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 trying to obtain a posterior predictive distribution for specified values of x from a simple linear regression in Jags. I could get the regression itself to work by adapting this example (from https://biometry.github.io/APES//LectureNotes/StatsCafe/Linear_models_jags.html) to my own data. I have supplied a smal chunk of this data here so that the code works here also.
library(rjags)
library(R2jags)
#create data
dw=c(-15.2,-13.0,-10.0,-9.8,-8.5,-8.5,-7.7,-7.5,-7.2,-6.1,-6.1,-6.1,-5.5,-5.0,-5.0,-5.0,-4.5,-4.0,-2.0,-1.0,1.3)
phos=c(11.8,12.9,15.0,14.4,17.3,16.1,20.8,16.6,16.2,18.2,18.8,19.2,15.6,17.0,18.9,22.1,18.9,22.8,21.6,20.5,21.1)
#convert to list
jagsdwphos=list(dw=dw,phos=phos,N=length(phos))
#write model function for linear regression
lm1_jags <- function(){
# Likelihood:
for (i in 1:N){
phos[i] ~ dnorm(mu[i], tau) # tau is precision (1 / variance)
mu[i] <- intercept + slope * dw[i]
}
# Priors:
intercept ~ dnorm(0, 0.01)
slope ~ dnorm(0, 0.01)
sigma ~ dunif(0, 100) # standard deviation
tau <- 1 / (sigma * sigma)
}
#specifiy paramters of MCMC sampler, choose posteriors to be reported and run the jags model
#set initial values for MCMC
init_values <- function(){
list(intercept = rnorm(1), slope = rnorm(1), sigma = runif(1))
}
#choose paramters to report on
params <- c("intercept", "slope", "sigma")
#run model in jags
lm_dwphos <- jags(data = jagsdwphos, inits = init_values, parameters.to.save = params, model.file = lm1_jags,
n.chains = 3, n.iter = 12000, n.burnin = 2000, n.thin = 10, DIC = F)
In addition to this regression, I would like to have an output of the posterior predictive distributions of particular phos values, but I cannot get it to work with this simple example I have written. I found a tutorial here https://doingbayesiandataanalysis.blogspot.com/2015/10/posterior-predicted-distribution-for.html and tried to implement it like this:
#create data
dw=c(-15.2,-13.0,-10.0,-9.8,-8.5,-8.5,-7.7,-7.5,-7.2,-6.1,-6.1,-6.1,-5.5,-5.0,-5.0,-5.0,-4.5,-4.0,-2.0,-1.0,1.3)
phos=c(11.8,12.9,15.0,14.4,17.3,16.1,20.8,16.6,16.2,18.2,18.8,19.2,15.6,17.0,18.9,22.1,18.9,22.8,21.6,20.5,21.1)
#specifiy phos values to use for posterior predictive distribution
phosprobe=c(14,18,22)
#convert to list
jagsdwphos=list(dw=dw,phos=phos,N=length(phos),xP=phosprobe)
#write model function for linear regression
lm1_jags <- function(){
# Likelihood:
for (i in 1:N){
phos[i] ~ dnorm(mu[i], tau) # tau is precision (1 / variance)
mu[i] <- intercept + slope * dw[i]
}
# Priors:
intercept ~ dnorm(0, 0.01) # intercept
slope ~ dnorm(0, 0.01) # slope
sigma ~ dunif(0, 100) # standard deviation
tau <- 1 / (sigma * sigma) # sigma^2 doesn't work in JAGS
nu <- nuMinusOne+1
nuMinusOne ~ dexp(1/29.0)
#prediction
for(i in 1:3){
yP ~ dt(intercept+slope*xP[i],tau,nu)
}
}
#specifiy paramters of MCMC sampler, choose posteriors to be reported and run the jags model
#set initial values for MCMC
init_values <- function(){
list(intercept = rnorm(1), slope = rnorm(1), sigma = runif(1))
}
#choose paramters to report on
params <- c("intercept", "slope", "sigma","xP","yP")
#run model in jags
lm_dwphos <- jags(data = jagsdwphos, inits = init_values, parameters.to.save = params, model.file = lm1_jags,
n.chains = 3, n.iter = 12000, n.burnin = 2000, n.thin = 10, DIC = F)
But I get the following error message:
Error in jags.model(model.file, data = data, inits = init.values, n.chains = n.chains, : RUNTIME ERROR: Compilation error on line 14. Attempt to redefine node yP[1]
I confess I don't quite understand exactly how the prediction was implemented in that example I used and could not find an explanation on what exactly nu is or where those numbers come from. So I presume that is where I made some mistake adapting to my example, but it was the only tutorial in Jags that I could find that gives the whole distribution of y values for the probed x instead of just the mean.
