R/bcontSurvGcont2Surv.R
In KironmoyDas/KD-STAT0035-GMupdate: Generalised Joint Regression Modelling
Defines functions
bcontSurvGcont2Surv
bcontSurvGcont2Surv <- function(params, respvec, VC, ps, AT = FALSE){
p1 <- p2 <- pdf1 <- pdf2 <- c.copula.be2 <- c.copula.be1 <- c.copula2.be1be2 <- NA
rotConst <- 1
etad <- etas1 <- etas2 <- l.ln <- NULL
params1 <- params[1:VC$X1.d2]
params2 <- params[(VC$X1.d2 + 1):(VC$X1.d2 + VC$X2.d2)]
params2[VC$mono.sm.pos2] <- exp( params2[VC$mono.sm.pos2] )
eta1 <- eta.tr(VC$X1%*%params1, VC$margins[1])
eta2 <- VC$X2%*%params2
etad <- etas1 <- etas2 <- l.ln <- NULL
Xd2P <- VC$Xd2%*%params2
Xd2P <- ifelse(Xd2P < VC$min.dn, VC$min.dn, Xd2P ) # safety thing, never used as per model definition
if(is.null(VC$X3)){
X3 <- X4 <- matrix(1, VC$n, 1)
sigma21.st <- etas1 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
}
if(!is.null(VC$X3)){
X3 <- VC$X3; X4 <- VC$X4
sigma21.st <- etas1 <- X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
teta.st <- etad <- X4%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2)]
}
##################
## Transformations
##################
sstr1 <- esp.tr(sigma21.st, VC$margins[1])
sigma21.st <- sstr1$vrb.st
sigma21 <- sstr1$vrb
resT <- teta.tr(VC, teta.st)
teta.st1 <- teta.st2 <- teta.st <- resT$teta.st
teta1 <- teta2 <- teta <- resT$teta
##################
Cop1 <- Cop2 <- VC$BivD
nC1 <- nC2 <- VC$nC
teta.ind1 <- as.logical(c(1,0,round(runif(VC$n-2))) )
teta.ind2 <- teta.ind1 == FALSE
if(!(VC$BivD %in% VC$BivD2) && length(teta.st) > 1){
teta.st1 <- teta.st[teta.ind1]
teta.st2 <- teta.st[teta.ind2]
teta1 <- teta[teta.ind1]
teta2 <- teta[teta.ind2]
}
###
if(VC$BivD %in% VC$BivD2){
if(VC$BivD %in% VC$BivD2[c(1:4,13:16)]) teta.ind1 <- ifelse(VC$my.env$signind*teta > exp(VC$zerov), TRUE, FALSE)
if(VC$BivD %in% VC$BivD2[5:12]) teta.ind1 <- ifelse(VC$my.env$signind*teta > exp(VC$zerov) + 1, TRUE, FALSE)
teta.ind2 <- teta.ind1 == FALSE
VC$my.env$signind <- ifelse(teta.ind1 == TRUE, 1, -1)
teta1 <- teta[teta.ind1]
teta2 <- -teta[teta.ind2]
teta.st1 <- teta.st[teta.ind1]
teta.st2 <- teta.st[teta.ind2]
if(length(teta) == 1) teta.ind2 <- teta.ind1 <- rep(TRUE, VC$n)
Cop1Cop2R <- Cop1Cop2(VC$BivD)
Cop1 <- Cop1Cop2R$Cop1
Cop2 <- Cop1Cop2R$Cop2
nC1 <- VC$ct[which(VC$ct[,1] == Cop1),2]
nC2 <- VC$ct[which(VC$ct[,1] == Cop2),2]
}
##################
dHs1 <- distrHs(respvec$y1, eta1, sigma21, sigma21.st, nu = 1, nu.st = 1, margin2 = VC$margins[1], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
p1 <- dHs1$p2
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derp1.dereta1 <- dHs1$derp2.dereta2
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
der2pdf1.dereta1 <- dHs1$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2pdf1.dereta1dersigma21.st <- dHs1$der2pdf2.dereta2dersigma2.st
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
pd2 <- probmS(eta2, VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
p2 <- pd2$pr
dS2eta2 <- pd2$dS
d2S2eta2 <- pd2$d2S
d3S2eta2 <- pd2$d3S
##################
if( length(teta1) != 0) dH1 <- copgHs(p1[teta.ind1], p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if( length(teta2) != 0) dH2 <- copgHs(p1[teta.ind2], p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
c.copula2.be1be2 <- c.copula.be1 <- c.copula.be2 <- p00 <- c.copula.theta <- c.copula.thet <- bit1.th2ATE <- NA
if( length(teta1) != 0){ c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula.be1[teta.ind1] <- dH1$c.copula.be1
c.copula.theta[teta.ind1] <- dH1$c.copula.theta
c.copula.thet[teta.ind1] <- dH1$c.copula.thet
bit1.th2ATE[teta.ind1] <- dH1$bit1.th2ATE
}
# CHECK THAT WE NEED ALL BITS ABOVE
if( length(teta2) != 0){ c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula.be1[teta.ind2] <- dH2$c.copula.be1
