I asked a similar question a while ago on how to get model predictions in JAGS for mixed models. Here's my original question.
This time, I'm trying to get predictions for the same model but using new data and not the original that was used to fit the model.
model<-"model {
# Priors
mu_int~dnorm(0, 0.0001)
sigma_int~dunif(0, 100)
tau_int <- 1/(sigma_int*sigma_int)
for (j in 1:(M)){
alpha[j] ~ dnorm(mu_int, tau_int)
}
beta~dnorm(0, 0.01)
sigma_res~dunif(0, 100)
tau_res <- 1/(sigma_res*sigma_res)
# Likelihood
for (i in 1:n) {
mu[i] <- alpha[Mat[i]]+beta*Temp[i] # Expectation
D47[i]~dnorm(mu[i], tau_res) # The actual (random) responses
}
for(i in 1:(n)){
D47_pred[i] <- dnorm(mu[i], tau_res)
}
}"
I know this mcan be done using the posterior distributions of the resulting parameters but I'm wondering if it could also be implemented inside jags.
Thank you!
It absolutely could be done inside JAGS. If you wanted predictions for new values of Temp for some of the same observations in Mat, you would just have to append them to the existing data with a corresponding D47 value of NA.
I am super new to JAGS and Bayesian statistics, and have simply been trying to follow the Chapter 22 on Bayesian statistics in Crawley's 2nd Edition R Book. I copy the code down exactly as it appears in the book for the simple linear model: growth = a + b *tannin, where there are 9 rows of two continuous variables: growth and tannins. The data and packages are this:
install.packages("R2jags")
library(R2jags)
growth <- c(12,10,8,11,6,7,2,3,3)
tannin <- c(0,1,2,3,4,5,6,7,8)
N <- c(1,2,3,4,5,6,7,8,9)
bay.df <- data.frame(growth,tannin,N)
The ASCII file looks like this:
model{
for(i in 1:N) {
growth[i] ~ dnorm(mu[i],tau)
mu[i] <- a+b*tannin[i]
}
a ~ dnorm(0.0, 1.0E-4)
b ~ dnorm(0.0, 1.0E-4)
sigma <- 1.0/sqrt(tau)
tau ~ dgamma(1.0E-3, 1.0E-3)
}
But then, when I use this code:
> practicemodel <- jags(data=data.jags,parameters.to.save = c("a","b","tau"),
+ n.iter=100000, model.file="regression.bugs.txt", n.chains=3)
I get an error message that says:
module glm loaded
Compiling model graph
Resolving undeclared variables
Deleting model
Error in jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, :
RUNTIME ERROR:
Non-conforming parameters in function :
The problem has been solved!
Basically the change is from N <- (1,2...) to N <- 9, but there is one other solution as well, where no N is specified in the beginning. You can specify N inside the data.jags function as the number of rows in the data frame; data.jags = list(growth=bay.df$growth, tannin=bay.df$tannin, N=nrow(bay.df)).
Here is the new code:
# Make the data frame
growth <- c(12,10,8,11,6,7,2,3,3)
tannin <- c(0,1,2,3,4,5,6,7,8)
# CHANGED : This is for the JAGS code to know there are 9 rows of data
N <- 9 code
bay.df <- data.frame(growth,tannin)
library(R2jags)
# Now, write the Bugs model and save it in a text file
sink("regression.bugs.txt") #tell R to put the following into this file
cat("
model{
for(i in 1:N) {
growth[i] ~ dnorm(mu[i],tau)
mu[i] <- a+b*tannin[i]
}
a ~ dnorm(0.0, 1.0E-4)
b ~ dnorm(0.0, 1.0E-4)
sigma <- 1.0/sqrt(tau)
tau ~ dgamma(1.0E-3, 1.0E-3)
}
", fill=TRUE)
sink() #tells R to stop putting things into this file.
#tell jags the names of the variables containing the data
data.jags <- list("growth","tannin","N")
# run the JAGS function to produce the function:
practicemodel <- jags(data=data.jags,parameters.to.save = c("a","b","tau"),
n.iter=100000, model.file="regression.bugs.txt", n.chains=3)
# inspect the model output. Important to note that the output will
# be different every time because there's a stochastic element to the model
practicemodel
# plots the information nicely, can visualize the error
# margin for each parameter and deviance
plot(practicemodel)
Thanks for the help! I hope this helps others.
[Code is updated and does not correspond to error messages anymore]
I am trying to understand how JAGS predicts outcome values (for a mixed markov model). I've trained the model on a dataset which includes outcome m and covariates x1, x2 and x3.
Predicting the outcome without fixing parameter values works in R, but the output seems completely random:
preds <- run.jags("model.txt",
data=list(x1=x1, x2=x2, x3=x3, m=m,
statealpha=rep(1,times=M), M=M, T=T, N=N), monitor=c("m_pred"),
n.chains=1, inits = NA, sample=1)
Compiling rjags model...
Calling the simulation using the rjags method...
Note: the model did not require adaptation
Burning in the model for 4000 iterations...
|**************************************************| 100%
Running the model for 1 iterations...
