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