Introduction to jagsUI

Installing JAGS

In addition to installing the jagsUI package, we also need to separately install the free JAGS software, which you can download here.

Once that’s installed, load the jagsUI library:

library(jagsUI)

Typical jagsUI Workflow

  1. Organize data into a named list
  2. Write model file in the BUGS language
  3. Specify initial MCMC values (optional)
  4. Specify which parameters to save posteriors for
  5. Specify MCMC settings
  6. Run JAGS
  7. Examine output

1. Organize data

We’ll use the longley dataset to conduct a simple linear regression. The dataset is built into R.

data(longley)
head(longley)
#      GNP.deflator     GNP Unemployed Armed.Forces Population Year Employed
# 1947         83.0 234.289      235.6        159.0    107.608 1947   60.323
# 1948         88.5 259.426      232.5        145.6    108.632 1948   61.122
# 1949         88.2 258.054      368.2        161.6    109.773 1949   60.171
# 1950         89.5 284.599      335.1        165.0    110.929 1950   61.187
# 1951         96.2 328.975      209.9        309.9    112.075 1951   63.221
# 1952         98.1 346.999      193.2        359.4    113.270 1952   63.639

We will model the number of people employed (Employed) as a function of Gross National Product (GNP). Each column of data is saved into a separate element of our data list. Finally, we add a list element for the number of data points n. In general, elements in the data list must be numeric, and structured as arrays, matrices, or scalars.

jags_data <- list(
  gnp = longley$GNP,
  employed = longley$Employed,
  n = nrow(longley)
)

2. Write BUGS model file

Next we’ll describe our model in the BUGS language. See the JAGS manual for detailed information on writing models for JAGS. Note that data you reference in the BUGS model must exactly match the names of the list we just created. There are various ways to save the model file, we’ll save it as a temporary file.

# Create a temporary file
modfile <- tempfile()

#Write model to file
writeLines("
model{

  # Likelihood
  for (i in 1:n){ 
    # Model data
    employed[i] ~ dnorm(mu[i], tau)
    # Calculate linear predictor
    mu[i] <- alpha + beta*gnp[i]
  }
    
  # Priors
  alpha ~ dnorm(0, 0.00001)
  beta ~ dnorm(0, 0.00001)
  sigma ~ dunif(0,1000)
  tau <- pow(sigma,-2)

}
", con=modfile)

3. Initial values

Initial values can be specified as a list of lists, with one list element per MCMC chain. Each list element should itself be a named list corresponding to the values we want each parameter initialized at. We don’t necessarily need to explicitly initialize every parameter. We can also just set inits = NULL to allow JAGS to do the initialization automatically, but this will not work for some complex models. We can also provide a function which generates a list of initial values, which jagsUI will execute for each MCMC chain. This is what we’ll do below.

inits <- function(){  
  list(alpha=rnorm(1,0,1),
       beta=rnorm(1,0,1),
       sigma=runif(1,0,3)
  )  
}

4. Parameters to monitor

Next, we choose which parameters from the model file we want to save posterior distributions for. We’ll save the parameters for the intercept (alpha), slope (beta), and residual standard deviation (sigma).

params <- c('alpha','beta','sigma')

5. MCMC settings

We’ll run 3 MCMC chains (n.chains = 3).

JAGS will start each chain by running adaptive iterations, which are used to tune and optimize MCMC performance. We will manually specify the number of adaptive iterations (n.adapt = 100). You can also try n.adapt = NULL, which will keep running adaptation iterations until JAGS reports adaptation is sufficient. In general you do not want to skip adaptation.

Next we need to specify how many regular iterations to run in each chain in total. We’ll set this to 1000 (n.iter = 1000). We’ll specify the number of burn-in iterations at 500 (n.burnin = 500). Burn-in iterations are discarded, so here we’ll end up with 500 iterations per chain (1000 total - 500 burn-in). We can also set the thinning rate: with n.thin = 2 we’ll keep only every 2nd iteration. Thus in total we will have 250 iterations saved per chain ((1000 - 500) / 2).

The optimal MCMC settings will depend on your specific dataset and model.

