I have fitted following simple linear regression Bayesian model using rjags.
I was able to run the model by specifying all the predictors separately(like for a lm object). Now I want to learn how to specify the predictors by introducing them as a matrix instead of specifying them separately.
So I ran the following code, but it gave some errors.
I used tobbaco data set in rrr package to provide a reproducible example.
library(rrr)
require(dplyr)
library(rjags)
tobacco <- as_data_frame(tobacco)
N1 = length(tobacco$Y1.BurnRate)
x1 = model.matrix(Y1.BurnRate~X2.PercentChlorine+X3.PercentPotassium ,data = tobacco)
bayes_model_mul1=
"model {
for(i in 1:N1){
Y1.BurnRate[i]~dnorm(mu1[i],tau1)
for(j in 1:3){
mu1[i]=beta1[j]*x1[i,j]
}
}
for (l in 1:3) { beta1[l] ~dnorm(0, 0.001) }
tau1 ~ dgamma(.01,.01)
sigma_tau1 = 1/tau1
}"
model3 <- jags.model(textConnection(bayes_model_mul1),
data = list(Y1.BurnRate=tobacco$Y1.BurnRate, x1=x1, N1=N1),
n.chains=1)
After I run model3 , I got following error.
Error in jags.model(textConnection(bayes_model_mul1), data = list(Y1.BurnRate = tobacco$Y1.BurnRate, :
RUNTIME ERROR:
Compilation error on line 6.
Attempt to redefine node mu1[1]
Can anyone help me figure this out ?
Does this due to introducing predictors as a matrix ?
There are a few ways to do this, here are two:
Use matrix multiplication outside of the likelihood loop
m1 =
"model {
mu1 = x1 %*% beta1 # ---> this
for(i in 1:N1){
Y1.BurnRate[i] ~ dnorm(mu1[i], tau1)
}
for (l in 1:3) { beta1[l] ~ dnorm(0, 0.001) }
tau1 ~ dgamma(.01,.01)
sigma_tau1 = 1/tau1
}"
Use inprod to multiply the parameters with the design matrix
m2 =
"model {
for(i in 1:N1){
mu1[i] = inprod(beta1, x1[i,]) #----> this
Y1.BurnRate[i] ~ dnorm(mu1[i], tau1)
}
for (l in 1:3) { beta1[l] ~ dnorm(0, 0.001) }
tau1 ~ dgamma(.01,.01)
sigma_tau1 = 1/tau1
}"
You received an error with for(j in 1:3){ mu1[i] = beta1[j]* x1[i,j] } as every time you loop though the parameter index j you overwrite mu1[i]. It also doesn't sum up the individual terms. You may be able to index mu1 with j as well and then sum but untested ...
Related
I want to perform a mixed effect regression in rjags, with a random slope and intercept. I define the following toy dataset:
library(ggplot2)
library(data.table)
global_slope <- 1
global_int <- 1
Npoints_per_group <- 50
N_groups <- 10
pentes <- rnorm(N_groups,-1,.5)
centers_x <- seq(0,10,length = N_groups)
center_y <- global_slope*centers_x + global_int
group_spread <- 2
group_names <- sample(LETTERS,N_groups)
df <- lapply(1:N_groups,function(i){
x <- seq(centers_x[i]-group_spread/2,centers_x[i]+group_spread/2,length = Npoints_per_group)
y <- pentes[i]*(x- centers_x[i])+center_y[i]+rnorm(Npoints_per_group)
data.table(x = x,y = y,ID = group_names[i])
}) %>% rbindlist()
ggplot(df,aes(x,y,color = as.factor(ID)))+
geom_point()
This is a typical situation of Simpson paradox: an overall increasing trend when you have a decreasing trend within each group (given by the ID variable).
I define the following model:
library(rjags)
model_code_simpson <-
" model
{
# first level
for (i in 1:n) {
y[i] ~ dnorm(alpha[i] + beta[i] * x[i], tau)
alpha[i] = alpha[group[i]] # random intercept
beta[i] = beta[group[i]] # random slope
}
# second level
for(j in 1:J){
alpha[j] ~ dnorm(mu.alpha, tau.alpha)
beta[j] ~ dnorm(mu.beta, tau.beta)
}
# Priors
mu.alpha ~ dnorm(0,0.001)
mu.beta ~ dnorm(0,0.001)
sigma ~ dunif(0,10)
sigma.alpha ~ dunif(0,10)
sigma.beta ~ dunif(0,10)
# Derived quantities
tau <- pow(sigma,-2)
tau.alpha <- pow(sigma.alpha,-2)
tau.beta <- pow(sigma.beta,-2)
}
"
# Choose the parameters to watch
model_parameters <- c("mu.alpha","tau.alpha","tau.beta","tau")
# define numeric grouping variable
df[,ID2 := .GRP,by = ID]
model_data <- list(n = nrow(df),
y = df$y,
x = df$x,
group = df$ID2,
J = df[,uniqueN(ID)])
model <- jags.model(textConnection(model_code_simpson),
data = model_data,
n.chains = 2)
I get the following error:
Compiling model graph
Resolving undeclared variables
Allocating nodes
Deleting model
Error in jags.model(textConnection(model_code_simpson), data = model_data, :
RUNTIME ERROR:
Compilation error on line 8.
