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# Nonlinearizable C-E3L
# Different variances for two segments
llsearch.E3L.CD <- function(x, y, n, jlo, jhi, start1, start2)
{
fj <- matrix(0, n)
fxy <- matrix(0, jhi - jlo + 1)
jgrid <- expand.grid(jlo:jhi)
k.ll <- apply(jgrid, 1, p.estFUN.CD, x = x, y = y, n = n, start1=start1, start2=start2)
fxy <- matrix(k.ll, nrow = jhi-jlo+1)
rownames(fxy) <- jlo:jhi
z <- findmax(fxy)
jcrit <- z$imax + jlo - 1
list(jhat = jcrit, value = max(fxy))
}
# Function for deriving the ML estimates of the change-points problem.
p.estFUN.CD <- function(j, x, y, n,start1, start2){
a <- p.est.E3L.CD(x,y,n,j,start1, start2)
s2 <- a$sigma2
t2<- a$tau2
return(p.ll.CD(n, j, s2, t2))
}
p.est.E3L.CD <- function(x,y,n,j,start1, start2){
xa <- x[1:j]
ya <- y[1:j]
jp1 <- j+1
xb <- x[jp1:n]
yb <- y[jp1:n]
g2 <- lm(yb ~ xb)
ypred <- g2$coef[1]+x[j]*g2$coef[2]
changepoint <- x[j]
fun1 <- function(x,a0,a1){ypred - a0*(1-exp(a1*(x-changepoint)))}
g1 <- nls(ya ~ fun1(xa,a0,a1), data=data.frame(xa,ya),start=list(a0=start1,a1=start2)) # -2.5 2
beta <-c(summary(g1)$parameter[1],summary(g1)$parameter[2],g2$coef[1],g2$coef[2])
s2<- sum((ya-predict(g1, list(x=xa)))^2)/j
t2 <- sum((yb-g2$fit)^2)/(n-j)
list(a0=beta[1],a1=beta[2],b0=beta[3],b1=beta[4],sigma2=s2,tau2=t2, xj=x[j])
}
# Function to compute the log-likelihood of the change-point problem
p.ll.CD <- function(n, j, s2, t2){
q1 <- n * log(sqrt(2 * pi))
q2 <- 0.5 * n * (1 + log(s2))
q3 <- 0.5 * (n - j) * (1 + log(t2))
- (q1 + q2 + q3)
}
findmax <-function(a)
{
maxa<-max(a)
imax<- which(a==max(a),arr.ind=TRUE)[1]
jmax<-which(a==max(a),arr.ind=TRUE)[2]
list(imax = imax, jmax = jmax, value = maxa)
}
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