Nothing
Btqr <-
function(x,y,tau=0.5, left = 0, runs=11000, burn=1000, thin=1) {
#x: matrix of predictors.
#y: vector of dependent variable.
#tau: quantile level.
#runs: the length of the Markov chain.
#burn: the length of burn-in.
#thin: thinning parameter of MCMC draws
x <- as.matrix(x)
if(ncol(x)==1) {x=x} else {
x=x
if (all(x[,2]==1)) x=x[,-2] }
# Calculate some useful quantities
n <- nrow(x)
p <- ncol(x)
n0 <-sum(y<=left)
id0<-which(y<=left)
x0=x[y<=left,]
y[y<=left]=left
yt <-y
# check input
if (tau<=0 || tau>=1) stop ("invalid tau: tau should be >= 0 and <= 1.
\nPlease respecify tau and call again.\n")
if(n != length(y)) stop("length(y) not equal to nrow(x)")
if(n == 0) return(list(coefficients=numeric(0),fitted.values=numeric(0),
deviance=numeric(0)))
if(!(all(is.finite(y)) || all(is.finite(x)))) stop(" All values must be
finite and non-missing")
# Saving output matrices
betadraw = matrix(nrow=runs, ncol=p)
sigmadraw = matrix(nrow=runs, ncol=1)
# Calculate some useful quantities
xi = (1 - 2*tau)
zeta = tau*(1-tau)
# Initial valus
beta = rep(0.99, p)
v = rep(1, n)
sigma = 1
# Draw from inverse Gaussian distribution
rInvgauss <- function(n, mu, lambda = 1){
un <- runif(n)
Xi <- rchisq(n,1)
f <- mu/(2*lambda)*(2*lambda+mu*Xi+sqrt(4*lambda*mu*Xi+mu^2*Xi^2))
s <- mu^2/f
ifelse(un < mu/(mu+s), s, f)}
# Start the algorithm
for (iter in 1: runs) {
# Draw the latent variable v from inverse Gaussian distribution.
lambda = 1/(2*sigma)
mu = 1/(abs(yt - x%*%beta))
v = c(1/rInvgauss(n, mu = mu, lambda = lambda))
# Draw sigma
shape = 3/2*n
rate = sum((yt - x%*%beta - xi*v)^2/(4*v))+zeta*sum(v)
sigma = 1/rgamma(1, shape= shape, rate= rate)
# Draw beta
V=diag(1/(2*sigma*v))
varcov <- chol2inv(chol(t(x)%*%V%*%x) )
betam <- varcov %*% t(x)%*%V %*% (yt-xi*v)
beta <-betam+t(chol(varcov))%*%rnorm(p)
# Draw yt
v0=v[id0]
Mu0=x0%*%beta + xi*v0
Sig0=sqrt(2*sigma*v0)
u0 = runif(n0)
xu0= u0*pnorm(left,Mu0,Sig0)
yt[id0]= qnorm(xu0,Mu0,Sig0)
# Sort beta and sigma
betadraw[iter,] = beta
sigmadraw[iter,] = sigma
}
coefficients =apply(as.matrix(betadraw[-(1:burn), ]),2,mean)
names(coefficients)=colnames(x)
if (all(x[,1]==1)) names(coefficients)[1]= "Intercept"
result <- list(beta = betadraw[seq(burn, runs, thin),],
sigma = sigmadraw[seq(burn, runs, thin),],
coefficients=coefficients)
return(result)
class(result) <- "Btqr"
result
}
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