltr"><<a href="mailto:gabriele.midolo@gmail.com" target="_blank">gabriele.midolo@gmail.com</a>></span> wrote:<br></div></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="m_-6276785066066874975h5"><div dir="ltr">Dear all,<br><br>I have a question that is more methodological but somehow related to metafor. <br>I want to conduct an (ecological) meta-analysis on specific leaf area (SLA) response to increased altitdue (i.e. elevation) in mountain ecosystems. Primary studies selected report the mean (+ SE and sample size) of SLA sampled at different altitudinal levels. The picture attached is an example of how row primary data are normally reported in the articles (modified, from Seguí et al 2018, fig.1c [<a href="https://doi.org/10.1007/s00035-017-0195-9%5D" target="_blank">https://doi.org/10.1007/s0003<wbr>5-017-0195-9]</a>). <br>The A, B and C (in red) values represents the mean values of SLA calculated at 1900, 2200 and 2350 m above the sea level (i.e. altitude) that should, in my opinion, be suitable for calculating log-transformed response ratios (RR) indicating how much SLA increases/decreases compared to a population of plants sampled to a lower altitiude. Thus, given the design of such studies, I propose that multiple RR (yi) must be calulcated within each study as follows:<br><br>yi1= ln(B/A)<br>yi2=ln(C/A)<br>yi3=ln(C/B)<br>... <br>if a D value would have been reported by the authors, sampled to a higher altitdue than 2350 m, then I woul also calculate yi4=ln(D/A), yi5=ln(D/B), yi6=ln(D/C) for this study.<br><br>This approach make sense to me because there is no "proper" control and treatment and you are not just interested to estimate SLA changes by comparing mean values reported at higher altitudes with only the one sampled at the lowest altitudinal level (yi1,yi2), but also between higer altitudinal levels (yi3). This is also supposed to allow to look in meta-regession how the altitudinal shift (so, the difference in altitudes e.g. 300m for yi1) affect the effect size responses. So - and here finally comes my question - with <a href="http://rma.mv" target="_blank">rma.mv</a> I should be able to safely account for non-independence by fitting a model with the "random =~1|Experiment/ID" structure (?). Is this type of data suitable for three-level mixed-effect meta-analysis? I used already this structure in a previous meta-analysis I conducted in the past, but back then I was working with multiple treatments compared to just one single control in each study.<br>I see some similar meta-analysis in the past have used the r-to-z transformed effect size and focused on the correlation
- in my case -
between altitude and SLA, but not sure this is what I would like to investigate in the first place...<br><br>Hope I was clear, and my apologies if I was messy.<br><br>Thanks a lot for reading this<br>Gabriele<br><br><img src="cid:ii_jfqzmxqo0_162a5f6c7131ed52" width="440" height="437"><br><br></div>
<br></div></div><span>______________________________<wbr>_________________<br>
R-sig-meta-analysis mailing list<br>
<a href="mailto:R-sig-meta-analysis@r-project.org" target="_blank">R-sig-meta-analysis@r-project.<wbr>org</a><br>
<a href="https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis" rel="noreferrer" target="_blank">https://stat.ethz.ch/mailman/l<wbr>istinfo/r-sig-meta-analysis</a><br>
<br></span></blockquote></div><br></div>
</blockquote></div></div></div><br></div>
</blockquote></div><br></div>