Simulation complete
Finished running the simulation
However, as soon as I try to fix parameters (i.e. use model estimates to predict outcome m, I get errors:
preds <- run.jags("model.txt",
data=list(x1=x1, x2=x2, x3=x3,
statealpha=rep(1,times=M), M=M, T=T, N=N, beta1=beta1), monitor=c("m"),
n.chains=1, inits = NA, sample=1)
Compiling rjags model...
Error: The following error occured when compiling and adapting the model using rjags:
Error in rjags::jags.model(model, data = dataenv, n.chains = length(runjags.object$end.state), :
RUNTIME ERROR:
Compilation error on line 39.
beta1[2,1] is a logical node and cannot be observed
beta1 in this case is a 2x2 matrix of coefficient estimates.
How is JAGS predicting m in the first example (no fixed parameters)? Is it just completely randomly choosing m?
How can I include earlier acquired model estimates to simulate new outcome values?
The model is:
model{
for (i in 1:N)
{
for (t in 1:T)
{
m[t,i] ~ dcat(ps[i,t,])
}
for (state in 1:M)
{
ps[i,1,state] <- probs1[state]
for (t in 2:T)
{
ps[i,t,state] <- probs[m[(t-1),i], state, i,t]
}
for (prev in 1:M){
for (t in 1:T) {
probs[prev,state,i,t] <- odds[prev,state,i,t]/totalodds[prev,i,t]
odds[prev,state,i,t] <- exp(alpha[prev,state,i] +
beta1[prev,state]*x1[t,i]
+ beta2[prev,state]*x2[t,i]
+ beta3[prev,state]*x3[t,i])
}}
alpha[state,state,i] <- 0
for (t in 1:T) {
totalodds[state,i,t] <- odds[state,1,i,t] + odds[state,2,i,t]
}
}
alpha[1,2,i] <- raneffs[i,1]
alpha[2,1,i] <- raneffs[i,2]
raneffs[i,1:2] ~ dmnorm(alpha.means[1:2],alpha.prec[1:2, 1:2])
}
for (state in 1:M)
{
beta1[state,state] <- 0
beta2[state,state] <- 0
beta3[state,state] <- 0
}
beta1[1,2] <- rcoeff[1]
beta1[2,1] <- rcoeff[2]
beta2[1,2] <- rcoeff[3]
beta2[2,1] <- rcoeff[4]
beta3[1,2] <- rcoeff[5]
beta3[2,1] <- rcoeff[6]
alpha.Sigma[1:2,1:2] <- inverse(alpha.prec[1:2,1:2])
probs1[1:M] ~ ddirich(statealpha[1:M])
for (par in 1:6)
{
alpha.means[par] ~ dt(T.constant.mu,T.constant.tau,T.constant.k)
rcoeff[par] ~ dt(T.mu, T.tau, T.k)
}
T.constant.mu <- 0
T.mu <- 0
T.constant.tau <- 1/T.constant.scale.squared
T.tau <- 1/T.scale.squared
T.constant.scale.squared <- T.constant.scale*T.constant.scale
T.scale.squared <- T.scale*T.scale
T.scale <- 2.5
T.constant.scale <- 10
T.constant.k <- 1
T.k <- 1
alpha.prec[1:2,1:2] ~ dwish(Om[1:2,1:2],2)
Om[1,1] <- 1
Om[1,2] <- 0
Om[2,1] <- 0
Om[2,2] <- 1
## Prediction
for (i in 1:N)
{
m_pred[1,i] <- m[1,i]
for (t in 2:T)
{
m_pred[t,i] ~ dcat(ps_pred[i,t,])
}
for (state in 1:M)
{
ps_pred[i,1,state] <- probs1[state]
for (t in 2:T)
{
ps_pred[i,t,state] <- probs_pred[m_pred[(t-1),i], state, i,t]
}
for (prev in 1:M)
{
for (t in 1:T)
{
probs_pred[prev,state,i,t] <- odds_pred[prev,state,i,t]/totalodds_pred[prev,i,t]
odds_pred[prev,state,i,t] <- exp(alpha[prev,state,i] +
beta1[prev,state]*x1[t,i]
+ beta2[prev,state]*x2[t,i]
+ beta3[prev,state]*x3[t,i])
}}
for (t in 1:T) {
totalodds_pred[state,i,t] <- odds_pred[state,1,i,t] + odds_pred[state,2,i,t]
}
}
}
TL;DR: I think you're just missing a likelihood.
Your model is complex, so perhaps I'm missing something, but as far as I can tell there is no likelihood. You are supplying the predictors x1, x2, and x3 as data, but you aren't giving any observed m. So in what sense can JAGS be "fitting" the model?
To answer your questions:
Yes, it appears that m is drawn as random from a categorical distribution conditioned on the rest of the model. Since there are no m supplied as data, none of the parameter distributions have cause for update, so your result for m is no different than you'd get if you just did random draws from all the priors and propagated them through the model in R or whatever.
