# multilevel meta analysis - interpretion

I wanted to do a multilevel meta analysis and I typed this command

model5<-rma.mv(yi, vi, mods=~factor(intcode)+basemf-1,     random=~1|stdy/id, data=salt)


where study is level 2 and id are communities (level 1) nested within level2. I have 18 studies with 28 ids (communities). I got the following output

Multivariate Meta-Analysis Model (k = 28; method: REML)
Variance Components:

estim    sqrt  nlvls  fixed   factor
sigma^2.1 0.0004 0.0200 18 no stdy sigma^2.2 0.0016 0.0406 28 no stdy/id
Test for Residual Heterogeneity: QE(df = 24) = 912.9175, p-val < .0001

Test of Moderators (coefficient(s) 1,2,3,4): QM(df = 4) = 124.2892, p-val < .0001

Model Results:

estimate   se     zval    pval    ci.lb    ci.ub
factor(intcode)1 -0.0360 0.0144 -2.5028 0.0123 -0.0643 -0.0078 *
factor(intcode)2  0.0482 0.0263  1.8323 0.0669 -0.0034  0.0998 .
factor(intcode)3 0.0019 0.0348 0.0551 0.9560 -0.0662 0.0700
basemf 0.0046 0.0007 6.8576 <.0001 0.0033 0.0060 ***

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.

> confint(model5) [[1]]

estimate  ci.lb  ci.ub
sigma^2.1 0.0004 0.0000 0.0028
sigma.1 0.0200 0.0000 0.0534

[[2]]

estimate  ci.lb  ci.ub
sigma^2.2 0.0016   0.0006 0.0039
sigma.2   0.0406   0.0250 0.0621


The output indicates that intervention 1 and basemf are significant predictors of proportion infected after 1 year of intervention. The variance components indicate the variablity between and within studies are very low. I have the follwing queries How do i interpret these findings? Is it possible to estimate a pooled effect size for this model? How do I get the values of I^2 as i need that to compare across models (random effects, mixed effects, multilevel random effects Vs multilevel mixed effects). As there are only 18 studies, i cannot add anymore predictors....so What should i do next? Regards Vidya

r

You can obtain $I^2$ like statistics by following the advice given in the post computing heterogeneity assigned to random factors in meta-analysis
It looks to me as though your variances are rather poorly estimated and I would strongly recommend using the profile command on your model to check the shape of the (pseudo)-likelihood. If it is flat it suggests that you do not have enough data to identify the model well. I may be wrong here of course and everything may be OK.
I agree with your statement that with that number of studies your ability to search for moderators is going to have to be limited. You can obtain a test of your factor moderator as a whole rather than relying on the test for each individual coefficient you need the btt parameter