# Fit Model
orangemod.rs <- 
    lmer(circumference ~ ageYears + (ageYears | Tree), data = Orange)
# First we need the design matrix (X), the number of observations (n)
# and the fixed effect estimates (Beta)
  X <- model.matrix(orangemod.rs)
  n <- nrow(X)
  Beta <- fixef(orangemod.rs)
# First the fixed effects variance (eqn 27 of Nakagawa & Schielzeth): 
  Sf <- var(X %*% Beta)
# Second, the list of covariance matrices of the random effects.
# Here the list has only a single element because there is only
# one level of random effects.
  (Sigma.list <- VarCorr(orangemod.rs))
# Use equation 11 in the paper to estimate the random effects variance 
# component.
# Using sapply ensures that the same code will work when there are multiple
# random effects (i.e. where length(Sigma.list) > 1)
  Sl <- 
    sum(
      sapply(Sigma.list,
        function(Sigma)
        {
          Z <-X[,rownames(Sigma)]
          sum(diag(Z %*% Sigma %*% t(Z)))/n
        }))
# As this model is an LMM, the additive dispersion variance, Se, is
# equivalent to the residual variance. The residual standard deviation
# is stored as an attribute of Sigma.list:
  
  Se <- attr(Sigma.list, "sc")^2
# Finally, the distribution-specific variance, Sd, is zero for LMMs:
  Sd <- 0
# Use eqns 29 and 30 from Nakagawa & Schielzeth to estimate marginal and
# conditional R-squared:
  total.var <- Sf + Sl + Se + Sd
  (Rsq.m <- Sf / total.var) 
  (Rsq.c <- (Sf + Sl) / total.var) 

# Second, the list of covariance matrices of the random effects.
# Here the list has only a single element because there is only
# one level of random effects.
  (Sigma.list <- VarCorr(orangemod.rs))
# Groups   Name        Std.Dev. Corr  
# Tree     (Intercept)  1.8966        
#          ageYears     8.7757  -1.000
# Residual             10.0062      

library(metafor)
library(tidyverse)
data("dat.konstantopoulos2011")
df=dat.konstantopoulos2011%>%
  as.data.frame()
#fit random slope model
m1=rma.mv(yi ~ year, vi, random = list(~year|study, ~year|district, ~1|school), data = df,
          cvvc = TRUE)
lme4::VarCorr(m1)
nlme::VarCorr(m1)
#potentially useful components
m1$V
m1$vvc
What I'm looking to recreate
# Groups   Name        Std.Dev. Corr  
# study    (Intercept)  [VALUE]        
#          ageYears     [VALUE]  [VALUE]
# district (Intercept)
#          ageYears              [VALUE]
# school   (Intercept)
# Residual             [VALUE]      

rma.mv(yi ~ year, vi, 
       random = list(~year|study, ~year|district, ~1|school),
       struct=c("GEN","GEN"), data = df)