c.copula.theta[teta.ind2] <- dH2$c.copula.theta
c.copula.thet[teta.ind2] <- dH2$c.copula.thet
bit1.th2ATE[teta.ind2] <- dH2$bit1.th2ATE
}
l.par <- VC$weights*( VC$c11*( log(c.copula2.be1be2) + log(pdf1) + log(-dS2eta2) + log(Xd2P) ) +
VC$c10*( log(c.copula.be1) + log(pdf1) )
)
res <- -sum(l.par)
##################
der.par1 <- der2.par1 <- params1; der.par2 <- der2.par2 <- params2
der.par2[-c( VC$mono.sm.pos2 )] <- 1
der2.par2[-c( VC$mono.sm.pos2 )] <- 0
der2eta2dery2b2 <- t(t(VC$Xd2)*der.par2)
dereta2derb2 <- t(t(VC$X2)*der.par2)
##################
##################
if( length(teta1) != 0) BITS1 <- copgHsCont(p1[teta.ind1], p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof - 2))
if( length(teta2) != 0) BITS2 <- copgHsCont(p1[teta.ind2], p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof - 2))
der2h.derp1p1 <- NA
if( length(teta1) != 0) der2h.derp1p1[teta.ind1] <- BITS1$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1[teta.ind2] <- BITS2$der2h.derp1p1
der2h.derp1p2 <- NA
if( length(teta1) != 0) der2h.derp1p2[teta.ind1] <- BITS1$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2[teta.ind2] <- BITS2$der2h.derp1p2
der2h.derp1teta <- NA
derteta.derteta.st <- NA
if( length(teta1) != 0) der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
if( length(teta1) != 0) derteta.derteta.st[teta.ind1] <- BITS1$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st[teta.ind2] <- BITS2$derteta.derteta.st
der2h.derp1teta.st <- der2h.derp1teta * derteta.derteta.st # new bit
derc.dersigma21.st <- der2h.derp1p1 * derp1.dersigma21.st
derc.dereta1 <- der2h.derp1p1 * derp1.dereta1
#################
#################
c.copula2.be1 <- c.copula2.be2 <- c.copula2.be1th <- c.copula2.be2th <- bit1.th2 <- c.copula2.be1t <- c.copula2.be2t <- NA
# CHECK THAT WE NEED ALL this
if( length(teta1) != 0){
c.copula2.be1[teta.ind1] <- dH1$c.copula2.be1
c.copula2.be2[teta.ind1] <- dH1$c.copula2.be2
c.copula2.be1th[teta.ind1] <- dH1$c.copula2.be1th
c.copula2.be2th[teta.ind1] <- dH1$c.copula2.be2th
c.copula2.be1t[teta.ind1] <- dH1$c.copula2.be1t
c.copula2.be2t[teta.ind1] <- dH1$c.copula2.be2t
bit1.th2[teta.ind1] <- dH1$bit1.th2
}
if( length(teta2) != 0){
c.copula2.be1[teta.ind2] <- dH2$c.copula2.be1
c.copula2.be2[teta.ind2] <- dH2$c.copula2.be2
c.copula2.be1th[teta.ind2] <- dH2$c.copula2.be1th
c.copula2.be2th[teta.ind2] <- dH2$c.copula2.be2th
c.copula2.be1t[teta.ind2] <- dH2$c.copula2.be1t
c.copula2.be2t[teta.ind2] <- dH2$c.copula2.be2t
bit1.th2[teta.ind2] <- dH2$bit1.th2
}
#################
#################
dl.dbe1 <- c(-VC$weights*(
VC$c11*( derpdf1.dereta1/pdf1 + derc.dereta1/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1 * derp1.dereta1 + derpdf1.dereta1 * pdf1^-1)
))*VC$X1
dl.dbe1 <- colSums(dl.dbe1)
dl.dbe2 <- -VC$weights*(
VC$c11*( c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*dereta2derb2 +
c(Xd2P^-1)*der2eta2dery2b2 )
+
VC$c10*( c(c.copula.be1^-1*c.copula2.be1be2*dS2eta2)*dereta2derb2 )
)
dl.dbe2 <- colSums(dl.dbe2)
dl.dsigma21.st <- c(-VC$weights*(
VC$c11*( derpdf1.dersigma21.st/pdf1 + derc.dersigma21.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1 * derp1.dersigma21.st + derpdf1.dersigma21.st * pdf1^-1 )
))*X3
dl.dsigma21.st <- colSums(dl.dsigma21.st)
dl.dteta.st <- c(-VC$weights*(
VC$c11*( der2h.derp1teta.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1th )
))*X4
dl.dteta.st <- colSums( dl.dteta.st)
G <- c( dl.dbe1, dl.dbe2, dl.dsigma21.st, dl.dteta.st )
#round(as.numeric(G + VC$S.h%*%params),4)
#round(as.numeric(gr),4)
#################################################################################################
der2c.derrho.derrho <- NA
der2c.derp1.derp1 <- NA
der2c.derp2.derp2 <- NA
der2c.derp1.derp2 <- NA
der2c.derp1.derrho <- NA
der2c.derp2.derrho <- NA
