R/bcontSurv.R
In KironmoyDas/KD-STAT0035-GMupdate: Generalised Joint Regression Modelling
Defines functions
bcontSurv
bcontSurv <- function(params, respvec, VC, ps, AT = FALSE){
p1 <- p2 <- pdf1 <- pdf2 <- c.copula.be2 <- c.copula.be1 <- c.copula2.be1be2 <- NA
eta1 <- VC$X1%*%params[1:VC$X1.d2]
eta2 <- VC$X2%*%params[(VC$X1.d2 + 1):(VC$X1.d2 + VC$X2.d2)]
etad <- etas1 <- etas2 <- l.ln <- NULL
if(is.null(VC$X3)){
sigma21.st <- etas1 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
sigma22.st <- etas2 <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 3)]
}
if(!is.null(VC$X3)){
sigma21.st <- etas1 <- VC$X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
sigma22.st <- etas2 <- VC$X4%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2)]
teta.st <- etad <- VC$X5%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2 + VC$X5.d2)]
}
##################
## Transformations
##################
sstr1 <- esp.tr(sigma21.st, VC$margins[1])
sstr2 <- esp.tr(sigma22.st, VC$margins[2])
sigma21.st <- sstr1$vrb.st
sigma22.st <- sstr2$vrb.st
sigma21 <- sstr1$vrb
sigma22 <- sstr2$vrb
eta1 <- eta.tr(eta1, VC$margins[1])
eta2 <- eta.tr(eta2, VC$margins[2])
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)
dHs2 <- distrHs(respvec$y2, eta2, sigma22, sigma22.st, nu = 1, nu.st = 1, margin2=VC$margins[2], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH1 <- copgHs(1-p1[teta.ind1], 1-p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if( length(teta2) != 0) dH2 <- copgHs(1-p1[teta.ind2], 1-p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
c.copula2.be1be2 <- c.copula.be1 <- c.copula.be2 <- p00 <- c.copula.theta <- NA
if( length(teta1) != 0){ c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula.be1[teta.ind1] <- dH1$c.copula.be1
c.copula.be2[teta.ind1] <- dH1$c.copula.be2
c.copula.theta[teta.ind1] <- dH1$c.copula.theta
p00[teta.ind1] <- mm(BiCDF(1-p1[teta.ind1], 1-p2[teta.ind1], nC1, teta1, VC$dof), min.pr = VC$min.pr, max.pr = VC$max.pr )
}
if( length(teta2) != 0){ c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula.be1[teta.ind2] <- dH2$c.copula.be1
c.copula.be2[teta.ind2] <- dH2$c.copula.be2
c.copula.theta[teta.ind2] <- dH2$c.copula.theta
p00[teta.ind2] <- mm(BiCDF(1-p1[teta.ind2], 1-p2[teta.ind2], nC2, teta2, VC$dof), min.pr = VC$min.pr, max.pr = VC$max.pr )
}
l.par <- VC$weights*( VC$c11*( log(c.copula2.be1be2) + log(pdf1) + log(pdf2) ) +
VC$c10*( log(c.copula.be1) + log(pdf1) ) +
VC$c01*( log(c.copula.be2) + log(pdf2) ) +
VC$c00*log(p00)
)
##################
##################
# cont-cont
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
derpdf2.dereta2 <- dHs2$derpdf2.dereta2
derpdf2.dersigma22.st <- dHs2$derpdf2.dersigma2.st
derp1.dereta1 <- dHs1$derp2.dereta2
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derp2.dereta2 <- dHs2$derp2.dereta2
derp2.dersigma22.st <- dHs2$derp2.dersigma.st
if( length(teta1) != 0) BITS1 <- copgHsCont(1-p1[teta.ind1], 1-p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, VC$dof, VC$dof)
if( length(teta2) != 0) BITS2 <- copgHsCont(1-p1[teta.ind2], 1-p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, VC$dof, VC$dof)
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
derc.dereta1 <- der2h.derp1p1 * derp1.dereta1
derc.dersigma21.st <- der2h.derp1p1 * derp1.dersigma21.st
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
derc.dereta2 <- der2h.derp1p2 * derp2.dereta2
derc.dersigma22.st <- der2h.derp1p2 * derp2.dersigma22.st
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
#################
#################
c.copula2.be1 <- c.copula2.be2 <- c.copula2.be1th <- c.copula2.be2th <- bit1.th2 <- c.copula2.be1t <- c.copula2.be2t <- NA
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 <- VC$weights*(
VC$c11*( derpdf1.dereta1/pdf1 + -derc.dereta1/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1 * derp1.dereta1 + derpdf1.dereta1 * pdf1^-1) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be1be2 * derp1.dereta1 ) +
VC$c00*( -derp1.dereta1*c.copula.be1/p00 )
)
dl.dbe2 <- VC$weights*(
VC$c11*( derpdf2.dereta2/pdf2 + -derc.dereta2/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1be2 * derp2.dereta2 ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be2 * derp2.dereta2 + derpdf2.dereta2 * pdf2^-1 ) +
