Nothing
PGfrailtyHL <-
function (x, z, y, del, Mi, idx2, t2, di, beta_h0, v_h0, alpha_h0,
mord, dord, varfixed = FALSE,varnonneg)
{
n <- nrow(x)
p <- ncol(x)
nrand <- length(z)
q <- rep(0, nrand)
for (i in 1:nrand) q[i] <- dim(z[[i]])[2]
qcum <- cumsum(c(0, q))
beta_h <- beta_h0
v_h <- v_h0
for (i in 1:nrand) {
if (alpha_h0[i] < 1e-06)
alpha_h0[i] <- 1e-06
}
alpha_h <- alpha_h0
zz <- z[[1]]
if (nrand > 1) {
index1 <- nrand
for (i in 2:index1) zz <- cbind(zz, z[[i]])
}
z <- matrix(0, n, qcum[nrand + 1])
z[1:n, 1:qcum[nrand + 1]] <- zz[1:n, 1:qcum[nrand + 1]]
muh <- x %*% beta_h0 + z %*% v_h0
expeta <- exp(muh)
cla0 <- di/(t(Mi) %*% expeta)
Wi <- diag(expeta[, 1])
Ai <- diag(cla0[, 1])
done <- matrix(1, idx2, 1)
oq <- matrix(1, qcum[nrand + 1], 1)
oq1 <- matrix(1, qcum[nrand + 1], 1)
clam0 <- Mi %*% Ai %*% done
for (i in 1:nrand) {
index1 <- qcum[i] + 1
oq1[index1:qcum[i + 1]] <- alpha_h[i]
}
D <- diag(oq1[, 1])
iD <- solve(D)
iu_h0 <- exp(v_h0)
U <- iD %*% diag(iu_h0[, 1])
dft1 <- t(x) %*% (del - Wi %*% clam0)
if (mord == 1) {
Bi <- diag(clam0[, 1])
temp4 <- cla0^2/di
As <- diag(temp4[, 1])
mat <- (Wi %*% Bi) - (Wi %*% Mi) %*% As %*% (t(Mi) %*%
Wi)
dinv <- solve(t(z) %*% mat %*% z + U)
mu0 <- exp(x %*% beta_h0 + z %*% v_h0)
mu <- exp(x %*% beta_h0 + z %*% v_h0) * clam0
dcla0be <- -As %*% (t(Mi) %*% Wi)
dcla0b <- matrix(0, idx2, p)
dv_db <- matrix(0, qcum[nrand + 1], p)
xz <- matrix(0, n, p)
dmu0 <- matrix(0, n, p)
dw_db1 <- matrix(0, n, p)
xk <- matrix(0, n, 1)
ad1 <- matrix(0, p, 1)
for (k in 1:p) {
xk[, 1] <- x[, k]
dv_db[, k] <- -dinv %*% (t(z) %*% mat %*% xk)
xz[, k] <- xk + z %*% (dv_db[, k])
dcla0b[, k] <- dcla0be %*% (xz[, k])
dc <- Mi %*% diag(dcla0b[, k]) %*% done
dmu0[, k] <- mu0 * (xz[, k])
dw_db1[, k] <- dc * mu0 + mu * xz[, k]
temp4 <- (2 * cla0/di) * (dcla0b[, k])
dw_db2 <- ((diag(dmu0[, k])) %*% Mi %*% As %*% t(Mi) %*%
Wi) + (Wi %*% Mi %*% diag(temp4[, 1]) %*% t(Mi) %*%
Wi) + (Wi %*% Mi %*% As %*% t(Mi) %*% (diag(dmu0[,
k])))
dw_db <- diag(dw_db1[, k]) - dw_db2
ad1[k, 1] <- sum(diag(dinv %*% (t(z) %*% dw_db %*%
z)))
}
dft1 <- dft1 - 0.5 * ad1
}
dft2 <- t(z) %*% (del - Wi %*% clam0) + (iD %*% oq) - (iD %*%
iu_h0)
dft <- rbind(dft1, dft2)
Bi <- diag(clam0[, 1])
temp4 <- cla0^2/di
Adi <- diag(temp4[, 1])