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0){ der2c.derrho.derrho[teta.ind1] <- BITS1$der2c.derrho.derrho
der2c.derp1.derp1[teta.ind1] <- BITS1$der2c.derp1.derp1
der2c.derp2.derp2[teta.ind1] <- BITS1$der2c.derp2.derp2
der2c.derp1.derp2[teta.ind1] <- BITS1$der2c.derp1.derp2
der2c.derp1.derrho[teta.ind1] <- BITS1$der2c.derp1.derrho
der2c.derp2.derrho[teta.ind1] <- BITS1$der2c.derp2.derrho }
if( length(teta2) != 0){ der2c.derrho.derrho[teta.ind2] <- BITS2$der2c.derrho.derrho
der2c.derp1.derp1[teta.ind2] <- BITS2$der2c.derp1.derp1
der2c.derp2.derp2[teta.ind2] <- BITS2$der2c.derp2.derp2
der2c.derp1.derp2[teta.ind2] <- BITS2$der2c.derp1.derp2
der2c.derp1.derrho[teta.ind2] <- BITS2$der2c.derp1.derrho
der2c.derp2.derrho[teta.ind2] <- BITS2$der2c.derp2.derrho }
if( length(teta1) != 0) der2teta.derteta.stteta.st[teta.ind1] <- BITS1$der2teta.derteta.stteta.st
if( length(teta2) != 0) der2teta.derteta.stteta.st[teta.ind2] <- BITS2$der2teta.derteta.stteta.st
########################
der3C.derp1p1p1 <- der3C.derp1tetateta <- der2h.derteta.teta.st <- der3C.p1p1teta <- der2h.derp2teta <- der2h.derp2p2 <- NA
if( length(teta1) != 0){der3C.derp1p1p1[teta.ind1] <- BITS1$der3C.derp1p1p1
der2h.derteta.teta.st[teta.ind1] <- BITS1$der2h.derteta.teta.st
der3C.derp1tetateta[teta.ind1] <- BITS1$der3C.derp1tetateta
der3C.p1p1teta[teta.ind1] <- BITS1$der3C.p1p1teta
der2h.derp2teta[teta.ind1] <- BITS1$der2h.derp2teta
der2h.derp2p2[teta.ind1] <- BITS1$der2h.derp2p2
der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
}
if( length(teta2) != 0){der3C.derp1p1p1[teta.ind2] <- BITS2$der3C.derp1p1p1
der2h.derteta.teta.st[teta.ind2] <- BITS2$der2h.derteta.teta.st
der3C.derp1tetateta[teta.ind2] <- BITS2$der3C.derp1tetateta
der3C.p1p1teta[teta.ind2] <- BITS2$der3C.p1p1teta
der2h.derp2teta[teta.ind2] <- BITS2$der2h.derp2teta
der2h.derp2p2[teta.ind2] <- BITS2$der2h.derp2p2
der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
}
########################
########################
d2l.be1.be1 <- -VC$weights*(
VC$c11*( (der2pdf1.dereta1 * pdf1 - derpdf1.dereta1^2) / pdf1^2 +
((der2c.derp1.derp1 * derp1.dereta1^2 + der2h.derp1p1 * der2p1.dereta1eta1) * c.copula2.be1be2 + -derc.dereta1^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1^2 + c.copula.be1^-1 * c.copula2.be1 * der2p1.dereta1eta1 + #-der2p1.dereta1eta1
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 )
)
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1), VC$X1)
be2.be2 <- -(
crossprod(VC$weights*VC$c11*c(-c.copula2.be1be2^-2*der2h.derp1p2^2*dS2eta2^2 + c.copula2.be1be2^-1*der2c.derp2.derp2*dS2eta2^2 + c.copula2.be1be2^-1*der2h.derp1p2*d2S2eta2 -dS2eta2^-2*d2S2eta2^2 + dS2eta2^-1*d3S2eta2)*dereta2derb2, dereta2derb2) +
diag( colSums( t( t(VC$weights*VC$c11*c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*VC$X2)*der2.par2 ) ) ) +
crossprod(VC$weights*VC$c11*c(-Xd2P^-2)*der2eta2dery2b2, der2eta2dery2b2) +
diag( colSums( t( t(VC$weights*VC$c11*c(Xd2P^-1)*VC$Xd2)*der2.par2 ) ) ) +
crossprod(VC$weights*VC$c10*c(-c.copula.be1^-2*c.copula2.be1be2^2*dS2eta2^2 + c.copula.be1^-1*der2h.derp1p2*dS2eta2^2 + c.copula.be1^-1*c.copula2.be1be2*d2S2eta2)*dereta2derb2, dereta2derb2) +
diag( colSums( t( t(VC$weights*VC$c10*c( c.copula.be1^-1*c.copula2.be1be2*dS2eta2 )*VC$X2)*der2.par2 ) ) )
)
be1.be2 <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p2*der2h.derp1p1 + c.copula2.be1be2^-1*der2c.derp1.derp2)*derp1.dereta1*dS2eta2)*VC$X1, dereta2derb2) +
crossprod(VC$weights*VC$c10*c((-c.copula.be1^-2*c.copula2.be1be2*c.copula2.be1 + c.copula.be1^-1*der2h.derp1p1)*derp1.dereta1*dS2eta2)*VC$X1, dereta2derb2)
)
if(VC$BivD %in% c("GAL180","C180","J180","G180","GAL90","C90","J90","G90","GAL270","C270","J270","G270") ) rotConst <- -1
if(VC$BivD %in% VC$BivD2) rotConst <- VC$my.env$signind
