For the three-level meta-analysis, the package "dmetar" provides a function that calculates the I^2 (dmetar::var.comp()). But, this function only works for three-level models. Is there any package or function that allows for calculating I^2 for, let's say, a five-level model?
Also, for such models with one or more moderators, are there any tools for calculating the R^2 for the effect of the moderator(s)?
You cannot really estimate a true R^2 for a multilevel meta-analysis. You can calculate a pseudo R^2 for fixed covariates in mixed models, but I would generally avoid inferring much from it. If you absolutely need R^2, you can calculate a very crude version based on the difference between models with/without the fixed covariate like so:
##using fictitious variables
##model with no predictors
model1
Thank you Jack Henry for your nicely elaborated answer.
I also found a more general formula for I^2 on the metafor website (https://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate), which allows one to account for non-independent sampling error, as is the case in such models. However, as Dr. Viechrbauer presented the formula for three-level models, I had a little doubt whether it can be applied to models with more levels (As unexpectedly no one presented any formula for such models, I thought there may be a problem here.) I contacted him, and he confirmed that the same formula applies.
Of note, for my data, the results from both formulas yielded very similar results.
Thank you.
Based on the general formula for I-squared and the codes provided in the metafor website (https://www.metafor-project.org/doku.php/tips:i2_multilevel_multivariate), I wrote a function to calculate I-squared for multilevel models with more than three levels. I share it here, as others may face a similar issue. It is for five-level models, but works for three- and four-level models as well, but the labels will not be correct:
#a function for I-squared in multilevel models
library(metafor)
i2.mv
Ali Zia-Tohidi Thank you for this, it is useful. I have fixed some errors in the function (eg. estimating the model inside of the function, using rownames, etc.) and generalised it to work with any number of levels with correct labelling. To avoid confusion, I have also used the same labelling convention for the levels as the rma.mv function uses.
i2.mv
Thank you Jack Henry. It is very nice.
I suggest a small modification. The function returns an error if there is any NA. For example:
dat
Ali Zia-Tohidi My mistake - I thought/assumed they were filtered out when the model was fitted. I have modified the code to account for this.
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Techniques
- Meta-Analysis