Attempt to redefine node beta[1]
I do not understand what is happening, and related questions did not help me much.
You defined beta twice. First, beta is a vector of length n when you are looping through the data. Second, beta is a vector of length J when you are creating the random effects. This "redefining" is causing this issue, but it is an easy fix. You just need to remove that first instance of beta in your model and it will compile (i.e., just move your nested indexing inside of dnorm() and you are good to go).
model_code_simpson <-
" model
{
# first level
for (i in 1:n) {
y[i] ~ dnorm(
alpha[group[i]] + beta[group[i]] * x[i],
tau
)
}
# second level
for(j in 1:J){
alpha[j] ~ dnorm(mu.alpha, tau.alpha)
beta[j] ~ dnorm(mu.beta, tau.beta)
}
# Priors
mu.alpha ~ dnorm(0,0.001)
mu.beta ~ dnorm(0,0.001)
sigma ~ dunif(0,10)
sigma.alpha ~ dunif(0,10)
sigma.beta ~ dunif(0,10)
# Derived quantities
tau <- pow(sigma,-2)
tau.alpha <- pow(sigma.alpha,-2)
tau.beta <- pow(sigma.beta,-2)
}
"
I am fitting a multivariate model in JAGS using the dirlichet distribution. I have a matrix y of 3 species proportional abundances.
#generate 3 columns of species proprotional abundance data
y <- matrix(ncol = 3, nrow = 100)
y[,] <- abs(rnorm(length(y)))
for(i in 1:nrow(y)){
y[i,] <- y[i,] / sum(y[i,])
}
I have a matrix x of predictor values, the first of which is an intercept.
#generate 2 columns of predictors and an intercept
x <- matrix(ncol = 2, nrow = 100)
x[,] <- rnorm(length(x), mean = 20, sd = 4)
x <- cbind(rep(1,nrow(x)),x)
I specify a multivariate jags model, jags.model:
jags.model = "
model {
#setup parameter priors for each species * predictor combination.
for(j in 1:N.spp){
for(k in 1:N.preds){
m[k,j] ~ dgamma(1.0E-3, 1.0E-3)
}
}
#go ahead and fit means of species abundances as a linear combination of predictor and parameters.
for(i in 1:N){
for(j in 1:N.spp){
log(a0[i,j]) <- m[,j] * x[i,]
}
y[i,1:N.spp] ~ ddirch(a0[i,1:N.spp])
}
} #close model loop.
"
I setup the JAGS data object, jags.data:
jags.data <- list(y = as.matrix(y), x = as.matrix(x),
N.spp = ncol(y), N.preds = ncol(x), N = nrow(y))
I fit the JAGS model using the runjags package in R.
jags.out <- runjags::run.jags(jags.model,
data=jags.data,
adapt = 100,
burnin = 200,
sample = 400,
n.chains=3,
monitor=c('m'))
I get the following error:
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:
Invalid vector argument to exp
What am I doing wrong here? For reference, spelling out each parameter by predictor combination still fits fine:
jags.model = "
model {
#setup parameter priors for each species * predictor combination.
for(j in 1:N.spp){
for(k in 1:N.preds){
m[k,j] ~ dgamma(1.0E-3, 1.0E-3)
}
}
#go ahead and fit means of species abundances as a linear combination of predictor and parameters.
for(i in 1:N){
for(j in 1:N.spp){
log(a0[i,j]) <- m[1,j] * x[i,1] + m[2,j] * x[i,2] + m[3,j] * x[i,3]
}
y[i,1:N.spp] ~ ddirch(a0[i,1:N.spp])
}
} #close model loop.
"
The solution to this problem is to take a dot product, or an inner product in JAGS. Change the line:
log(a0[i,j]) <- m[,j] * x[i,]
to:
log(a0[i,j]) <- inprod(m[,j] , x[i,])
And everything should work fine. Full model below.
jags.model = "
model {
#setup parameter priors for each species * predictor combination.
for(j in 1:N.spp){
for(k in 1:N.preds){
m[k,j] ~ dgamma(1.0E-3, 1.0E-3)
}
}
#go ahead and fit means of species abundances as a linear combination of predictor and parameters.
for(i in 1:N){
for(j in 1:N.spp){
log(a0[i,j]) <- inprod(m[,j] , x[i,])
}
y[i,1:N.spp] ~ ddirch(a0[i,1:N.spp])
}
} #close model loop.