d2l.rho.rho <- -(
VC$weights*VC$c11*( -c.copula2.be1be2^-2*der2h.derp1teta^2*derteta.derteta.st^2 + c.copula2.be1be2^-1*der2c.derrho.derrho*derteta.derteta.st^2 + c.copula2.be1be2^-1*der2h.derp1teta*der2teta.derteta.stteta.st) +
VC$weights*VC$c10*( -c.copula.be1^-2*c.copula2.be1t^2*derteta.derteta.st^2 + c.copula.be1^-1*der3C.derp1tetateta*derteta.derteta.st^2 + rotConst*c.copula.be1^-1*c.copula2.be1t*der2teta.derteta.stteta.st )
)
rho.rho <- crossprod(X4*c(d2l.rho.rho), X4)
be1.rho <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p1*der2h.derp1teta + c.copula2.be1be2^-1*der2c.derp1.derrho)*derp1.dereta1*derteta.derteta.st)*VC$X1, X4) +
crossprod(VC$weights*VC$c10*c((rotConst*-c.copula.be1^-2*c.copula2.be1*c.copula2.be1t + c.copula.be1^-1*der3C.p1p1teta)*derp1.dereta1*derteta.derteta.st)*VC$X1, X4)
)
be2.rho <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p2*der2h.derp1teta + c.copula2.be1be2^-1*der2c.derp2.derrho)*dS2eta2*derteta.derteta.st)*dereta2derb2, X4) +
crossprod(VC$weights*VC$c10*c((rotConst*-c.copula.be1^-2*c.copula2.be1be2*c.copula2.be1t + c.copula.be1^-1*der2h.derp1teta)*dS2eta2*derteta.derteta.st)*dereta2derb2, X4)
)
d2l.sigma21.sigma21 <- -VC$weights*(
VC$c11*( (der2pdf1.dersigma21.st2 * pdf1 - derpdf1.dersigma21.st^2) / pdf1^2 +
((der2c.derp1.derp1*derp1.dersigma21.st^2+der2h.derp1p1*der2p1.dersigma21.st2)*c.copula2.be1be2 - derc.dersigma21.st^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dersigma21.st^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dersigma21.st^2 + c.copula.be1^-1 * c.copula2.be1 * der2p1.dersigma21.st2 +
der2pdf1.dersigma21.st2 * pdf1^-1 + derpdf1.dersigma21.st^2*-pdf1^-2 )
)
sigma21.sigma21 <- crossprod(X3*c(d2l.sigma21.sigma21),X3)
d2l.be1.sigma21 <- -VC$weights*(
VC$c11*( (der2pdf1.dereta1dersigma21.st * pdf1 - derpdf1.dereta1*derpdf1.dersigma21.st) / pdf1^2 +
((der2c.derp1.derp1 * derp1.dereta1* derp1.dersigma21.st+der2h.derp1p1*der2p1.dereta1dersigma21.st) * c.copula2.be1be2 - derc.dereta1*derc.dersigma21.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1*derp1.dersigma21.st + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1*derp1.dersigma21.st + c.copula.be1^-1 * c.copula2.be1 * der2p1.dereta1dersigma21.st +
der2pdf1.dereta1dersigma21.st * pdf1^-1 + derpdf1.dereta1*derpdf1.dersigma21.st*-pdf1^-2 )
)
be1.sigma21 <- crossprod(VC$X1*c(d2l.be1.sigma21), X3)
dl.dbe2 <- -VC$weights*(
VC$c11*( c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*dereta2derb2 )
+
VC$c10*( c(c.copula.be1^-1*c.copula2.be1be2*dS2eta2)*dereta2derb2 )
)
be2.sigma21 <- -(
crossprod( VC$weights*VC$c11*( c(-(c.copula2.be1be2)^-2*derc.dersigma21.st*der2h.derp1p2*dS2eta2 + c.copula2.be1be2^-1*der2c.derp1.derp2*derp1.dersigma21.st*dS2eta2 )*dereta2derb2 ), X3)
+
crossprod( VC$weights*VC$c10*( c(-(c.copula.be1)^-2*c.copula2.be1*derp1.dersigma21.st*c.copula2.be1be2*dS2eta2 + c.copula.be1^-1*der2h.derp1p1*derp1.dersigma21.st*dS2eta2)*dereta2derb2 ) , X3)
)
d2l.rho.sigma21 <- -VC$weights*(
VC$c11*( (der2c.derp1.derrho*derp1.dersigma21.st*derteta.derteta.st*c.copula2.be1be2 - derc.dersigma21.st*der2h.derp1teta *derteta.derteta.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1 * derp1.dersigma21.st + c.copula.be1^-1 * der3C.p1p1teta *derteta.derteta.st*derp1.dersigma21.st )
)
rho.sigma21 <- crossprod(X3*c(d2l.rho.sigma21), X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sigma21.sigma21, rho.sigma21),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma21), rho.rho ) )
########################################################################
if(VC$extra.regI == "pC") H <- regH(H, type = 1)
S.h <- ps$S.h
if( length(S.h) != 1){
S.h1 <- 0.5*crossprod(params,S.h)%*%params # as(S.h, "sparseMatrix") not sure about advantage...
