R/MethCon2.C.R

In hcp: Change Point Estimation for Regression with Heteroscedastic Data

# MethCon2-Yulei.s
# Common variance for all three segments

con2.search.C <- function(x, y, n, jlo, jhi, klo, khi,plot)
{
	fjk <- matrix(0, n, n)
	fxy <- matrix(0, (jhi - jlo + 1), (khi - klo + 1))
	
 ##Yulei's edit to avoid using for-loop
	jkgrid <- expand.grid(jlo:jhi, klo:khi)
	res <- data.frame(j = jkgrid[,1],
	                  k = jkgrid[,2],
	                  k.ll = apply(jkgrid, 1, con2.parmsFUN.C, x = x, 
	                               y = y, n = n))
	
	res.m <- matrix(res$k.ll, nrow = jhi-jlo+1, ncol = khi-klo+1)
	rownames(res.m) <- jlo:jhi
	colnames(res.m) <- klo:khi
  
	fxy <- res.m
 if (plot == "TRUE") {
   jx<-jlo:jhi
   ky<-klo:khi
   persp(jx, ky, fxy, xlab = "j", ylab = "k", zlab = "LL(x,y,j,k)")
   title("Log-likelihood Surface")
 }
	z <- findmax(fxy)
	jcrit <- z$imax + jlo - 1
	kcrit <- z$jmax + klo - 1
	list(jhat = jcrit, khat = kcrit, value = max(fxy))
}
con2.parmsFUN.C <-
  function(jk,x,y,n){
    j = jk[1]
    k = jk[2]
    a <- con2.parms.C(x,y,n,j,k,1)
nr <- nrow(a$theta)
est <- a$theta[nr,  ]
b <- con2.est.C(x[j], x[k], est)
s2 <- 1/b$eta1
return(p.ll.C(n, j, k, s2))
}
con2.parms.C <- function(x,y,n,j0,k0,e10){

th <- matrix(0,100,7)

# Iteration 0

 th[1,1] <- e10
 bc <- beta2.calc.C(x,y,n,j0,k0,e10)
 th[1,2:6] <- bc$B

# Iterate to convergence (100 Iter max)

 for (iter in 2:100){
 m <- iter-1
 ec <- eta2.calc.C(x,y,n,j0,k0,th[m,2:6])
 th[iter,1] <- ec$eta1
 bc <- beta2.calc.C(x,y,n,j0,k0,ec$eta1)
 th[iter,2:6] <- bc$B
 theta <- th[1:iter,]
 #delta <- abs(th[iter,]-th[m,])
 delta <- abs(th[iter,]-th[m,])/th[m,]
 if( (delta[1]<.001) & (delta[2]<.001) & (delta[3]<.001)
   & (delta[4]<.001) & (delta[5]<.001) & (delta[6]<.001)
   )
 break
 }
 list(theta=theta)
}
con2.est.C <- function(xj, xk, est)
{
	eta1 <- est[1]
	a0 <- est[2]
	a1 <- est[3]
	b1 <- est[4]
        b2 <- est[5]
	c1 <- est[6]
	b0 <- a0 + (a1 - b1) * xj - b2 * xj^2
	c0 <- b0 + (b1 - c1) * xk + b2 * xk^2
	list(eta1 = eta1, a0 = a0, a1 = a1, b0 = b0, b1 = b1, 
             b2 = b2, c0 = c0, c1 = c1)
}
con2.vals.C <- function(x, y, n, j, k)
{
	a <- con2.parms.C(x, y, n, j, k, 1)
	nr <- nrow(a$theta)
	est <- a$theta[nr,  ]
	b <- con2.est.C(x[j], x[k], est)
	eta <- c(b$eta1)
	beta <- c(b$a0, b$a1, b$b0, b$b1, b$b2, b$c0, b$c1)
	tau <- c(x[j], x[k])
	list(eta = eta, beta = beta, tau = tau)
}
p.ll.C <- function(n, j, k, s2){
 q1 <- n * log(sqrt(2 * pi))
 q2 <- 0.5 * (n) * (1 + log(s2))
 - (q1 + q2)
}

