I gave initial values for all the stochastic nodes, but WinBUGS still gives me the message that
this initial value does not correspond to a stochastic nodes
What node I am missing here?
#Model
model
{
for( i in 1 :N) {
Y[i] ~ dnorm(mu[i], tau)
Z[i] ~ dnorm(mu[i], tau)
mu[i] <- theta[1] + theta[2]* exp(-exp(-theta[3]*(x[i]-theta[4])))
}
theta[1]<-1.8
theta[2] ~ dnorm(0,0.01)
theta[3] ~ dnorm(0,0.01)
theta[4] ~ dnorm(0,0.01)
tau ~ dgamma(0.001, 0.001)
sigma <- 1 / sqrt(tau)
}
#Data
list(x=c(1971,1976,1981,1986,1991,1996,2001,2006,2011,2016,2021,2026,2031,2036,2041,2046,2051,2056,2061),
Y=c(5.2,4.7,4.5,4.2,3.6,3.4,3.1,2.8,2.4,2.3,NA,NA,NA,NA,NA,NA,NA,NA,NA), N=19)
#Initial values
list(theta=c(0,0,0), tau=1)
Related
I have a question about this model in JAGS, I want to make a bayesian linear regression with a y[i] that follows not a normal distribution but a gamma.
The model is this:
"model {
Priors:
a ~ dnorm(0, 0.0001) # mean, precision = N(0, 10^4)
b ~ dnorm(0, 0.0001)
shape ~ dunif(0, 100)
# Likelihood data model:
for (i in 1:N) {
linear_predictor[i] <- a + b * x[i]
# dgamma(shape, rate) in JAGS:
y[i] ~ dgamma(shape, shape / exp(linear_predictor[i]))
}
}
"
What should I change to make this code usable for a multiple linear regression with this data?
dataListGamma = list(
x = x,
y = y,
Nx = dim(x)[2],
Ntotal = dim(x)[1]
)
i'm receiving this error:
Error in node (shape/(exp(linear_predictor[1331])))
how can this be possible? i cant understand
if i run it again it changes the value that makes the problem
Something like this (making b a vector with identical, independent priors for each element, and constructing the linear predictor with a for loop) should work:
model {
# Priors:
a ~ dnorm(0, 0.0001) # mean, precision = N(0, 10^4)
for (j in 1:Nx)
b[i] ~ dnorm(0, 0.0001)
}
shape ~ dunif(0, 100)
# Likelihood data model:
linear_predictor[i] <- a
for (i in 1:Ntotal) {
for (j in 1:Nx) {
linear_predictor[i] <- linear_predictor[i] + b[j]*N[i][j]
}
y[i] ~ dgamma(shape, shape / exp(linear_predictor[i]))
}
}
I use my JAGS model, and then use that model to make predictions, propogating parameter uncertainty into those predictions. I currently have a zero-inflated Poisson (ZIP) model that runs fine making a single prediction. It looks like this:
j.model ="
model{
for (i in 1:N){
#this fits the blended model to your data.
y[i] ~ dpois(m[i]*t[i])
#This blends the poisson and zero inflation models
m[i] <- mu[i]*x[i] + 0.00001
#this is the bernoulli outcome of the zero inflation
x[i] ~ dbern(pro[i])
#this logit transforms the theta model for 0-1 probability of zero inflation
logit(pro[i]) <- theta[i]
#mu[i] is predictors for poisson model- log link function.
log(mu[i]) <- int.p + x1[i]*b1.p + x2[i]*b2.p + x3[i]*b3.p + x4[i]*b4.p + x5[i]*b5.p
#theta[i] is predictors for zero inflation
theta[i] <- int.z + x1[i]*b1.z + x2[i]*b2.z + x3[i]*b3.z + x4[i]*b4.z + x5[i]*b5.z
}
#predictions
#This gets the range of pred.m blended model values, before they get sent through the poisson distribution, and corrected for time.
#x5 prediction
for (i in 1:N.pred){
x5.pred[i] <- pred5.mu[i]*pred5.x[i] + 0.00001
pred5.x[i] ~ dbern(pred5.pro[i])
logit(pred5.pro[i]) <- pred5.theta[i]
log(pred5.mu[i]) <- int.p + x1.m*b1.p + x2.m*b2.p + x3.m*b3.p + x4.m*b4.p + x5.r[i]*b5.p
pred5.theta[i] <- int.z + x1.m*b1.z + x2.m*b2.z + x3.m*b3.z + x4.m*b4.z + x5.r[i]*b5.z
}
#priors
b1.p ~ dnorm(0, .0001)
b2.p ~ dnorm(0, .0001)
b3.p ~ dnorm(0, .0001)
b4.p ~ dnorm(0, .0001)
b5.p ~ dnorm(0, .0001)
b1.z ~ dnorm(0, .0001)
b2.z ~ dnorm(0, .0001)
b3.z ~ dnorm(0, .0001)
b4.z ~ dnorm(0, .0001)
b5.z ~ dnorm(0, .0001)
int.p ~ dnorm(0, .0001)
int.z ~ dnorm(0, .0001)
}
"
However, if I insert a second prediction loop into this model for predictor x4 I get an error. The second prediction loops looks like this, and is inserted between the model loop and the x5 prediction loop.