I would appreciate any help or explanation.
Thanks!
This error occurs because you are not indexing yP. You have written this loop like this:
#prediction
for(i in 1:3){
yP ~ dt(intercept+slope*xP[i],tau,nu)
}
As i moves from 1 to 3 the element yP is being written over. You need to index it like you have done with xP.
#prediction
for(i in 1:3){
yP[i] ~ dt(intercept+slope*xP[i],tau,nu)
}
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.
How can I do difference in means (ttest) for a multivariate using R and WinBUGS14
I have a multivariate outcome y and the categorical variable x. I am able to get the means of the MCMC sampled values from the multivariate using the code below, but how can I test for the difference in means by variable x?
Here is the R code
library(R2WinBUGS)
library(MASS) # need to mvrnorm
library(MCMCpack) # need for rwish
# Generate synthetic data
N <- 500
#we use this to simulate the data
S <- matrix(c(1,.2,.2,5),nrow=2)
#Produces one or more samples from the specified multivariate normal distribution.
#produces 2 variables with the given distribution
y <- mvrnorm(n=N,mu=c(1,3),Sigma=S)
x <- rbinom(500, 1, 0.5)
# Set up for WinBUGS
#set up of the mu0 values
mu0 <- as.vector(c(0,0))
#covariance matrices
# the precisions
S2 <- matrix(c(1,0,0,1),nrow=2)/1000 #precision for unkown mu
# precison matrix to be passes to the wishart distribution for the tau
S3 <- matrix(c(1,0,0,1),nrow=2)/10000
#the data for the winbug code
data <- list("y","N","S2","S3","mu0")
inits <- function(){
list( mu=mvrnorm(1,mu0,matrix(c(10,0,0,10),nrow=2) ),
tau <- rwish(3,matrix(c(.02,0,0,.04),nrow=2)) )
}
# Run WinBUGS
bug_file <- paste0(getwd(), "/codes/mult_normal.bug")
multi_norm.sim <- bugs(data,inits,model.file=bug_file,
parameters=c("mu","tau"),n.chains = 2,n.iter=4010,n.burnin=10,n.thin=1,
bugs.directory="../WinBUGS14/",codaPkg=F)
print(multi_norm.sim,digits=3)
and this is the WinBUGS14 code called mult_normal.bug
model{
for(i in 1:N)
{
y[i,1:2] ~ dmnorm(mu[],tau[,])
}
mu[1:2] ~ dmnorm(mu0[],S2[,])
#parameters of a wishart
tau[1:2,1:2] ~ dwish(S3[,],3)
}
2 Steps:
Load a function to run the t.test using sample statistics instead of doing it directly.
t.test2 <- function(m1,m2,s1,s2,n1,n2,m0=0,equal.variance=FALSE)
{
if( equal.variance==FALSE )
{
se <- sqrt( (s1^2/n1) + (s2^2/n2) )
# welch-satterthwaite df
df <- ( (s1^2/n1 + s2^2/n2)^2 )/( (s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1) )
} else
{
# pooled standard deviation, scaled by the sample sizes
se <- sqrt( (1/n1 + 1/n2) * ((n1-1)*s1^2 + (n2-1)*s2^2)/(n1+n2-2) )
df <- n1+n2-2
}
t <- (m1-m2-m0)/se
dat <- c(m1-m2, se, t, 2*pt(-abs(t),df))
names(dat) <- c("Difference of means", "Std Error", "t", "p-value")
return(dat)
}
Parse out the mean and standard deviation of the things we want to test against x, then pass them to the function.