S.h2 <- S.h%*%params
} else S.h <- S.h1 <- S.h2 <- 0
S.res <- res
res <- S.res + S.h1
G <- G + S.h2
H <- H + S.h
if(VC$extra.regI == "sED") H <- regH(H, type = 2)
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2,
l=S.res, l.ln = l.ln, l.par=l.par, ps = ps,
eta1=eta1, eta2=eta2, etad=etad, etas1 = sigma21.st, etas2 = 1,
BivD=VC$BivD, p1 = p1, p2 = p2, pdf1 = pdf1, pdf2 = -dS2eta2,
c.copula.be2 = c.copula.be2,
c.copula.be1 = c.copula.be1,
c.copula2.be1be2 = c.copula2.be1be2,
dl.dbe1 = NULL,
dl.dbe2 = NULL,
dl.dteta.st = NULL,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
KironmoyDas/KD-STAT0035-GMupdate documentation built on Feb. 15, 2021, 12:17 a.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions bcontSurvGcont2Surv
bcontSurvGcont2Surv <- function(params, respvec, VC, ps, AT = FALSE){
p1 <- p2 <- pdf1 <- pdf2 <- c.copula.be2 <- c.copula.be1 <- c.copula2.be1be2 <- NA
rotConst <- 1
etad <- etas1 <- etas2 <- l.ln <- NULL
params1 <- params[1:VC$X1.d2]
params2 <- params[(VC$X1.d2 + 1):(VC$X1.d2 + VC$X2.d2)]
params2[VC$mono.sm.pos2] <- exp( params2[VC$mono.sm.pos2] )
eta1 <- eta.tr(VC$X1%*%params1, VC$margins[1])
eta2 <- VC$X2%*%params2
etad <- etas1 <- etas2 <- l.ln <- NULL
Xd2P <- VC$Xd2%*%params2
Xd2P <- ifelse(Xd2P < VC$min.dn, VC$min.dn, Xd2P ) # safety thing, never used as per model definition
if(is.null(VC$X3)){
X3 <- X4 <- matrix(1, VC$n, 1)
sigma21.st <- etas1 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
}
if(!is.null(VC$X3)){
X3 <- VC$X3; X4 <- VC$X4
sigma21.st <- etas1 <- X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
teta.st <- etad <- X4%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2)]
}
##################
## Transformations
##################
sstr1 <- esp.tr(sigma21.st, VC$margins[1])
sigma21.st <- sstr1$vrb.st
sigma21 <- sstr1$vrb
resT <- teta.tr(VC, teta.st)
teta.st1 <- teta.st2 <- teta.st <- resT$teta.st
teta1 <- teta2 <- teta <- resT$teta
##################
Cop1 <- Cop2 <- VC$BivD
nC1 <- nC2 <- VC$nC
teta.ind1 <- as.logical(c(1,0,round(runif(VC$n-2))) )
teta.ind2 <- teta.ind1 == FALSE
if(!(VC$BivD %in% VC$BivD2) && length(teta.st) > 1){
teta.st1 <- teta.st[teta.ind1]
teta.st2 <- teta.st[teta.ind2]
teta1 <- teta[teta.ind1]
teta2 <- teta[teta.ind2]
}
###
if(VC$BivD %in% VC$BivD2){
if(VC$BivD %in% VC$BivD2[c(1:4,13:16)]) teta.ind1 <- ifelse(VC$my.env$signind*teta > exp(VC$zerov), TRUE, FALSE)
if(VC$BivD %in% VC$BivD2[5:12]) teta.ind1 <- ifelse(VC$my.env$signind*teta > exp(VC$zerov) + 1, TRUE, FALSE)
teta.ind2 <- teta.ind1 == FALSE
VC$my.env$signind <- ifelse(teta.ind1 == TRUE, 1, -1)
teta1 <- teta[teta.ind1]
teta2 <- -teta[teta.ind2]
teta.st1 <- teta.st[teta.ind1]
teta.st2 <- teta.st[teta.ind2]
if(length(teta) == 1) teta.ind2 <- teta.ind1 <- rep(TRUE, VC$n)
Cop1Cop2R <- Cop1Cop2(VC$BivD)
Cop1 <- Cop1Cop2R$Cop1
Cop2 <- Cop1Cop2R$Cop2
nC1 <- VC$ct[which(VC$ct[,1] == Cop1),2]
nC2 <- VC$ct[which(VC$ct[,1] == Cop2),2]
}
##################
dHs1 <- distrHs(respvec$y1, eta1, sigma21, sigma21.st, nu = 1, nu.st = 1, margin2 = VC$margins[1], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
p1 <- dHs1$p2
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derp1.dereta1 <- dHs1$derp2.dereta2
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
der2pdf1.dereta1 <- dHs1$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2pdf1.dereta1dersigma21.st <- dHs1$der2pdf2.dereta2dersigma2.st
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
pd2 <- probmS(eta2, VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
p2 <- pd2$pr
dS2eta2 <- pd2$dS
d2S2eta2 <- pd2$d2S
d3S2eta2 <- pd2$d3S
##################
if( length(teta1) != 0) dH1 <- copgHs(p1[teta.ind1], p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if( length(teta2) != 0) dH2 <- copgHs(p1[teta.ind2], p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
c.copula2.be1be2 <- c.copula.be1 <- c.copula.be2 <- p00 <- c.copula.theta <- c.copula.thet <- bit1.th2ATE <- NA
if( length(teta1) != 0){ c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula.be1[teta.ind1] <- dH1$c.copula.be1
