Hello! I run the binary multilevel model using **brms** . I should calculate the variance partition coefficient (VPC) to represent the percentage variance explained at the group level (\sigma_μ^2). I first set up a null model with only random intercept. The code is as below.

```
fm.obj.v00<-bf(Relief3 ~ 1 + (1 | Group))
fit.obj.v00<-brm(formula = fm.obj.v00, data = orgin, family=bernoulli(link = "logit"),
control = list(adapt_delta = 0.99, max_treedepth=15),
iter=8000, warmup=4000, thin=4, chains=1, cores=1)
fit.obj.v00<-add_criterion(fit.obj.v00, c("loo", "waic"))
```

I then would like to calculate VPC based on **brms** output. However, I don’t know how to calculate the variance at the individual level (\sigma_ε^2 )and that at the group level (\sigma_u^2). Below is the equation for VPC. Just wondering if it’s possible to provide the code to calculate VPC based on **brms** output.

I have used the code as below to calculate the mean and variance of posterior samples. However, I don’t think `r_mean`

represents the variance of residuals at the group level. If so, how can I calculate VPC based on the output of **brms**?

```
vars <- posterior_samples(fit.obj.v00, pars = "^sd_")^2
r_mean<-apply(vars, 2, mean)
r_variance<-apply(vars, 2, sd)
```

I have also review one topic “extracting variance components” and it shows codes as below. Can I replace “post” with “fit.obj.v00”? How to interprate the output in summary()? Does the calculation results represent the variance components or proportion of variance at the group level?

```
PPD <- posterior_predict(post)
vars <- apply(PPD, MARGIN = 1, FUN = var)
PPD_0 <- posterior_predict(post, re.form = ~ 0)
vars_0 <- apply(PPD_0, MARGIN = 1, FUN = var)
summary(vars - vars_0)
```

Another way is to use “performance” package and adopt icc() function. I run it and the code and results are as below. Just wonder if it’s right for the output of **brms**.

```
library("performance")
icc(fit.obj.v00, by_group="Group")
#Intraclass Correlation Coefficient
#Adjusted ICC: 0.449
#Conditional ICC: 0.449
```

**P.S.:** Please find the relevant documents on VPC in http://seis.bris.ac.uk/~frwjb/materials/wbvpc.pdf.

Best,

**MODERATOR EDIT:** This post was edited for code and math formatting by @martinmodrak