"
I am puzzled by a simple question in R JAGS. I have for example, 10 parameters: d[1], d[2], ..., d[10]. It is intuitive from the data that they should be increasing. So I want to put a constraint on them.
Here is what I tried to do but it give error messages saying "Node inconsistent with parents":
model{
...
for (j in 1:10){
d.star[j]~dnorm(0,0.0001)
}
d=sort(d.star)
}
Then I tried this:
d[1]~dnorm(0,0.0001)
for (j in 2:10){
d[j]~dnorm(0,0.0001)I(d[j-1],)
}
This worked, but I don't know if this is the correct way to do it. Could you share your thoughts?
Thanks!
If you are ever uncertain about something like this, it is best to just simulate some data to determine if the model structure you suggest works (spoiler alert: it does).
Here is the model that I used:
cat('model{
d[1] ~ dnorm(0, 0.0001) # intercept
d[2] ~ dnorm(0, 0.0001)
for(j in 3:11){
d[j] ~ dnorm(0, 0.0001) I(d[j-1],)
}
for(i in 1:200){
y[i] ~ dnorm(mu[i], tau)
mu[i] <- inprod(d, x[i,])
}
tau ~ dgamma(0.01,0.01)
}',
file = "model_example.R")```
And here are the data I simulated to use with this model.
library(run.jags)
library(mcmcplots)
# intercept with sorted betas
set.seed(161)
betas <- c(1,sort(runif(10, -5,5)))
# make covariates, 1 for intercept
x <- cbind(1,matrix(rnorm(2000), nrow = 200, ncol = 10))
# deterministic part of model
y_det <- x %*% betas
# add noise
y <- rnorm(length(y_det), y_det, 1)
data_list <- list(y = as.numeric(y), x = x)
# fit the model
mout <- run.jags('model_example.R',monitor = c("d", "tau"), data = data_list)
Following this, we can plot out the estimates and overlay the true parameter values
caterplot(mout, "d", reorder = FALSE)
points(rev(c(1:11)) ~ betas, pch = 18,cex = 0.9)
The black points are the true parameter values, the blue points and lines are the estimates. Looks like this set up does fine so long as there are enough data to estimate all of those parameters.
It looks like there is an syntax error in the first implementation. Just try:
model{
...
for (j in 1:10){
d.star[j]~dnorm(0,0.0001)
}
d[1:10] <- sort(d.star) # notice d is indexed.
}
and compare the results with those of the second implementation. According to the documentation, these are both correct, but it is advised to use the function sort.
I am a student studying bayesian statistics and have just begun to use JAGS using a intro script written by my lecturer, with us (the students) having to only enter the data and the number of iterations. The following is the script with my data added into it:
setwd("C:\\Users\\JohnSmith\\Downloads")
rawdata = read.table("bwt.txt",header=TRUE)
Birthweight = rawdata$Birthweight
Age = rawdata$Age
model = "model
{
beta0 ~ dnorm(0, 1/1000^2)
beta1 ~ dnorm(0, 1/1000^2)
log_sigma ~ dunif(-10, 10)
sigma <- exp(log_sigma)
for(i in 1:N)
{
mu[i] <- beta0 + beta1 * Age[i]
Birthweight[i] ~ dnorm(mu[i], 1/sigma^2)
}
}
"
data = list(x=Birthweight, y=Age, N=24)
# Variables to monitor
variable_names = c('beta0','beta1')
# How many burn-in steps?
burn_in = 1000
# How many proper steps?
steps = 100000
# Thinning?
thin = 10
# Random number seed
seed = 2693795
# NO NEED TO EDIT PAST HERE!!!
# Just run it all and use the results list.
library('rjags')
# Write model out to file
fileConn=file("model.temp")
writeLines(model, fileConn)
close(fileConn)
if(all(is.na(data)))
{
m = jags.model(file="model.temp", inits=list(.RNG.seed=seed, .RNG.name="base::Mersenne-Twister"))
} else
{
m = jags.model(file="model.temp", data=data, inits=list(.RNG.seed=seed, .RNG.name="base::Mersenne-Twister"))
}
update(m, burn_in)
draw = jags.samples(m, steps, thin=thin, variable.names = variable_names)
# Convert to a list
make_list <- function(draw)
{
results = list()
for(name in names(draw))
{
# Extract "chain 1"
results[[name]] = as.array(draw[[name]][,,1])
# Transpose 2D arrays
if(length(dim(results[[name]])) == 2)
results[[name]] = t(results[[name]])
}
return(results)
}
results = make_list(draw)
However, when I run the following code I get the following error message:
Error in jags.model(file = "model.temp", data = data, inits = list(.RNG.seed = seed, :
RUNTIME ERROR:
Compilation error on line 11.