VC$c00*( -derp2.dereta2*c.copula.be2/p00 )
)
dl.dsigma21.st <- VC$weights*(
VC$c11*( derpdf1.dersigma21.st/pdf1 + -derc.dersigma21.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1 * derp1.dersigma21.st + derpdf1.dersigma21.st * pdf1^-1 ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be1be2 * derp1.dersigma21.st ) +
VC$c00*( -derp1.dersigma21.st*c.copula.be1/p00 )
)
dl.dsigma22.st <- VC$weights*(
VC$c11*( derpdf2.dersigma22.st/pdf2 + -derc.dersigma22.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1be2 * derp2.dersigma22.st ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be2 * derp2.dersigma22.st + derpdf2.dersigma22.st * pdf2^-1 ) +
VC$c00*( -derp2.dersigma22.st*c.copula.be2/p00 )
)
dl.dteta.st <- VC$weights*(
VC$c11*( der2h.derp1teta.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1th ) +
VC$c01*( c.copula.be2^-1 * c.copula2.be2th ) +
VC$c00*( c.copula.theta/p00 )
)
#################################################################################################
# cont-cont
der2c.derrho.derrho <- NA
der2c.derp1.derp1 <- NA
der2c.derp2.derp2 <- NA
der2c.derp1.derp2 <- NA
der2c.derp1.derrho <- NA
der2c.derp2.derrho <- NA
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0){ der2c.derrho.derrho[teta.ind1] <- BITS1$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$der2teta.derteta.stteta.st
der2pdf1.dereta1 <- dHs1$der2pdf2.dereta2
der2pdf2.dereta2 <- dHs2$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2pdf2.dersigma22.st2 <- dHs2$der2pdf2.dersigma2.st2
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p2.dereta2eta2 <- dHs2$der2p2.dereta2eta2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2p2.dersigma22.st2 <- dHs2$der2p2.dersigma2.st2
der2pdf1.dereta1dersigma21.st <- dHs1$der2pdf2.dereta2dersigma2.st
der2pdf2.dereta2dersigma22.st <- dHs2$der2pdf2.dereta2dersigma2.st
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
der2p2.dereta2dersigma22.st <- dHs2$der2p2.dereta2dersigma2.st
########################
########################
bit1.b1b1 <- c.copula2.be1*derp1.dereta1^2 + -c.copula.be1*der2p1.dereta1eta1
bit1.s1s1 <- c.copula2.be1*derp1.dersigma21.st^2 + -c.copula.be1*der2p1.dersigma21.st2
bit1.b1s1 <- c.copula2.be1*derp1.dereta1*derp1.dersigma21.st + -c.copula.be1*der2p1.dereta1dersigma21.st
bit1.b2s1 <- c.copula2.be1be2*derp2.dereta2*derp1.dersigma21.st
bit1.b1s2 <- c.copula2.be1be2*derp1.dereta1*derp2.dersigma22.st
bit1.b2b2 <- c.copula2.be2*derp2.dereta2^2 + -c.copula.be2*der2p2.dereta2eta2
bit1.s2s2 <- c.copula2.be2*derp2.dersigma22.st^2 + -c.copula.be2*der2p2.dersigma22.st2
bit1.b2s2 <- c.copula2.be2*derp2.dereta2*derp2.dersigma22.st + -c.copula.be2*der2p2.dereta2dersigma22.st
bit1.b1b2 <- c.copula2.be1be2*derp1.dereta1*derp2.dereta2
bit1.b1th <- -c.copula2.be1th*derp1.dereta1
bit1.b2th <- -c.copula2.be2th*derp2.dereta2
bit1.s1th <- -c.copula2.be1th*derp1.dersigma21.st
bit1.s2th <- -c.copula2.be2th*derp2.dersigma22.st
bit1.s1s2 <- c.copula2.be1be2*derp1.dersigma21.st*derp2.dersigma22.st
########################
########################
der3C.derp1p1p1 <- der3C.derp1tetateta <- der2h.derteta.teta.st <- der3C.p1p1teta <- der2h.derp2teta <- der2h.derp2p2 <- NA
if( length(teta1) != 0){der3C.derp1p1p1[teta.ind1] <- BITS1$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$der2h.derp2p2
}
if( length(teta2) != 0){der3C.derp1p1p1[teta.ind2] <- BITS2$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$der2h.derp2p2
}
########################
######################## der2h.derp1p1 * derp1.dereta1
d2l.be1.be1 <- -VC$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 +
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1eta1 ) +
VC$c00*( (bit1.b1b1*p00 - (-c.copula.be1*derp1.dereta1)^2)/p00^2 )
)
d2l.be2.be2 <- -VC$weights*(
VC$c11*( (der2pdf2.dereta2 * pdf2 - derpdf2.dereta2^2) / pdf2^2 +
((der2c.derp2.derp2 * derp2.dereta2^2 + der2h.derp1p2 * -der2p2.dereta2eta2) * c.copula2.be1be2 - derc.dereta2^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dereta2^2 + c.copula.be1^-1 * der2h.derp1p2 * derp2.dereta2^2 + c.copula.be1^-1 * c.copula2.be1be2 * -der2p2.dereta2eta2) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dereta2^2 + c.copula.be2^-1 * der2h.derp2p2 * derp2.dereta2^2 + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dereta2eta2 +