c.copula.theta[teta.ind1] <- dH1$c.copula.theta
c.copula.thet[teta.ind1] <- dH1$c.copula.thet
bit1.th2ATE[teta.ind1] <- dH1$bit1.th2ATE
}
# CHECK THAT WE NEED ALL BITS ABOVE
if( length(teta2) != 0){ c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula.be1[teta.ind2] <- dH2$c.copula.be1
c.copula.theta[teta.ind2] <- dH2$c.copula.theta
c.copula.thet[teta.ind2] <- dH2$c.copula.thet
bit1.th2ATE[teta.ind2] <- dH2$bit1.th2ATE
}
l.par <- VC$weights*( VC$c11*( log(c.copula2.be1be2) + log(pdf1) + log(-dS2eta2) + log(Xd2P) ) +
VC$c10*( log(c.copula.be1) + log(pdf1) )
)
res <- -sum(l.par)
##################
der.par1 <- der2.par1 <- params1; der.par2 <- der2.par2 <- params2
der.par2[-c( VC$mono.sm.pos2 )] <- 1
der2.par2[-c( VC$mono.sm.pos2 )] <- 0
der2eta2dery2b2 <- t(t(VC$Xd2)*der.par2)
dereta2derb2 <- t(t(VC$X2)*der.par2)
##################
##################
if( length(teta1) != 0) BITS1 <- copgHsCont(p1[teta.ind1], p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof - 2))
if( length(teta2) != 0) BITS2 <- copgHsCont(p1[teta.ind2], p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof - 2))
der2h.derp1p1 <- NA
if( length(teta1) != 0) der2h.derp1p1[teta.ind1] <- BITS1$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1[teta.ind2] <- BITS2$der2h.derp1p1
der2h.derp1p2 <- NA
if( length(teta1) != 0) der2h.derp1p2[teta.ind1] <- BITS1$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2[teta.ind2] <- BITS2$der2h.derp1p2
der2h.derp1teta <- NA
derteta.derteta.st <- NA
if( length(teta1) != 0) der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
if( length(teta1) != 0) derteta.derteta.st[teta.ind1] <- BITS1$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st[teta.ind2] <- BITS2$derteta.derteta.st
der2h.derp1teta.st <- der2h.derp1teta * derteta.derteta.st # new bit
derc.dersigma21.st <- der2h.derp1p1 * derp1.dersigma21.st
derc.dereta1 <- der2h.derp1p1 * derp1.dereta1
#################
#################
c.copula2.be1 <- c.copula2.be2 <- c.copula2.be1th <- c.copula2.be2th <- bit1.th2 <- c.copula2.be1t <- c.copula2.be2t <- NA
# CHECK THAT WE NEED ALL this
if( length(teta1) != 0){
c.copula2.be1[teta.ind1] <- dH1$c.copula2.be1
c.copula2.be2[teta.ind1] <- dH1$c.copula2.be2
c.copula2.be1th[teta.ind1] <- dH1$c.copula2.be1th
c.copula2.be2th[teta.ind1] <- dH1$c.copula2.be2th
c.copula2.be1t[teta.ind1] <- dH1$c.copula2.be1t
c.copula2.be2t[teta.ind1] <- dH1$c.copula2.be2t
bit1.th2[teta.ind1] <- dH1$bit1.th2
}
if( length(teta2) != 0){
c.copula2.be1[teta.ind2] <- dH2$c.copula2.be1
c.copula2.be2[teta.ind2] <- dH2$c.copula2.be2
c.copula2.be1th[teta.ind2] <- dH2$c.copula2.be1th
c.copula2.be2th[teta.ind2] <- dH2$c.copula2.be2th
c.copula2.be1t[teta.ind2] <- dH2$c.copula2.be1t
c.copula2.be2t[teta.ind2] <- dH2$c.copula2.be2t
bit1.th2[teta.ind2] <- dH2$bit1.th2
}
#################
#################
dl.dbe1 <- c(-VC$weights*(
VC$c11*( derpdf1.dereta1/pdf1 + derc.dereta1/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1 * derp1.dereta1 + derpdf1.dereta1 * pdf1^-1)
))*VC$X1
dl.dbe1 <- colSums(dl.dbe1)
dl.dbe2 <- -VC$weights*(
VC$c11*( c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*dereta2derb2 +
c(Xd2P^-1)*der2eta2dery2b2 )
+
VC$c10*( c(c.copula.be1^-1*c.copula2.be1be2*dS2eta2)*dereta2derb2 )
)
dl.dbe2 <- colSums(dl.dbe2)
dl.dsigma21.st <- c(-VC$weights*(
VC$c11*( derpdf1.dersigma21.st/pdf1 + derc.dersigma21.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1 * derp1.dersigma21.st + derpdf1.dersigma21.st * pdf1^-1 )
))*X3
dl.dsigma21.st <- colSums(dl.dsigma21.st)
dl.dteta.st <- c(-VC$weights*(
VC$c11*( der2h.derp1teta.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1th )
))*X4
dl.dteta.st <- colSums( dl.dteta.st)
G <- c( dl.dbe1, dl.dbe2, dl.dsigma21.st, dl.dteta.st )
#round(as.numeric(G + VC$S.h%*%params),4)
#round(as.numeric(gr),4)
#################################################################################################
der2c.derrho.derrho <- NA
der2c.derp1.derp1 <- NA
der2c.derp2.derp2 <- NA
der2c.derp1.derp2 <- NA
der2c.derp1.derrho <- NA
der2c.derp2.derrho <- NA
