## A really helpful function I wrote to make the MCMC output from NIMBLE or JAGS so much easier to work with for model predictions and plotting

When fitting complex models in NIMBLE or JAGS you can end up with hundreds or even thousands of parameters. Take, for example, a multi-species occupancy model. In NIMBLE that would look something like this:

multi_species_occupancy <- nimble::nimbleCode(
{
# Latent state part of model
for(species in 1:nspecies){
for(site in 1:nsite){
# logit-linear predictor latent state
logit(mu_psi[site,species]) <- inprod(
psi_beta[species,1:nbeta_psi],
psi_design_matrix[site,1:nbeta_psi]
)
z[site,species] ~ dbern(
mu_psi[site,species]
)
}
}
# Detection part of model
for(species in 1:nspecies){
for(site in 1:nsite){
for(visit in 1:nvisit){
# assuming covariates for sites and visits
logit(mu_rho[site,species,visit]) <- inprod(
rho_beta[species, 1:nbeta_rho],
rho_design_matrix[site, visit, 1:nbeta_rho]
)
y[site,visit,species] ~ dbern(
mu_rho[site,species,visit] * z[site,species]
)
}
}
}
# Priors for among-species average
for(ipsi in 1:nbeta_psi){
psi_beta_mu[ipsi] ~ dnorm(0, sd = 1)
psi_beta_sd[ipsi] ~ dgamma(1, 1)
}
for(irho in 1:nbeta_rho){
rho_beta_mu[irho] ~ dnorm(0, sd = 1)
rho_beta_sd[irho] ~ dgamma(1, 1)
}
# species-specific parameters
for(ipsi in 1:nbeta_psi){
for(species in 1:nspecies){
psi_beta[species,ipsi] ~ dnorm(psi_beta_mu[ipsi], sd = psi_beta_sd[ipsi])
}
}
for(irho in 1:nbeta_rho){
for(species in 1:nspecies){
rho_beta[species,irho] ~ dnorm(rho_beta_mu[irho], sd = rho_beta_sd[irho])
}
}
}
)


From this model we would want to track the species-level parameters (psi_beta and rho_beta), as well as the among-species parameters (psi_beta_mu, rho_beta_mu, psi_beta_sd, and rho_beta_sd). When we track these parameters across multiple chains, most MCMC software will return a list-style object with each element representing a MCMC matrix that has a number of rows equal to the number of samples in the chain and a number of columns equal to the total number of parameters monitored. For example, I fitted the model above to some simulated data for 7 species where nbeta_psi = 2 and nbeta_rho = 2. This resulted in 36 parameters that were tracked

# Assuming we have an object called my_model_ouput
colnames(
my_model_output$chain1 ) [1] "psi_beta[1, 1]" "psi_beta[2, 1]" [3] "psi_beta[3, 1]" "psi_beta[4, 1]" [5] "psi_beta[5, 1]" "psi_beta[6, 1]" [7] "psi_beta[7, 1]" "psi_beta[1, 2]" [9] "psi_beta[2, 2]" "psi_beta[3, 2]" [11] "psi_beta[4, 2]" "psi_beta[5, 2]" [13] "psi_beta[6, 2]" "psi_beta[7, 2]" [15] "psi_beta_mu[1]" "psi_beta_mu[2]" [17] "psi_beta_sd[1]" "psi_beta_sd[2]" [19] "rho_beta[1, 1]" "rho_beta[2, 1]" [21] "rho_beta[3, 1]" "rho_beta[4, 1]" [23] "rho_beta[5, 1]" "rho_beta[6, 1]" [25] "rho_beta[7, 1]" "rho_beta[1, 2]" [27] "rho_beta[2, 2]" "rho_beta[3, 2]" [29] "rho_beta[4, 2]" "rho_beta[5, 2]" [31] "rho_beta[6, 2]" "rho_beta[7, 2]" [33] "rho_beta_mu[1]" "rho_beta_mu[2]" [35] "rho_beta_sd[1]" "rho_beta_sd[2]"  You can see above that the indexing gets added to the column names. This is great as we can use it to determine what species the parameter is associated to as well as if the parameter is an intercept or slope term. However, it makes it a bit difficult to work with the MCMC output, especially when we get around to making predictions from the model. Instead, it would be awesome if we could make it so that each parameter type (e.g., psi_beta, rho_beta, etc.) was appropriately indexed in an array instead of storing the array information in the column name itself. A couple months back I wrote a function to do exactly this, and have been using it for the last few analyses I’ve been working on, and I absolutely love it. I’m regularly sending said function to collaborators and the like, and as a result I figured it would be a good idea to showcase it here so you can use it as well! The function, split_mcmc(), takes in the full MCMC matrix (i.e., you have to join together all of the chains into one big matrix) and then returns a named list object, one name for every parameter type, that is indexed exactly as it would be in your Bayesian model, save for the fact that the first dimension is always your MCMC samples. The code for this function is: split_mcmc <- function(x){ # get parameter names pars <- colnames(x) # unique parameters unq_pars <- unique( gsub( "\$.*\$", "", pars ) ) # make list object to store arrays in result_list <- vector( "list", length = length(unq_pars) ) # name the list names(result_list) <- unq_pars # fill in the arrays for(i in 1:length(result_list)){ # get just the parameters tmp <- pars[grep( paste0( "^",unq_pars[i], "\$" ), pars )] if(length(tmp) == 0){ tmp <- pars[grep( paste0("^",unq_pars[i],""), pars )] } # and then the array dimensions arr_dim <- gsub( paste0( unq_pars[i],"\\[|\$" ), "", tmp ) arr_dim <- strsplit( arr_dim, "," ) ndim <- length(arr_dim[[1]]) npar <- length(arr_dim) # make a matrix arr_ind <- suppressWarnings( matrix( as.numeric( unlist(arr_dim) ), ncol = ndim, nrow = npar, byrow = TRUE ) ) if(nrow(arr_ind) == 1 & ncol(arr_ind) == 1){ arr_ind[1,1] <- 1 } # get max index for each max_ind <- apply(arr_ind, 2, max) # and then fill in the array result_list[[i]] <- array( x[,tmp], dim = c(nrow(x), max_ind) ) } return(result_list) }  Let’s use that function on the NIMBLE output of this model and see what it looks like # combine all MCMC chains my_mcmc <- do.call( "rbind", my_model_output ) # use split_mcmc() my_mcmc <- split_mcmc( my_mcmc ) # check out names of list names(my_mcmc) [1] "psi_beta" "psi_beta_mu" [3] "psi_beta_sd" "rho_beta" [5] "rho_beta_mu" "rho_beta_sd"  And now let’s look at the dimensions of psi_beta. Again, we have seven species and two parameters for each species.  dim(my_mcmc$psi_beta)
[1] 10000     7     2