As <- Adi
mat <- (Wi %*% Bi) - (Wi %*% Mi) %*% Adi %*% (t(Mi) %*% Wi)
U <- iD %*% diag(iu_h0[, 1])
H <- rbind(cbind(t(x) %*% mat %*% x, t(x) %*% mat %*% z),
cbind(t(z) %*% mat %*% x, t(z) %*% mat %*% z + U))
H0 <- rbind(cbind(t(x) %*% mat %*% x, t(x) %*% mat %*% z),
cbind(t(z) %*% mat %*% x, t(z) %*% mat %*% z))
Hinv <- solve(H)
be_h0 <- rbind(beta_h0, v_h0)
be_h <- be_h0 + (Hinv %*% dft)
beta_h[1:p, 1] <- be_h[1:p, 1]
se_beta_h <- matrix(0, p, 1)
for (i in 1:p) se_beta_h[i, 1] <- sqrt(Hinv[i, i])
index2 <- qcum[nrand + 1]
index3 <- p + 1
index4 <- p + qcum[nrand + 1]
v_h[1:index2, 1] <- be_h[index3:index4, 1]
for (i in 1:nrand) {
ial <- 1/alpha_h[i]
dp <- digamma(ial)
ddp <- trigamma(ial)
oq <- matrix(1, q[i], 1)
one <- matrix(1, n, 1)
u_h <- exp(v_h)
eta <- x %*% beta_h + z %*% v_h
expeta <- exp(eta)
Wi <- diag(expeta[, 1])
Wei <- (Wi %*% Bi)
U <- iD %*% diag(u_h[, 1])
term <- (t(z) %*% mat %*% z + U)
C <- matrix(0, qcum[nrand + 1], qcum[nrand + 1])
index1 <- qcum[i] + 1
index2 <- qcum[i + 1]
for (j in index1:index2) C[j, j] <- 1
iA <- iD
iB <- iA %*% C %*% iA
c_vh <- iB %*% (u_h - 1)
invt <- solve(term)
dv <- invt %*% c_vh
dexpeta <- expeta * (z %*% dv)
dcla0 <- -(di/((t(Mi) %*% expeta)^2)) * (t(Mi) %*% dexpeta)
temp4 <- expeta * (z %*% dv)
dWi <- diag(temp4[, 1])
dAi <- diag(dcla0[, 1])
temp4 <- Mi %*% dAi %*% done
dBi <- diag(temp4[, 1])
dvec <- 2 * (cla0 * dcla0)
temp4 <- dvec/di
dAs <- diag(temp4[, 1])
dmat <- (dWi %*% Bi) + (Wi %*% dBi) - (dWi %*% Mi %*%
As %*% t(Mi) %*% Wi) - (Wi %*% Mi %*% dAs %*% t(Mi) %*%
Wi) - (Wi %*% Mi %*% As %*% t(Mi) %*% dWi)
uad1 <- u_h * dv
temp4 <- -iB %*% u_h + ial * uad1
dia1 <- diag(temp4[, 1])
Hd <- rbind(cbind(t(x) %*% dmat %*% x, t(x) %*% dmat %*%
z), cbind(t(z) %*% dmat %*% x, t(z) %*% dmat %*%
z + dia1))
if (dord == 0) {
temp4 <- -iD %*% iD %*% u_h
dia1_k <- diag(temp4[, 1])
zero1 <- matrix(0, p, p)
zero2 <- matrix(0, p, qcum[nrand + 1])
Hd_k <- rbind(cbind(zero1, zero2), cbind(t(zero2),
dia1_k))
hinv2 <- solve(t(z) %*% mat %*% z + U)
Hd2 <- t(z) %*% dmat %*% z + dia1
dk2 <- -0.5 * sum(diag(Hinv %*% Hd_k))
vv_h <- matrix(0, q[i], 1)
index3 <- 1
index4 <- q[i]
vv_h[1:q[i], 1] <- v_h[index1:index2, 1]
uu_h <- exp(vv_h)
nonneg_adj=0
if (varnonneg == TRUE) nonneg_adj=alpha_h[i]
