Dear all, Do you think it is possible to perform a multilevel meta-analysis without sampling variance (from both the conceptual and the statistical point of view), using only the number of replicates to weight the importance of studies? I am using mean species abundance (MSA) as effect size, a quite unusual metric for biodiversity intactness in ecological meta-analysis (see an example in Ben?tez-L?pez et al., 2010 <http://serengetiwatch.org/wp-content/uploads/2010/08/Benitez_lopez-et-al_Roads_2010.pdf>). MSA is the mean of the response ratio of abundance values (Treatment/Control) for each individual species in a given ecological experiment/study. However, individual ratios are truncated at 1 if Treatment>Control, so MSA ranges between 0 and 1. Few studies included in my analysis report values of SD in the treatment and control plots. Additionaly, the type of data I am working with makes quite difficult -impossible, to my knowledge - to apply imputation techniques to estimate variance. However, all the studies included in the analysis report at least the number of replicates. Some of my co-authors suggested to weight the meta-analysis by the number of replicates, instead to limit the analysis to an "unweighted meta-analysis". Assuming this makes sense to you as well, how can I implement this in metafor? So far I am trying to arbitrarily assign the same variance to each study vi=1 and then use the W term to weight the importance by the number of replicates. Something like the following: dat$vi<-1 res <- rma.mv(MSA, vi, W=Replicates, random =~1|Experiment/ID, data=dat) However, probably better, I am trying to fit something similar to a meta-analytic model with the following: lme(MSA~1, random =~1|Experiment/ID, weights=varIdent(~Replicates), data=dat) I am aware - based on Wolfgang's website - that fitting via lme() is not really the same than using 'rma.mv()' but maybe the latter is a more suitable model I am looking for given my specific case (?). (sorry - my first post here - let me know if I can share the data with you or if I missed something)
[R-meta] Dealing with missing variance in multilevel models: using number of replicates instead in ecological meta-analysis
2 messages · Gabriele Midolo, James Pustejovsky
Gabriele, I think using lme() is a very reasonable strategy in this case. The main difference between models implemented in lme() versus those implemented in metafor() is that lme() treats the residual variance at the lowest level (so in this case, the variance of the effect size estimate, nested within an experiment) as unknown and estimates based on a homoskedasticity assumption or other some other posited structure, whereas metafor treats the variances of the effect size estimates as known quantities. In your situation, it seems that the variances really are unknown, and so it would be appropriate to treat them as such, modeling them as inversely proportional to the number of replicates. You might also consider reporting cluster-robust variance estimates for the overall average effect size estimate (or meta-regression coefficients, if you are going to look at moderators too). This approach would allow for the possibility that the assumption that the variances are inversely proportional to the number of replicates is not correct. Here's an example of what the model might look like--note too that I think you need to use varFixed() rather than varIdent(): meta_fit <- lme(MSA~1, random = ~ 1 | Experiment, weights=varFixed(~ 1 / Replicates), data=dat) library(clubSandwich) coef_test(meta_fit, vcov = "CR2") # this will automatically cluster on the highest-level grouping variable, Also, this approach could be extended to another level to model the individual (species-specific) response ratios, nested within experiments, rather than modeling only the aggregated mean species abundance estimates. One potential advantage of doing so is that it would allow you to study species-level moderators of effects. James On Fri, Oct 6, 2017 at 4:25 AM, Gabriele Midolo <gabriele.midolo at gmail.com> wrote:
Dear all, Do you think it is possible to perform a multilevel meta-analysis without sampling variance (from both the conceptual and the statistical point of view), using only the number of replicates to weight the importance of studies? I am using mean species abundance (MSA) as effect size, a quite unusual metric for biodiversity intactness in ecological meta-analysis (see an example in Ben?tez-L?pez et al., 2010 <http://serengetiwatch.org/wp-content/uploads/2010/08/ Benitez_lopez-et-al_Roads_2010.pdf>). MSA is the mean of the response ratio of abundance values (Treatment/Control) for each individual species in a given ecological experiment/study. However, individual ratios are truncated at 1 if Treatment>Control, so MSA ranges between 0 and 1. Few studies included in my analysis report values of SD in the treatment and control plots. Additionaly, the type of data I am working with makes quite difficult -impossible, to my knowledge - to apply imputation techniques to estimate variance. However, all the studies included in the analysis report at least the number of replicates. Some of my co-authors suggested to weight the meta-analysis by the number of replicates, instead to limit the analysis to an "unweighted meta-analysis". Assuming this makes sense to you as well, how can I implement this in metafor? So far I am trying to arbitrarily assign the same variance to each study vi=1 and then use the W term to weight the importance by the number of replicates. Something like the following: dat$vi<-1 res <- rma.mv(MSA, vi, W=Replicates, random =~1|Experiment/ID, data=dat) However, probably better, I am trying to fit something similar to a meta-analytic model with the following: lme(MSA~1, random =~1|Experiment/ID, weights=varIdent(~Replicates), data=dat) I am aware - based on Wolfgang's website - that fitting via lme() is not really the same than using 'rma.mv()' but maybe the latter is a more suitable model I am looking for given my specific case (?). (sorry - my first post here - let me know if I can share the data with you or if I missed something) [[alternative HTML version deleted]]
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