6. Run JAGS

We’re finally ready to run JAGS, via the jags function. We provide our data to the data argument, initial values function to inits, our vector of saved parameters to parameters.to.save, and our model file path to model.file. After that we specify the MCMC settings described above.

out <- jags(data = jags_data,
            inits = inits,
            parameters.to.save = params,
            model.file = modfile,
            n.chains = 3,
            n.adapt = 100,
            n.iter = 1000,
            n.burnin = 500,
            n.thin = 2)
# 
# Processing function input....... 
# 
# Done. 
#  
# Compiling model graph
#    Resolving undeclared variables
#    Allocating nodes
# Graph information:
#    Observed stochastic nodes: 16
#    Unobserved stochastic nodes: 3
#    Total graph size: 74
# 
# Initializing model
# 
# Adaptive phase, 100 iterations x 3 chains 
# If no progress bar appears JAGS has decided not to adapt 
#  
# 
#  Burn-in phase, 500 iterations x 3 chains 
#  
# 
# Sampling from joint posterior, 500 iterations x 3 chains 
#  
# 
# Calculating statistics....... 
# 
# Done.

We should see information and progress bars in the console.

If we have a long-running model and a powerful computer, we can tell jagsUI to run each chain on a separate core in parallel by setting argument parallel = TRUE:

out <- jags(data = jags_data,
            inits = inits,
            parameters.to.save = params,
            model.file = modfile,
            n.chains = 3,
            n.adapt = 100,
            n.iter = 1000,
            n.burnin = 500,
            n.thin = 2,
            parallel = TRUE)

While this is usually faster, we won’t be able to see progress bars when JAGS runs in parallel.

7. Examine output

Our first step is to look at the output object out:

out
# JAGS output for model '/tmp/RtmpmLnXQM/file5296fe27115', generated by jagsUI.
# Estimates based on 3 chains of 1000 iterations,
# adaptation = 100 iterations (sufficient),
# burn-in = 500 iterations and thin rate = 2,
# yielding 750 total samples from the joint posterior. 
# MCMC ran for 0.001 minutes at time 2024-11-26 06:24:49.707471.
# 
#            mean    sd   2.5%    50%  97.5% overlap0 f  Rhat n.eff
# alpha    51.811 0.716 50.403 51.803 53.161    FALSE 1 1.004   750
# beta      0.035 0.002  0.031  0.035  0.039    FALSE 1 1.004   750
# sigma     0.719 0.159  0.496  0.694  1.113    FALSE 1 1.000   750
# deviance 33.283 2.957 30.081 32.414 40.483    FALSE 1 1.003   750
# 
# Successful convergence based on Rhat values (all < 1.1). 
# Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
# For each parameter, n.eff is a crude measure of effective sample size. 
# 
# overlap0 checks if 0 falls in the parameter's 95% credible interval.
# f is the proportion of the posterior with the same sign as the mean;
# i.e., our confidence that the parameter is positive or negative.
# 
# DIC info: (pD = var(deviance)/2) 
# pD = 4.4 and DIC = 37.658 
# DIC is an estimate of expected predictive error (lower is better).

We first get some information about the MCMC run. Next we see a table of summary statistics for each saved parameter, including the mean, median, and 95% credible intervals. The overlap0 column indicates if the 95% credible interval overlaps 0, and the f column is the proportion of posterior samples with the same sign as the mean.

The out object is a list with many components:

names(out)
#  [1] "sims.list"   "mean"        "sd"          "q2.5"        "q25"        
#  [6] "q50"         "q75"         "q97.5"       "overlap0"    "f"          
# [11] "Rhat"        "n.eff"       "pD"          "DIC"         "summary"    
# [16] "samples"     "modfile"     "model"       "parameters"  "mcmc.info"  
# [21] "run.date"    "parallel"    "bugs.format" "calc.DIC"

We’ll describe some of these below.

Diagnostics

We should pay special attention to the Rhat and n.eff columns in the output summary, which are MCMC diagnostics. The Rhat (Gelman-Rubin diagnostic) values for each parameter should be close to 1 (typically, < 1.1) if the chains have converged for that parameter. The n.eff value is the effective MCMC sample size and should ideally be close to the number of saved iterations across all chains (here 750, 3 chains * 250 samples per chain). In this case, both diagnostics look good.

We can also visually assess convergence using the traceplot function:

traceplot(out)

We should see the lines for each chain overlapping and not trending up or down.

