I want to calculate the proportion of total variance in a multi-level meta-analysis with 2+ random effect terms according to pp. 1261 & equation (24) in Nakagawa & Santos 2012 https://www.researchgate.net/profile/Shinichi_Nakagawa2/publication/233341316_Methodological_issues_and_advances_in_biological_meta-analysis/links/00b495157aec0585c0000000.pdf
I have the following output from function rma.mv
in R package metafor
with the model structure
test.meta = rma.mv(d, Var.d., random = list(~1|Study, ~1|Order.class), data=data).
How can I obtain the total heterogeneity (variance) by which to divide each of the sigma^2 terms?
Multivariate Meta-Analysis Model (k = 274; method: REML)
logLik Deviance AIC BIC AICc
-1264.4201 2528.8403 2534.8403 2545.6687 2534.9295
Variance Components:
estim sqrt nlvls fixed factor
sigma^2.1 1.1223 1.0594 65 no Study
sigma^2.2 0.4060 0.6372 7 no Order.class
Test for Heterogeneity:
Q(df = 273) = 2660.6043, p-val < .0001
Model Results:
estimate se zval pval ci.lb ci.ub
-0.6585 0.3125 -2.1074 0.0351 -1.2710 -0.0461 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
A similar example with only one random-effect term is here http://www.metafor-project.org/doku.php/tips:rma.uni_vs_rma.mv under "Random effects model."