Unknown parameter Age
In addition: Warning messages:
1: In jags.model(file = "model.temp", data = data, inits = list(.RNG.seed = seed, :
Unused variable "x" in data
2: In jags.model(file = "model.temp", data = data, inits = list(.RNG.seed = seed, :
Unused variable "y" in data
But as far as I can see, line 11 is blank, which leaves me stumped as to where the error is coming from. If anyone can give me some tips as to solve this, it will be greatly appreciated.
The names of the elements of your list of data (data) should match the names of the variables in your model.
You have:
data = list(x=Birthweight, y=Age, N=24)
so JAGS is looking for variables called x and y in your model. However, in your model, you have:
mu[i] <- beta0 + beta1 * Age[i]
Birthweight[i] ~ dnorm(mu[i], 1/sigma^2)
That is, your variables are called Age and Birthweight.
So, either change your list to:
data <- list(Birthweight=Birthweight, Age=Age, N=24)
or change your model to:
mu[i] <- beta0 + beta1 * y[i]
x[i] ~ dnorm(mu[i], 1/sigma^2)
Had you done readLines('model.temp') (or opened model.temp in a text editor), you would have seen that line 11 of that file refers to the line that contains mu[i] <- beta0 + beta1 * Age[i], which is the first error that JAGS encountered due to the reference to Age, for which neither data nor a prior was provided.
Using JAGS I am trying to estimate a model including a unit-specific time trend.
However, the problem is that I don't know how to model this and so far I have been unable to find a solution.
As an example, consider we have the following data:
rain<-rnorm(200) # Explanatory variable
n1<-rnorm(200) # Some noise
gdp<-rain+n1 # Outcome variable
ccode<-rep(1:10,20) # Unit codes
year<-rep(1:20,10) # Years
Using normal linear regression, we would estimate the model as:
m1<-lm(gdp~rain+factor(ccode)*year)
Where factor(ccode)*year is the unit-specific time trend. Now I want to estimate the model using JAGS. So I create parameters for the indexing:
N<-200
J<-max(ccode)
T<-max(year)
And estimate the model,
library(R2jags)
library(rjags)
set.seed(42); runif(1)
dat<-list(gdp=gdp,
rain=rain,
ccode=ccode,
year=year,
N=N,J=J,T=T)
parameters<-c("b1","b0")
model.file <- "~/model.txt"
system.time(m1<-jags(data=dat,inits=NULL,parameters.to.save=parameters,
model.file=model.file,
n.chains=4,n.iter=500,n.burnin=125,n.thin=2))
with the following model file, and this is where the error is at the moment:
# Simple model
model {
# For N observations
for(i in 1:N) {
gdp[i] ~ dnorm(yhat[i], tau)
yhat[i] <- b1*rain[i] + b0[ccode[i]*year[i]]
}
for(t in 1:T) {
for(j in 1:J) {
b0[t,j] ~ dnorm(0, .01)
}
}
# Priors
b1 ~ dnorm(0, .01)
# Hyperpriors
tau <- pow(sd, -2)
sd ~ dunif(0,20)
}
I am fairly sure that the way in which I define b0 and the indexing is incorrect given the error I get when using the code: Compilation error on line 7. Dimension mismatch taking subset of b0.
However, I don't know how to solve this so I wondered whether someone here has suggestions about this?
Your lm example can also be written:
m1 <- lm(gdp ~ -1 + rain + factor(ccode) + factor(ccode):year)
The equivalent JAGS model would be:
M <- function() {
for(i in 1:N) {
gdp[i] ~ dnorm(yhat[i], sd^-2)
yhat[i] <- b0[ccode[i]] + b1*rain[i] + b2[ccode[i]]*year[i]
}
b1 ~ dnorm(0, 0.001)
for (j in 1:J) {
b0[j] ~ dnorm(0, 0.001)
b2[j] ~ dnorm(0, 0.001)
}
sd ~ dunif(0, 100)
}
parameters<-c('b0', 'b1', 'b2')
mj <- jags(dat, NULL, parameters, M, 3)
Comparing coefficients:
par(mfrow=c(1, 2), mar=c(5, 5, 1, 1))
plot(mj$BUGSoutput$summary[grep('^b0', row.names(mj$BUGSoutput$summary)), '50%'],
coef(m1)[grep('^factor\\(ccode\\)\\d+$', names(coef(m1)))],
xlab='JAGS estimate', ylab='lm estimate', pch=20, las=1,
main='b0')
abline(0, 1)
plot(mj$BUGSoutput$summary[grep('^b2', row.names(mj$BUGSoutput$summary)), '50%'],
coef(m1)[grep('^factor\\(ccode\\)\\d+:', names(coef(m1)))],
xlab='JAGS estimate', ylab='lm estimate', pch=20, las=1,
main='b2')
abline(0, 1)