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0){ der2c.derrho.derrho[teta.ind1] <- BITS1$der2c.derrho.derrho
der2c.derp1.derp1[teta.ind1] <- BITS1$der2c.derp1.derp1
der2c.derp2.derp2[teta.ind1] <- BITS1$der2c.derp2.derp2
der2c.derp1.derp2[teta.ind1] <- BITS1$der2c.derp1.derp2
der2c.derp1.derrho[teta.ind1] <- BITS1$der2c.derp1.derrho
der2c.derp2.derrho[teta.ind1] <- BITS1$der2c.derp2.derrho }
if( length(teta2) != 0){ der2c.derrho.derrho[teta.ind2] <- BITS2$der2c.derrho.derrho
der2c.derp1.derp1[teta.ind2] <- BITS2$der2c.derp1.derp1
der2c.derp2.derp2[teta.ind2] <- BITS2$der2c.derp2.derp2
der2c.derp1.derp2[teta.ind2] <- BITS2$der2c.derp1.derp2
der2c.derp1.derrho[teta.ind2] <- BITS2$der2c.derp1.derrho
der2c.derp2.derrho[teta.ind2] <- BITS2$der2c.derp2.derrho }
if( length(teta1) != 0) der2teta.derteta.stteta.st[teta.ind1] <- BITS1$der2teta.derteta.stteta.st
if( length(teta2) != 0) der2teta.derteta.stteta.st[teta.ind2] <- BITS2$der2teta.derteta.stteta.st
########################
der3C.derp1p1p1 <- der3C.derp1tetateta <- der2h.derteta.teta.st <- der3C.p1p1teta <- der2h.derp2teta <- der2h.derp2p2 <- NA
if( length(teta1) != 0){der3C.derp1p1p1[teta.ind1] <- BITS1$der3C.derp1p1p1
der2h.derteta.teta.st[teta.ind1] <- BITS1$der2h.derteta.teta.st
der3C.derp1tetateta[teta.ind1] <- BITS1$der3C.derp1tetateta
der3C.p1p1teta[teta.ind1] <- BITS1$der3C.p1p1teta
der2h.derp2teta[teta.ind1] <- BITS1$der2h.derp2teta
der2h.derp2p2[teta.ind1] <- BITS1$der2h.derp2p2
der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
}
if( length(teta2) != 0){der3C.derp1p1p1[teta.ind2] <- BITS2$der3C.derp1p1p1
der2h.derteta.teta.st[teta.ind2] <- BITS2$der2h.derteta.teta.st
der3C.derp1tetateta[teta.ind2] <- BITS2$der3C.derp1tetateta
der3C.p1p1teta[teta.ind2] <- BITS2$der3C.p1p1teta
der2h.derp2teta[teta.ind2] <- BITS2$der2h.derp2teta
der2h.derp2p2[teta.ind2] <- BITS2$der2h.derp2p2
der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
}
########################
########################
d2l.be1.be1 <- -VC$weights*(
VC$c11*( (der2pdf1.dereta1 * pdf1 - derpdf1.dereta1^2) / pdf1^2 +
((der2c.derp1.derp1 * derp1.dereta1^2 + der2h.derp1p1 * der2p1.dereta1eta1) * c.copula2.be1be2 + -derc.dereta1^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1^2 + c.copula.be1^-1 * c.copula2.be1 * der2p1.dereta1eta1 + #-der2p1.dereta1eta1
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 )
)
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1), VC$X1)
be2.be2 <- -(
crossprod(VC$weights*VC$c11*c(-c.copula2.be1be2^-2*der2h.derp1p2^2*dS2eta2^2 + c.copula2.be1be2^-1*der2c.derp2.derp2*dS2eta2^2 + c.copula2.be1be2^-1*der2h.derp1p2*d2S2eta2 -dS2eta2^-2*d2S2eta2^2 + dS2eta2^-1*d3S2eta2)*dereta2derb2, dereta2derb2) +
diag( colSums( t( t(VC$weights*VC$c11*c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*VC$X2)*der2.par2 ) ) ) +
crossprod(VC$weights*VC$c11*c(-Xd2P^-2)*der2eta2dery2b2, der2eta2dery2b2) +
diag( colSums( t( t(VC$weights*VC$c11*c(Xd2P^-1)*VC$Xd2)*der2.par2 ) ) ) +
crossprod(VC$weights*VC$c10*c(-c.copula.be1^-2*c.copula2.be1be2^2*dS2eta2^2 + c.copula.be1^-1*der2h.derp1p2*dS2eta2^2 + c.copula.be1^-1*c.copula2.be1be2*d2S2eta2)*dereta2derb2, dereta2derb2) +
diag( colSums( t( t(VC$weights*VC$c10*c( c.copula.be1^-1*c.copula2.be1be2*dS2eta2 )*VC$X2)*der2.par2 ) ) )
)
be1.be2 <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p2*der2h.derp1p1 + c.copula2.be1be2^-1*der2c.derp1.derp2)*derp1.dereta1*dS2eta2)*VC$X1, dereta2derb2) +
crossprod(VC$weights*VC$c10*c((-c.copula.be1^-2*c.copula2.be1be2*c.copula2.be1 + c.copula.be1^-1*der2h.derp1p1)*derp1.dereta1*dS2eta2)*VC$X1, dereta2derb2)
)
if(VC$BivD %in% c("GAL180","C180","J180","G180","GAL90","C90","J90","G90","GAL270","C270","J270","G270") ) rotConst <- -1
if(VC$BivD %in% VC$BivD2) rotConst <- VC$my.env$signind
d2l.rho.rho <- -(
VC$weights*VC$c11*( -c.copula2.be1be2^-2*der2h.derp1teta^2*derteta.derteta.st^2 + c.copula2.be1be2^-1*der2c.derrho.derrho*derteta.derteta.st^2 + c.copula2.be1be2^-1*der2h.derp1teta*der2teta.derteta.stteta.st) +