## Yulei's edit to avoid using for-loop
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)
}

beta2.calc.C <- function(x, y, n, j, k, e1)
{
	aa <- wmat2.C(x, y, n, j, k, e1)
	W <- aa$w
	bb <- rvec2.C(x, y, n, j, k, e1)
	R <- bb$r
	beta <- solve(W, R)
	list(B = beta)
} 
eta2.calc.C <- function(x, y, n, j, k, theta)
{
	jp1 <- j + 1
	kp1 <- k + 1
	a0 <- theta[1]
	a1 <- theta[2]
	b1 <- theta[3]
        b2 <- theta[4]
	c1 <- theta[5]
	b0 <- a0 + (a1 - b1) * x[j] - b2 * x[j]^2
	c0 <- b0 + (b1 - c1) * x[k] + b2 * x[k]^2
	rss1 <- sum((y[1:j] - a0 - a1 * x[1:j])^2)
	rss2 <- sum((y[jp1:k] - b0 - b1 * x[jp1:k] - b2 * x[jp1:k]^2)^2)
	rss3 <- sum((y[kp1:n] - c0 - c1 * x[kp1:n])^2)
	e1 <- (n)/(rss1 + rss2 + rss3)
	list(eta1 = e1)
}
wmat2.C <- function(x, y, n, j, k, e1, e2)
{
	W <- matrix(0, 5, 5)
	jp1 <- j + 1
	kp1 <- k + 1
	W[1, 1] <- e1 * (n - k + j) + e1 * (k - j)
	W[1, 2] <- e1 * (sum(x[1:j]) + (n - k) * x[j]) + e1 * (k - j) * x[j]
	W[1, 3] <- e1 * (n - k) * (x[k] - x[j]) + e1 * sum(x[jp1:k] - x[j])
        W[1, 4] <- e1 * (n - k) * (x[k]^2 - x[j]^2) + e1 * sum(x[jp1:k]^2 - x[j]^2)
	W[1, 5] <- e1 * sum(x[kp1:n] - x[k])
	W[2, 2] <- e1 * (sum(x[1:j] * x[1:j]) + (n - k) * x[j] * x[j]) + e1 * (k - j) *
 		x[j] * x[j]
	W[2, 3] <- e1 * (n - k) * x[j] * (x[k] - x[j]) + e1 * x[j] * sum(x[jp1:k] - x[
		j])
        W[2, 4] <- e1 * (n - k) * x[j] * (x[k]^2 - x[j]^2) + e1 * x[j] * sum(x[jp1:k]^2 - x[
		j]^2)
	W[2, 5] <- e1 * x[j] * sum(x[kp1:n] - x[k])
	W[3, 3] <- e1 * (n - k) * (x[k] - x[j]) * (x[k] - x[j]) + e1 * sum((x[jp1:k] - 
		x[j]) * (x[jp1:k] - x[j]))
        W[3, 4] <- e1 * (n - k) * (x[k] - x[j]) * (x[k]^2 - x[j]^2) + e1 * sum((x[jp1:k] - 
		x[j]) * (x[jp1:k]^2 - x[j]^2))
	W[3, 5] <- e1 * (x[k] - x[j]) * sum(x[kp1:n] - x[k])
        W[4, 4] <- e1 * (n - k) * (x[k]^2 - x[j]^2) * (x[k]^2 - x[j]^2) + e1 * sum((x[jp1:k]^2 - 
		x[j]^2) * (x[jp1:k]^2 - x[j]^2))
        W[4, 5] <- e1 * (x[k]^2 - x[j]^2) * sum(x[kp1:n] - x[k])
	W[5, 5] <- e1 * sum((x[kp1:n] - x[k]) * (x[kp1:n] - x[k]))
	W[2, 1] <- W[1, 2]
	W[3, 1] <- W[1, 3]
	W[4, 1] <- W[1, 4]
        W[5, 1] <- W[1, 5]
	W[3, 2] <- W[2, 3]
	W[4, 2] <- W[2, 4]
        W[5, 2] <- W[2, 5]
	W[4, 3] <- W[3, 4]
        W[5, 3] <- W[3, 5]
        W[5, 4] <- W[4, 5]
	list(w = W)
}
rvec2.C <- function(x, y, n, j, k, e1)
{
	R <- array(0, 5)
	jp1 <- j + 1
	kp1 <- k + 1
	y1j <- sum(y[1:j])
	yjk <- sum(y[jp1:k])
	ykn <- sum(y[kp1:n])
	xy1j <- sum(x[1:j] * y[1:j])
	xyjk <- sum(x[jp1:k] * y[jp1:k])
        x2yjk <- sum(x[jp1:k]^2 * y[jp1:k])
	xykn <- sum(x[kp1:n] * y[kp1:n])
	R[1] <- e1 * (y1j + ykn) + e1 * yjk
	R[2] <- e1 * (xy1j + x[j] * ykn) + e1 * x[j] * yjk
	R[3] <- e1 * (x[k] - x[j]) * ykn + e1 * (xyjk - x[j] * yjk)
        R[4] <- e1 * (x[k]^2 - x[j]^2) * ykn + e1 * (x2yjk - x[j]^2 * yjk) 
	R[5] <- e1 * (xykn - x[k] * ykn)
	list(r = R)
}

p2.est.C <- function(x, y, n, j, k)
{
	xa <- x[1:j]
	ya <- y[1:j]
	jp1 <- j + 1
	xb <- x[jp1:k]
	xb2 <- x[jp1:k]^2
	yb <- y[jp1:k]
	kp1 <- k + 1
	xc <- x[kp1:n]
	yc <- y[kp1:n]
	g1 <- lm(ya ~ xa)
	g2 <- lm(yb ~ xb + xb2)
	g3 <- lm(yc ~ xc)
	beta<-c(g1$coef[1],g1$coef[2],g2$coef[1],g2$coef[2],g2$coef[3],g3$coef[1],g3$coef[2])
	s2 <- (sum((ya - g1$fit)^2) + sum((yb - g2$fit)^2) + sum((yc - g3$fit)^2))/(n)
	xj <- x[j]
	xk <- x[k]
	list(a0=beta[1],a1=beta[2],b0=beta[3],b1=beta[4],b2=beta[5],c0=beta[6],c1=beta[7], sigma2 = 
		s2, xj = xj, xk = xk)
}