mu1 <- as.data.frame(multi_norm.sim$mean)$mu[1]
sdmu1 <- multi_norm.sim$sd$mu[1]
t.test2( mean(x), as.numeric(mu1), s1 = sd(x), s2 = sdmu1, 500, 500)
Difference of means Std Error t p-value
-4.950656e-01 2.246905e-02 -2.203323e+01 5.862968e-76
When I copied the results from my screen to SO it was hard to make the labels of the results properly spaced apart, my apologies.
I'm working on a binomial mixture model using OpenBUGS and R package R2OpenBUGS. I've successfully built simpler models, but once I add another level for imperfect detection, I consistently receive the error variable X is not defined in model or in data set. I've tried a number of different things, including changing the structure of my data and entering my data directly into OpenBUGS. I'm posting this in the hope that someone else has experience with this error, and perhaps knows why OpenBUGS is not recognizing variable X even though it is clearly defined as far as I can tell.
I've also gotten the error expected the collection operator c error pos 8 - this is not an error I've been getting previously, but I am similarly stumped.
Both the model and the data-simulation function come from Kery's Introduction to WinBUGS for Ecologists (2010). I will note that the data set here is in lieu of my own data, which is similar.
I am including the function to build the dataset as well as the model. Apologies for the length.
# Simulate data: 200 sites, 3 sampling rounds, 3 factors of the level 'trt',
# and continuous covariate 'X'
data.fn <- function(nsite = 180, nrep = 3, xmin = -1, xmax = 1, alpha.vec = c(0.01,0.2,0.4,1.1,0.01,0.2), beta0 = 1, beta1 = -1, ntrt = 3){
y <- array(dim = c(nsite, nrep)) # Array for counts
X <- sort(runif(n = nsite, min = xmin, max = xmax)) # covariate values, sorted
# Relationship expected abundance - covariate
x2 <- rep(1:ntrt, rep(60, ntrt)) # Indicator for population
trt <- factor(x2, labels = c("CT", "CM", "CC"))
Xmat <- model.matrix(~ trt*X)
lin.pred <- Xmat[,] %*% alpha.vec # Value of lin.predictor
lam <- exp(lin.pred)
# Add Poisson noise: draw N from Poisson(lambda)
N <- rpois(n = nsite, lambda = lam)
table(N) # Distribution of abundances across sites
sum(N > 0) / nsite # Empirical occupancy
totalN <- sum(N) ; totalN
# Observation process
# Relationship detection prob - covariate
p <- plogis(beta0 + beta1 * X)
# Make a 'census' (i.e., go out and count things)
for (i in 1:nrep){
y[,i] <- rbinom(n = nsite, size = N, prob = p)
}
# Return stuff
return(list(nsite = nsite, nrep = nrep, ntrt = ntrt, X = X, alpha.vec = alpha.vec, beta0 = beta0, beta1 = beta1, lam = lam, N = N, totalN = totalN, p = p, y = y, trt = trt))
}
data <- data.fn()
And here is the model:
sink("nmix1.txt")
cat("
model {
# Priors
for (i in 1:3){ # 3 treatment levels (factor)
alpha0[i] ~ dnorm(0, 0.01)
alpha1[i] ~ dnorm(0, 0.01)
}
beta0 ~ dnorm(0, 0.01)
beta1 ~ dnorm(0, 0.01)
# Likelihood
for (i in 1:180) { # 180 sites
C[i] ~ dpois(lambda[i])
log(lambda[i]) <- log.lambda[i]
log.lambda[i] <- alpha0[trt[i]] + alpha1[trt[i]]*X[i]
for (j in 1:3){ # each site sampled 3 times
y[i,j] ~ dbin(p[i,j], C[i])
lp[i,j] <- beta0 + beta1*X[i]
p[i,j] <- exp(lp[i,j])/(1+exp(lp[i,j]))
}
}
# Derived quantities
}
",fill=TRUE)
sink()
# Bundle data
trt <- data$trt
y <- data$y
X <- data$X
ntrt <- 3
# Standardise covariates
s.X <- (X - mean(X))/sd(X)
win.data <- list(C = y, trt = as.numeric(trt), X = s.X)
# Inits function
inits <- function(){ list(alpha0 = rnorm(ntrt, 0, 2),
alpha1 = rnorm(ntrt, 0, 2),
beta0 = rnorm(1,0,2), beta1 = rnorm(1,0,2))}
# Parameters to estimate
parameters <- c("alpha0", "alpha1", "beta0", "beta1")
# MCMC settings
ni <- 1200
nb <- 200
nt <- 2
nc <- 3
# Start Markov chains
out <- bugs(data = win.data, inits, parameters, "nmix1.txt", n.thin=nt,
n.chains=nc, n.burnin=nb, n.iter=ni, debug = TRUE)
Note: This answer has gone through a major revision, after I noticed another problem with the code.