VC$weights*VC$c10*( -c.copula.be1^-2*c.copula2.be1t^2*derteta.derteta.st^2 + c.copula.be1^-1*der3C.derp1tetateta*derteta.derteta.st^2 + rotConst*c.copula.be1^-1*c.copula2.be1t*der2teta.derteta.stteta.st )
)
rho.rho <- crossprod(X4*c(d2l.rho.rho), X4)
be1.rho <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p1*der2h.derp1teta + c.copula2.be1be2^-1*der2c.derp1.derrho)*derp1.dereta1*derteta.derteta.st)*VC$X1, X4) +
crossprod(VC$weights*VC$c10*c((rotConst*-c.copula.be1^-2*c.copula2.be1*c.copula2.be1t + c.copula.be1^-1*der3C.p1p1teta)*derp1.dereta1*derteta.derteta.st)*VC$X1, X4)
)
be2.rho <- -(
crossprod(VC$weights*VC$c11*c((-c.copula2.be1be2^-2*der2h.derp1p2*der2h.derp1teta + c.copula2.be1be2^-1*der2c.derp2.derrho)*dS2eta2*derteta.derteta.st)*dereta2derb2, X4) +
crossprod(VC$weights*VC$c10*c((rotConst*-c.copula.be1^-2*c.copula2.be1be2*c.copula2.be1t + c.copula.be1^-1*der2h.derp1teta)*dS2eta2*derteta.derteta.st)*dereta2derb2, X4)
)
d2l.sigma21.sigma21 <- -VC$weights*(
VC$c11*( (der2pdf1.dersigma21.st2 * pdf1 - derpdf1.dersigma21.st^2) / pdf1^2 +
((der2c.derp1.derp1*derp1.dersigma21.st^2+der2h.derp1p1*der2p1.dersigma21.st2)*c.copula2.be1be2 - derc.dersigma21.st^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dersigma21.st^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dersigma21.st^2 + c.copula.be1^-1 * c.copula2.be1 * der2p1.dersigma21.st2 +
der2pdf1.dersigma21.st2 * pdf1^-1 + derpdf1.dersigma21.st^2*-pdf1^-2 )
)
sigma21.sigma21 <- crossprod(X3*c(d2l.sigma21.sigma21),X3)
d2l.be1.sigma21 <- -VC$weights*(
VC$c11*( (der2pdf1.dereta1dersigma21.st * pdf1 - derpdf1.dereta1*derpdf1.dersigma21.st) / pdf1^2 +
((der2c.derp1.derp1 * derp1.dereta1* derp1.dersigma21.st+der2h.derp1p1*der2p1.dereta1dersigma21.st) * c.copula2.be1be2 - derc.dereta1*derc.dersigma21.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1*derp1.dersigma21.st + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1*derp1.dersigma21.st + c.copula.be1^-1 * c.copula2.be1 * der2p1.dereta1dersigma21.st +
der2pdf1.dereta1dersigma21.st * pdf1^-1 + derpdf1.dereta1*derpdf1.dersigma21.st*-pdf1^-2 )
)
be1.sigma21 <- crossprod(VC$X1*c(d2l.be1.sigma21), X3)
dl.dbe2 <- -VC$weights*(
VC$c11*( c(c.copula2.be1be2^-1*der2h.derp1p2*dS2eta2 + dS2eta2^-1*d2S2eta2)*dereta2derb2 )
+
VC$c10*( c(c.copula.be1^-1*c.copula2.be1be2*dS2eta2)*dereta2derb2 )
)
be2.sigma21 <- -(
crossprod( VC$weights*VC$c11*( c(-(c.copula2.be1be2)^-2*derc.dersigma21.st*der2h.derp1p2*dS2eta2 + c.copula2.be1be2^-1*der2c.derp1.derp2*derp1.dersigma21.st*dS2eta2 )*dereta2derb2 ), X3)
+
crossprod( VC$weights*VC$c10*( c(-(c.copula.be1)^-2*c.copula2.be1*derp1.dersigma21.st*c.copula2.be1be2*dS2eta2 + c.copula.be1^-1*der2h.derp1p1*derp1.dersigma21.st*dS2eta2)*dereta2derb2 ) , X3)
)
d2l.rho.sigma21 <- -VC$weights*(
VC$c11*( (der2c.derp1.derrho*derp1.dersigma21.st*derteta.derteta.st*c.copula2.be1be2 - derc.dersigma21.st*der2h.derp1teta *derteta.derteta.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1 * derp1.dersigma21.st + c.copula.be1^-1 * der3C.p1p1teta *derteta.derteta.st*derp1.dersigma21.st )
)
rho.sigma21 <- crossprod(X3*c(d2l.rho.sigma21), X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sigma21.sigma21, rho.sigma21),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma21), rho.rho ) )
########################################################################
if(VC$extra.regI == "pC") H <- regH(H, type = 1)
S.h <- ps$S.h
if( length(S.h) != 1){
S.h1 <- 0.5*crossprod(params,S.h)%*%params # as(S.h, "sparseMatrix") not sure about advantage...
S.h2 <- S.h%*%params
} else S.h <- S.h1 <- S.h2 <- 0
S.res <- res
res <- S.res + S.h1
G <- G + S.h2
H <- H + S.h
if(VC$extra.regI == "sED") H <- regH(H, type = 2)
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2,
l=S.res, l.ln = l.ln, l.par=l.par, ps = ps,
eta1=eta1, eta2=eta2, etad=etad, etas1 = sigma21.st, etas2 = 1,
BivD=VC$BivD, p1 = p1, p2 = p2, pdf1 = pdf1, pdf2 = -dS2eta2,
c.copula.be2 = c.copula.be2,
c.copula.be1 = c.copula.be1,
c.copula2.be1be2 = c.copula2.be1be2,
dl.dbe1 = NULL,
dl.dbe2 = NULL,
dl.dteta.st = NULL,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
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