k2 <- (t(oq) %*% (vv_h - uu_h)) + (q[i] * (-log(alpha_h[i]) +
1 - dp))-nonneg_adj
mu <- exp(x %*% beta_h) * clam0
zd <- t(z) %*% del
zmu <- t(z) %*% mu
cor1 <- (1 + (alpha_h[i] * zd))^(-2)
dk3 <- sum(cor1)/12
k2 <- -((alpha_h[i]^-2) * k2) + dk2
dterm <- t(z) %*% dmat %*% z + dia1
ddv <- -invt %*% (dterm) %*% invt %*% c_vh + invt %*%
(-2 * ial^3 * (u_h - 1) + ial^2 * uad1)
ddcla0 <- -dAs %*% (t(Mi) %*% Wi %*% z) %*% dv -
As %*% (t(Mi) %*% dWi %*% z) %*% dv - As %*%
(t(Mi) %*% Wi %*% z) %*% ddv
uad2 <- (uad1 * dv) + (u_h * ddv)
ddAi <- diag(ddcla0[, 1])
ddclam0 <- Mi %*% ddAi %*% done
ddBi <- diag(ddclam0[, 1])
temp4 <- expeta * (z %*% dv) * (z %*% dv) + (expeta *
(z %*% ddv))
ddWi <- diag(temp4[, 1])
ddm1 <- (ddWi %*% Bi) + (2 * dWi %*% dBi) + (Wi %*%
ddBi)
ddm2 <- ddWi %*% Mi %*% As %*% t(Mi) %*% Wi + (2 *
dWi %*% Mi %*% dAs %*% t(Mi) %*% Wi) + (2 * dWi %*%
Mi %*% As %*% t(Mi) %*% dWi)
ddvec <- (2 * (dcla0^2)) + (2 * (cla0 * ddcla0))
temp4 <- ddvec/di
ddAs = diag(temp4[, 1])
ddm3 <- (Wi %*% Mi %*% ddAs %*% t(Mi) %*% Wi) + (2 *
Wi %*% Mi %*% dAs %*% t(Mi) %*% dWi) + Wi %*%
Mi %*% As %*% t(Mi) %*% ddWi
ddmat <- ddm1 - (ddm2 + ddm3)
temp4 <- (2 * ial^3 * u_h) - (2 * ial^2 * uad1) +
(ial * uad2)
dia2 <- diag(temp4[, 1])
Hdd2 <- t(z) %*% ddmat %*% z + dia2
k21 <- t(oq) %*% (2 * (vv_h - uu_h)) + (q[i] * ((-2 *
log(alpha_h[i])) + 3 - (2 * dp) - ((1/alpha_h[i]) *
ddp)))
al <- ial^3
k21 <- al * k21
cor2 <- (1 + (alpha_h[i] * zd))^(-3)
cor22 <- cor2 * zd
kcor <- sum(cor22)/6
kcor <- 0
k22 <- -k21 + 0.5 * (sum(diag(hinv2 * Hdd2)) - sum(diag(hinv2 *
Hd2 * hinv2 * Hd2))) + kcor
ialp <- 1/k22
if (varfixed == FALSE)
alpha_h[i] <- alpha_h[i] + (ialp * k2)
}
if (dord == 1 | dord == 2) {
hinv2 <- solve(t(z) %*% mat %*% z + U)
Hd2 <- t(z) %*% dmat %*% z + dia1
dk2 <- -0.5 * sum(diag(Hinv %*% Hd))
vv_h <- matrix(0, q[i], 1)
index3 <- 1
index4 <- q[i]
vv_h[1:index4, 1] <- v_h[index1:index2, 1]
uu_h <- exp(vv_h)
nonneg_adj=0
if (varnonneg == TRUE) nonneg_adj=alpha_h[i]
k2 <- (t(oq) %*% (vv_h - uu_h)) + (q[i] * (-log(alpha_h[i]) +
1 - dp))-nonneg_adj
mu <- exp(x %*% beta_h) * clam0
zd <- t(z) %*% del
zmu <- t(z) %*% mu
cor1 <- (1 + (alpha_h[i] * zd))^(-2)
dk3 <- sum(cor1)/12
if (dord == 1)
k2 <- -((alpha_h[i]^(-2)) * k2) + dk2
if (dord == 2)