Posteriors

We can quickly visualize the posterior distributions of each parameter using the densityplot function:

densityplot(out)

The traceplots and posteriors can be plotted together using plot:

plot(out)

We can also generate a posterior plot manually. To do this we’ll need to extract the actual posterior samples for a parameter. These are contained in the sims.list element of out.

post_alpha <- out$sims.list$alpha
hist(post_alpha, xlab="Value", main = "alpha posterior")

Update

If we need more iterations or want to save different parameters, we can use update:

# Now save mu also
params <- c(params, "mu")
out2 <- update(out, n.iter=300, parameters.to.save = params)
# Compiling model graph
#    Resolving undeclared variables
#    Allocating nodes
# Graph information:
#    Observed stochastic nodes: 16
#    Unobserved stochastic nodes: 3
#    Total graph size: 74
# 
# Initializing model
# 
# Adaptive phase..... 
# Adaptive phase complete 
#  
# No burn-in specified 
#  
# Sampling from joint posterior, 300 iterations x 3 chains 
#  
# 
# Calculating statistics....... 
# 
# Done.

The mu parameter is now in the output:

out2
# JAGS output for model '/tmp/RtmpmLnXQM/file5296fe27115', generated by jagsUI.
# Estimates based on 3 chains of 1300 iterations,
# adaptation = 100 iterations (sufficient),
# burn-in = 1000 iterations and thin rate = 2,
# yielding 450 total samples from the joint posterior. 
# MCMC ran for 0 minutes at time 2024-11-26 06:24:50.558631.
# 
#            mean    sd   2.5%    50%  97.5% overlap0 f  Rhat n.eff
# alpha    51.850 0.794 50.339 51.826 53.457    FALSE 1 1.002   450
# beta      0.035 0.002  0.030  0.035  0.039    FALSE 1 1.001   450
# sigma     0.718 0.154  0.493  0.689  1.098    FALSE 1 1.018   244
# mu[1]    59.995 0.355 59.308 59.979 60.723    FALSE 1 1.005   278
# mu[2]    60.868 0.312 60.271 60.855 61.483    FALSE 1 1.006   245
# mu[3]    60.821 0.314 60.216 60.807 61.442    FALSE 1 1.006   247
# mu[4]    61.743 0.272 61.250 61.731 62.287    FALSE 1 1.007   214
# mu[5]    63.286 0.213 62.894 63.285 63.709    FALSE 1 1.009   167
# mu[6]    63.913 0.196 63.551 63.913 64.285    FALSE 1 1.010   155
# mu[7]    64.552 0.184 64.198 64.549 64.897    FALSE 1 1.011   150
# mu[8]    64.473 0.185 64.119 64.470 64.820    FALSE 1 1.011   150
# mu[9]    65.667 0.179 65.309 65.673 66.027    FALSE 1 1.010   166
# mu[10]   66.422 0.189 66.043 66.423 66.790    FALSE 1 1.009   201
# mu[11]   67.242 0.209 66.849 67.230 67.652    FALSE 1 1.007   267
# mu[12]   67.304 0.211 66.906 67.289 67.719    FALSE 1 1.007   273
# mu[13]   68.630 0.260 68.116 68.631 69.164    FALSE 1 1.004   442
# mu[14]   69.322 0.290 68.750 69.333 69.914    FALSE 1 1.003   450
# mu[15]   69.863 0.315 69.238 69.870 70.503    FALSE 1 1.003   450
# mu[16]   71.140 0.378 70.354 71.142 71.895    FALSE 1 1.002   450
# deviance 33.281 2.930 30.082 32.499 41.240    FALSE 1 1.011   354
# 
# Successful convergence based on Rhat values (all < 1.1). 
# Rhat is the potential scale reduction factor (at convergence, Rhat=1). 
# For each parameter, n.eff is a crude measure of effective sample size. 
# 
# overlap0 checks if 0 falls in the parameter's 95% credible interval.
# f is the proportion of the posterior with the same sign as the mean;
# i.e., our confidence that the parameter is positive or negative.
# 
# DIC info: (pD = var(deviance)/2) 
# pD = 4.3 and DIC = 37.567 
# DIC is an estimate of expected predictive error (lower is better).

This is a good opportunity to show the whiskerplot function, which plots the mean and 95% CI of parameters in the jagsUI output:

whiskerplot(out2, 'mu')