#x4 prediction
for (i in 1:N.pred){
map.pred[i] <- pred4.mu[i]*pred4.x[i] + 0.00001
pred4.x[i] ~ dbern(pred4.pro[i])
logit(pred4.pro[i]) <- pred4.theta[i]
log(pred4.mu[i]) <- int.p + x1.m*b1.p + x2.m*b2.p + x3.m*b3.p + x4.r[i]*b4.p + x5.m*b5.p
pred4.theta[i] <- int.z + x1.m*b1.z + x2.m*b2.z + x3.m*b3.z + x4.r[i]*b4.z + x5.m*b5.z
}
It returns this error:
RUNTIME ERROR:
Compilation error on line 20.
Unable to resolve node pred4.mu[1]
This may be due to an undefined ancestor node or a directed cycle in the graph
This surprises me, as this prediction loop is formatted exactly the same as the x5 prediction loop, so I know everything should be defined, as it worked great before. Is there something about having two of these that is causing the problem?
I am attempting to use knitr trough Rstudio to document a model that save a text string to a *txt file.
When doing so, i get this R markdown error message:
*Error in parse(text = x, srcfile = src) : <text>:2:24: unexpected
INCOMPLETE_STRING 14: var.m <- 1/tau.m # between-trial variance 15:
Calls: <Anonymous> ... <Anonymous> -> parse_all -> parse_all.character -> parse*
Anyone know to fix this?
This string works fine:
Modelstring.baseline = " Text goes here "
This string works fine:
Modelstring.baseline = "
# Binomial likelihood, logit link, MTC
# Fixed effect model
#CV mortality
model{ # *** PROGRAM STARTS
for(i in 1:ns){ # LOOP THROUGH STUDIES
mu[i] ~ dnorm(0,.0001) # vague priors for all trial baselines
for (k in 1:na[i]) { # LOOP THROUGH ARMS
r[i,k] ~ dbin(p[i,k],n[i,k]) # binomial likelihood
logit(p[i,k]) <- mu[i] + d[t[i,k]]-d[t[i,1]] # model for linear predictor
rhat[i,k] <- p[i,k] * n[i,k] # expected value of the numerators
dev[i,k] <- 2 * (r[i,k] * (log(r[i,k])-log(rhat[i,k])) # Deviance contribution
+ (n[i,k]-r[i,k]) * (log(n[i,k]-r[i,k]) - log(n[i,k]-rhat[i,k])))
}
resdev[i] <- sum(dev[i,1:na[i]]) # summed residual deviance contribution for this trial
}
totresdev <- sum(resdev[]) # Total Residual Deviance
d[1]<- 0 # treatment effect is zero for reference treatment
for (k in 2:nt) { d[k] ~ dnorm(0,.0001) } # vague priors for treatment effects
"
Whiles this string generate a parser error:
Modelstring.baseline = "
model{ # *** PROGRAM STARTS
for (i in 1:ns)
{ # LOOP THROUGH STUDIES
r[i] ~ dbin(p[i],n[i]) # Likelihood
logit(p[i]) <- mu[i] # Log-odds of response
mu[i] ~ dnorm(m,tau.m) # Random effects model
}
mu.new ~ dnorm(m,tau.m) # predictive dist. (log-odds)
m ~ dnorm(0,.0001) # vague prior for mean
var.m <- 1/tau.m # between-trial variance
#---Non-informative prior
#tau.m <- pow(sd.m,-2)
#sd.m ~ dunif(0,5)
#---Vaguely informative prior
#tau.m ~ dgamma(0.001,.001)
#sd.m ~ pow(tau.m,-0.5)
#---Informative prior R.M Turner et al LN(-3.95, 1.79)
tau.m <- 1/tausq
tausq ~ dlnorm(-3.95, 0.31) #0.31 = 1/(1.79*1.79)
}
"
I've read the JAGS manual but did not find a way to assign the same prior distribution to multiple parameters in a JAGS / R2JAGS model.