k2 <- -((alpha_h[i]^(-2)) * k2) + dk2 + dk3
dterm <- t(z) %*% dmat %*% z + dia1
ddv <- -invt %*% (dterm) %*% invt %*% c_vh + invt %*%
(-2 * ial^3 * (u_h - 1) + ial^2 * uad1)
ddcla0 <- -dAs %*% (t(Mi) %*% Wi %*% z) %*% dv -
As %*% (t(Mi) %*% dWi %*% z) %*% dv - As %*%
(t(Mi) %*% Wi %*% z) %*% ddv
uad2 <- (uad1 * dv) + (u_h * ddv)
ddAi <- diag(ddcla0[, 1])
ddclam0 <- Mi %*% ddAi %*% done
ddBi <- diag(ddclam0[, 1])
temp4 <- expeta * (z %*% dv) * (z %*% dv) + (expeta *
(z %*% ddv))
ddWi <- diag(temp4[, 1])
ddm1 <- (ddWi %*% Bi) + (2 * dWi %*% dBi) + (Wi %*%
ddBi)
ddm2 <- ddWi %*% Mi %*% As %*% t(Mi) %*% Wi + (2 *
dWi %*% Mi %*% dAs %*% t(Mi) %*% Wi) + (2 * dWi %*%
Mi %*% As %*% t(Mi) %*% dWi)
ddvec <- (2 * (dcla0^2)) + (2 * (cla0 * ddcla0))
temp4 <- ddvec/di
ddAs <- diag(temp4[, 1])
ddm3 <- (Wi %*% Mi %*% ddAs %*% t(Mi) %*% Wi) + (2 *
Wi %*% Mi %*% dAs %*% t(Mi) %*% dWi) + Wi %*%
Mi %*% As %*% t(Mi) %*% ddWi
ddmat <- ddm1 - (ddm2 + ddm3)
temp4 <- (2 * ial^3 * u_h) - (2 * ial^2 * uad1) +
(ial * uad2)
dia2 <- diag(temp4[, 1])
Hdd <- rbind(cbind(t(x) %*% ddmat %*% x, t(x) %*%
ddmat %*% z), cbind(t(z) %*% ddmat %*% x, t(z) %*%
ddmat %*% z + dia2))
Hdd2 <- t(z) %*% ddmat %*% z + dia2
k21 <- t(oq) %*% (2 * (vv_h - uu_h)) + (q[i] * ((-2 *
log(alpha_h[i])) + 3 - (2 * dp) - ((1/alpha_h[i]) *
ddp)))
al <- ial^3
k21 <- al * k21
cor2 <- (1 + (alpha_h[i] * zd))^(-3)
cor22 <- cor2 * zd
kcor <- sum(cor22)/6
if (dord == 1)
kcor <- 0
k22 <- -k21 + 0.5 * (sum(diag(Hinv %*% Hdd)) - sum(diag(Hinv %*%
Hd %*% Hinv %*% Hd))) + kcor
ialp <- 1/k22
if (varfixed == FALSE)
alpha_h[i] <- alpha_h[i] + (ialp * k2)
if (alpha_h[i] <= 0)
alpha_h[i] <- alpha_h0/2
}
}
## u-sclae
ialp_h<-1/alpha_h[1]
u_h<-exp(v_h)
mu1 <- exp(x %*% beta_h) * clam0
zmu=t(z) %*% mu1
exp_xb<-exp(x%*%beta_h)
W0=diag(exp_xb[,1])
Bi <- diag(clam0[, 1])
mat1=(W0%*%Bi)-(W0%*%Mi)%*%Adi%*%(t(Mi)%*%W0)
U1 = (ialp_h+zmu)/u_h
U1 = diag(U1[,1])
U2=t(z)%*%((W0%*%Mi)%*%Adi%*%(t(Mi)%*%W0))%*%z
Hu = rbind(cbind(t(x)%*%mat%*%x, t(x)%*%mat1%*%z),
cbind(t(z)%*%mat1%*%x, U1-U2 ))
Hinv_u=solve(Hu)
res <- list(x, z, y, del, Mi, idx2, t2, di, beta_h0, v_h0,
beta_h, v_h, alpha_h0, alpha_h, dft, Hinv, clam0, H,
mat, se_beta_h, U, H0, u_h,Hinv_u)
return(res)
}
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