The first dimension is for the 10,000 MCMC samples, the second dimension is for species, and the third is for the two parameters associated to that species. So, if I wanted to take a peek at the first few MCMC samples of the intercept and slope for the third species, I can just subset the second dimension of my_mcmc$psi_beta! head(my_mcmc$psi_beta[,3,])
[,1]      [,2]
[1,] 4.282852 0.6882747
[2,] 4.282852 0.4528713
[3,] 4.282852 0.7064803
[4,] 5.730312 0.2103931
[5,] 4.517122 0.6484852
[6,] 5.473493 0.4883727


Other parameter types were not matrices in NIMBLE, like the among-species parameters. These elements have fewer dimensions in my_mcmc

dim(my_mcmc$psi_beta_mu) [1] 10000 2  Here we just have a matrix with 10,000 MCMC samples and two parameters. I cannot stress how much easier this makes it to work with the model output / make model predictions with. See the plotting part of this blog post here as an example. Anways, I just wanted to highlight this function as it has definitely made my life easier when working with more complex outputs from different analyses. And just to demonstrate that it works correctly, here is a little matrix you can use to test it with. Enjoy! # testing split_mcmc test_matrix <- matrix( rep(1:10, each = 3), ncol = 10, nrow = 3 ) # give column names like they would appear in NIMBLE # or JAGS. colnames(test_matrix) <- c( "a", "b[1,1]", "b[2,1]", "b[1,2]", "b[2,2]", "c[1]", "c[2]", "c[3]", "c[4]", "c[5]" ) # take a look at this object test_matrix a b[1,1] b[2,1] b[1,2] b[2,2] c[1] c[2] c[3] c[4] c[5] [1,] 1 2 3 4 5 6 7 8 9 10 [2,] 1 2 3 4 5 6 7 8 9 10 [3,] 1 2 3 4 5 6 7 8 9 10 # use split_mcmc! test_mcmc <- split_mcmc( test_matrix ) # should be a matrix, three rows, one column, all 1's test_mcmc$a

[,1]
[1,]    1
[2,]    1
[3,]    1

# should be a matrix, three rows, two columns, 2 and 3's
test_mcmc$b[,,1] [,1] [,2] [1,] 2 3 [2,] 2 3 [3,] 2 3 # should be a matrix, three rows, two columns, 4 and 5's test_mcmc$b[,,2]
[,1] [,2]
[1,]    4    5
[2,]    4    5
[3,]    4    5

# should be amatrix, 3 rows, 5 columns, 6 through 10
test_mcmc\$c
[,1] [,2] [,3] [,4] [,5]
[1,]    6    7    8    9   10
[2,]    6    7    8    9   10
[3,]    6    7    8    9   10


Written on March 4, 2023