For example, currently I have to repeat a lot of code like this:
reg.model <- function() {
# Model structure
for(i in 1:N){
Y[i] ~ dnorm(mu[i], phi)
mu[i] <- beta0 + beta1*x1[i] + beta2*x2[i]
}
sigma2 <- 1 / phi
# Priors (Lots of re-typing here for beta0, beta1, beta2)
phi ~ dgamma(1,1)
beta0 ~ dnorm(0, 0.01*phi)
beta1 ~ dnorm(0, 0.01*phi)
beta2 ~ dnorm(0, 0.01*phi)
}
How to DRY this code?
You can do this if you pass your independent variables as a matrix, put your coefficients into a vector, and use matrix multiplication (with inprod or %*%) to calculate your linear predictor.
For example:
M <- function() {
for (i in 1:n) {
y[i] ~ dnorm(mu[i], sd^-2)
mu[i] <- X[i, ] %*% beta
}
sd ~ dunif(0, 100)
for (j in 1:J) {
beta[j] ~ dnorm(0, 0.0001)
}
}
We generate some dummy data, below:
set.seed(1)
n <- 1000
J <- 3
X <- cbind(1, matrix(runif(n * J), ncol=J))
head(X)
# [,1] [,2] [,3] [,4]
# [1,] 1 0.2655087 0.53080879 0.8718050
# [2,] 1 0.3721239 0.68486090 0.9671970
# [3,] 1 0.5728534 0.38328339 0.8669163
# [4,] 1 0.9082078 0.95498800 0.4377153
# [5,] 1 0.2016819 0.11835658 0.1919378
# [6,] 1 0.8983897 0.03910006 0.0822944
b <- rnorm(J + 1, 0, 10)
sigma <- runif(1)
y <- c(X %*% b) + rnorm(n, 0, sigma)
And fit the model:
library(R2jags)
out <- jags(list(y=y, X=X, n=n, J=ncol(X)), NULL, c('beta', 'sd'), M)
Now compare the estimated coefficients and standard deviation to their true values:
out$BUGSoutput$summary[, '50%']
# beta[1] beta[2] beta[3] beta[4] deviance sd
# 8.5783315 -9.3849277 8.9632598 -9.4242272 2196.1535645 0.7264754
b # True betas
# [1] 8.500435 -9.253130 8.935812 -9.410097
sigma # True sd
# [1] 0.70504
I'm trying to implement a Bayesian ANCOVA that takes account of heteroscedasticity in R using JAGS. However, despite going through several tutorials of Bayesian simple regression and ANOVA, I can't understand how to prepare the file for JAGS. Here is my code so far:
y1 = rexp(57, rate=0.8) # dependent variable
x1 = hist(rbeta(57, 6, 2)) # continuous factor
x2 = rep(c(1, 2), 57/2) # categorical factor
groups = 2
n = 57
# list of variables
lddados <- list(g=groups, n=length(x), y=y, x1=x1, x2=x2)
sink('reglin.txt') # nome do arquivo aqui
cat('
# model
{
for(i in 1:n){
mu[i] = a0 + a[i]
y[i] = a0 + x1*a[ x2[i] ] + ε[i]
}
priors
y ~ dgamma(0.001,0.01)
for(i in 1:n){
inter[i] ~ dgamma(0.001,0.001)
coef[i] ~ dnorm(0.0,1.0E-
likelihood
got stuck...
}
}#------fim do modelo
')
sink()
Im currently trying out ANCOVA using rjags myself...
From my understanding, I would test this (untested);
require(rjags)
require(coda)
model_string <- "
model {
for ( i in 1:n ){
mu[i] <- a0 + a[x2[i]] + a3 * x1[i] # linear predictor
y[i] ~ dnorm(mu[i], prec) # y is norm. dist.
}
# priors
a0 ~ dnorm(0, 1.0E-6) # intercept
a[1] ~ dnorm(0, 1.0E-6) # effect of x1 at x2 level 1
a[2] ~ dnorm(0, 1.0E-6) # effect of x1 at x2 level 2
a3 ~ dnorm(0, 1.0E-6) # regression coefficient for x1 (covariate)
prec ~ dgamma(0.001, 0.001) # precision (inverse of variance)
}
"
# initial values for the mcmc
inits_list <- list(a=0, b=c(0,0), prec=100)
# model, initial values and data in right format
jags_model <- jags.model(textConnection(model_string), data=data, inits=inits_list, n.adapt = 500, n.chains = 3, quiet = T)
# burn-in
update(jags_model, 10000)
# run the mcmc chains using the coda package
mcmc_samples <- coda.samples(jags_model, c("mu", "a", "a1", "a2", "prec"), n.iter = 100000)
Tell me if it works...
Recommended books; McCarthy M. Bayesian Methods for Ecology and Kruschke JK. Doing Bayesian Data Analysis