Though it still wouldn't constitute fitting the model in any sense, you would be free to supply values for beta1 if they weren't already defined completely in the model. JAGS is complaining because currently beta1[i] = rcoeff[i] ~ dt(T.mu, T.tau, T.k), and the parameters to the T distribution are all fixed. If any of (T.mu, T.tau, T.k) were instead given priors (identifying them as random), then beta1 could be supplied as data and JAGS would treat rcoeff[i] ~ dt(T.mu, T.tau, T.k) as a likelihood. But in the model's current form, as far as JAGS is concerned if you supply beta1 as data, that's in conflict with the fixed definition already in the model.
I'm stretching here, but my guess is if you're using JAGS you have (or would like to) fit the model in JAGS too. It's a common pattern to include both an observed response and a desired predicted response in a jags model, e.g. something like this:
model {
b ~ dnorm(0, 1) # prior on b
for(i in 1:N) {
y[i] ~ dnorm(b * x[i], 1) # Likelihood of y | b (and fixed precision = 1 for the example)
}
for(i in 1:N_pred) {
pred_y[i] ~ dnorm(b * pred_x[i], 1) # Prediction
}
}
In this example model, x, y, and pred_x are supplied as data, the unknown parameter b is to be estimated, and we desire the posterior predictions pred_y at each value of pred_x. JAGS knows that the distribution in the first for loop is a likelihood, because y is supplied as data. Posterior samples of b will be constrained by this likelihood. The second for loop looks similar, but since pred_y is not supplied as data, it can do nothing to constrain b. Instead, JAGS knows to simply draw pred_y samples conditioned on b and the supplied pred_x. The values of pred_x are commonly defined to be the same as observed x, giving a predictive interval for each observed data point, or as a regular sequence of values along the x axis to generate a smooth predictive interval.
I am learning how to fit Bayesian multinomial logistic models in R. This is my first attempt at using JAGS via rjags. The code illustrates with a MWE what I am trying to do:
## simulate data
set.seed(123)
n=2000
rr<-rmultinom(n, 3, c(.1,.3,.2))
r2=as.numeric(rr==1)
r3=as.numeric(rr==2)
r4=as.numeric(rr==3)
abt=rbinom(n,1,.1);smk=rbinom(n,1,.3)
age=rnorm(n);bmi=rnorm(n)
## load programs
library("rjags")
## model
NMMmodel.string <- "
model{
for (i in 1:N){
## outcome levels 2, 3, and 4
r2[i] ~ dbern(pi2[i])
r3[i] ~ dbern(pi3[i])
r4[i] ~ dbern(pi4[i])
## linear predictors
logit(pi2[i]) <- g[1]+g[2]*age[i]+g[3]*abt[i]+g[4]*smk[i]
logit(pi3[i]) <- g[5]+g[6]*bmi[i]+g[7]*age[i]+g[8]*smk[i]
logit(pi4[i]) <- g[9]+g[10]*age[i]+g[11]*smk[i]+g[12]*bmi[i]
## probability that outcome is level 1
pi1[i] <- 1-pi2[i]-pi3[i]-pi4[i]
}
for (j in 1:12) {
g[j] ~ dnorm(0, 0.01)
}
}
"
NMMmodel.spec<-textConnection(NMMmodel.string)
## fit model w JAGS
jags <- jags.model(NMMmodel.spec,
data = list('r2'=r2,'r3'=r3,'r4'=r4,
'abt'=abt,'smk'=smk,
'age'=age,'bmi'=bmi,'N'=n),
n.chains=4,
n.adapt=100)
Here are two questions, in order of decreasing importance:
Question 1: I would like to put a constraint on the estimated parameters indexed by g[1] to g[12] such that pi1 lies between some arbitrary upper and lower bound: say, a=0.25 and b=0.75. One way is to use rejection sampling, where rjags will reject all samples that return pi1 less than a or greater b. How can I do this?
Question 2: What, exactly, is this program doing? For example, if this program implements a Gibbs sampler, is there a way to code it up without resorting to JAGS, or STAN, or BUGS? Something like the first set of code on this website?
I am using the R2WinBugs package. I would like to pass two parameter that are calculated previously in the R script to the model function
c0yy <- 0.1
syy <- 0.0001
#Model
model <- function(c0yy,syy){
#Likelihood
for(i in 1:n){
y[i] ~ dnorm(mu[i],cyy)
}
#Regression formula
for(i in 1:n){
mu[i] <- alpha + gamma * x[i]
}
#Priors for the regression parameters
alpha ~ dnorm(0,0.000001)
gamma ~ dnorm(0,0.000001)
#Priors for the precision parameter
cyy ~ dnorm(c0yy,syy)
#Monitored variables
beta <- gamma/(alpha-1)
}
filename <- file.path(tempdir(), "Olm.txt")
write.model(model, filename)
but I get this error
made use of undefined node c0yy
while if I substitute the values for c0yy and syy inside the model function it works.. Any help?
Thanks
The values you are tying to pass to the model are data. In BUGS (and R2WinBUGS) data is passed to the program as a separate entity from the model that you have defined. In order to include the data you can put them into a list, something like;
my.mcmc <- bugs(data = list(c0yy = 0.1, syy= 0.0001), params = "beta', model.file = "Olm.txt", n.iter=10000)
You will also need to drop the <- function(c0yy,syy) from your model script.