If I understand your model correctly, you are mixing up the y and N from the simulated data, and what is passed as C to Bugs. You are passing the y variable (a matrix) to the C variable in the Bugs model, but this is accessed as a vector. From what I can see C is representing the number of "trials" in your binomial draw (actual abundances), i.e. N in your data set. The variable y (a matrix) is called the same thing in both the simulated data and in the Bugs model.
This is a reformulation of your model, as I understand it, and this runs ok:
sink("nmix1.txt")
cat("
model {
# Priors
for (i in 1:3){ # 3 treatment levels (factor)
alpha0[i] ~ dnorm(0, 0.01)
alpha1[i] ~ dnorm(0, 0.01)
}
beta0 ~ dnorm(0, 0.01)
beta1 ~ dnorm(0, 0.01)
# Likelihood
for (i in 1:180) { # 180 sites
C[i] ~ dpois(lambda[i])
log(lambda[i]) <- log.lambda[i]
log.lambda[i] <- alpha0[trt[i]] + alpha1[trt[i]]*X[i]
for (j in 1:3){ # each site sampled 3 times
y[i,j] ~ dbin(p[i,j], C[i])
lp[i,j] <- beta0 + beta1*X[i]
p[i,j] <- exp(lp[i,j])/(1+exp(lp[i,j]))
}
}
# Derived quantities
}
",fill=TRUE)
sink()
# Bundle data
trt <- data$trt
y <- data$y
X <- data$X
N<- data$N
ntrt <- 3
# Standardise covariates
s.X <- (X - mean(X))/sd(X)
win.data <- list(y = y, trt = as.numeric(trt), X = s.X, C= N)
# Inits function
inits <- function(){ list(alpha0 = rnorm(ntrt, 0, 2),
alpha1 = rnorm(ntrt, 0, 2),
beta0 = rnorm(1,0,2), beta1 = rnorm(1,0,2))}
# Parameters to estimate
parameters <- c("alpha0", "alpha1", "beta0", "beta1")
# MCMC settings
ni <- 1200
nb <- 200
nt <- 2
nc <- 3
# Start Markov chains
out <- bugs(data = win.data, inits, parameters, "nmix1.txt", n.thin=nt,
n.chains=nc, n.burnin=nb, n.iter=ni, debug = TRUE)
Overall, the results from this model looks ok, but there are long autocorrelation lags for beta0 and beta1. The estimate of beta1 also seems a bit off(~= -0.4), so you might want to recheck the Bugs model specification, so that it is matching the simulation model (i.e. that you are fitting the correct statistical model). At the moment, I'm not sure that it does, but I don't have the time to check further right now.
I got the same message trying to pass a factor to OpenBUGS. Like so,
Ndata <- list(yrs=N$yrs, site=N$site), ... )
The variable "site" was not passed by the "bugs" function. It simply was not in list passed
to OpenBUGS
I solved the problem by passing site as numeric,
Ndata <- list(yrs=N$yrs, site=as.numeric(N$site)), ... )