der2pdf2.dereta2 * pdf2^-1 + derpdf2.dereta2^2*-pdf2^-2 ) +
VC$c00*( (bit1.b2b2*p00 - (-c.copula.be2*derp2.dereta2)^2)/p00^2 )
)
####################################################
####################################################
if( !(VC$BivD %in% VC$BivD2) ){
if(VC$BivD %in% c("GAL90","C90","GAL180","C180","GAL270","C270","J90","J180","J270","G90","G180","G270")){
bit2rho <- VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th^2 + c.copula.be1^-1 * der3C.derp1tetateta * derteta.derteta.st^2 - c.copula.be1^-1 * c.copula2.be1t * der2teta.derteta.stteta.st)
bit3rho <- VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th^2 + c.copula.be2^-1 * der2h.derteta.teta.st * derteta.derteta.st^2 - c.copula.be2^-1 * c.copula2.be2t * der2teta.derteta.stteta.st)
}else{
bit2rho <- VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th^2 + c.copula.be1^-1 * der3C.derp1tetateta * derteta.derteta.st^2 + c.copula.be1^-1 * c.copula2.be1t * der2teta.derteta.stteta.st)
bit3rho <- VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th^2 + c.copula.be2^-1 * der2h.derteta.teta.st * derteta.derteta.st^2 + c.copula.be2^-1 * c.copula2.be2t * der2teta.derteta.stteta.st)
}
}
if( VC$BivD %in% VC$BivD2 ){
bit2rho <- bit3rho <- NA
if(Cop1 %in% c("GAL0","C0","J0","G0")){
bit2rho[teta.ind1] <- VC$c10[teta.ind1]*( -(c.copula.be1[teta.ind1])^-2 * c.copula2.be1th[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * der3C.derp1tetateta[teta.ind1] * derteta.derteta.st[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * c.copula2.be1t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
bit3rho[teta.ind1] <- VC$c01[teta.ind1]*( -(c.copula.be2[teta.ind1])^-2 * c.copula2.be2th[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * der2h.derteta.teta.st[teta.ind1] * derteta.derteta.st[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * c.copula2.be2t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
}
if(Cop1 %in% c("GAL180","C180","J180","G180")){
bit2rho[teta.ind1] <- VC$c10[teta.ind1]*( -(c.copula.be1[teta.ind1])^-2 * c.copula2.be1th[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * der3C.derp1tetateta[teta.ind1] * derteta.derteta.st[teta.ind1]^2 - c.copula.be1[teta.ind1]^-1 * c.copula2.be1t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
bit3rho[teta.ind1] <- VC$c01[teta.ind1]*( -(c.copula.be2[teta.ind1])^-2 * c.copula2.be2th[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * der2h.derteta.teta.st[teta.ind1] * derteta.derteta.st[teta.ind1]^2 - c.copula.be2[teta.ind1]^-1 * c.copula2.be2t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
}
if(Cop2 %in% c("GAL90","C90","J90","G90","GAL270","C270","J270","G270")){
bit2rho[teta.ind2] <- VC$c10[teta.ind2]*( -(c.copula.be1[teta.ind2])^-2 * c.copula2.be1th[teta.ind2]^2 + c.copula.be1[teta.ind2]^-1 * der3C.derp1tetateta[teta.ind2] * derteta.derteta.st[teta.ind2]^2 - c.copula.be1[teta.ind2]^-1 * c.copula2.be1t[teta.ind2] * der2teta.derteta.stteta.st[teta.ind2])
bit3rho[teta.ind2] <- VC$c01[teta.ind2]*( -(c.copula.be2[teta.ind2])^-2 * c.copula2.be2th[teta.ind2]^2 + c.copula.be2[teta.ind2]^-1 * der2h.derteta.teta.st[teta.ind2] * derteta.derteta.st[teta.ind2]^2 - c.copula.be2[teta.ind2]^-1 * c.copula2.be2t[teta.ind2] * der2teta.derteta.stteta.st[teta.ind2])
}
}
############################
d2l.rho.rho <- -VC$weights*(
VC$c11*( ((der2c.derrho.derrho*derteta.derteta.st^2 + der2h.derp1teta *der2teta.derteta.stteta.st)*c.copula2.be1be2 - der2h.derp1teta.st^2) /c.copula2.be1be2^2 ) +
bit2rho +
bit3rho +
VC$c00*( (bit1.th2*p00 - (c.copula.theta)^2)/p00^2 )
)
###################################################
###################################################
d2l.sigma21.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dersigma21.st^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dersigma21.st^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dersigma21.st2 ) +
VC$c00*( (bit1.s1s1*p00 - (-c.copula.be1*derp1.dersigma21.st)^2)/p00^2 )
)
d2l.sigma22.sigma22 <- -VC$weights*(
VC$c11*( (der2pdf2.dersigma22.st2 * pdf2 - derpdf2.dersigma22.st^2) / pdf2^2 +
((der2c.derp2.derp2*derp2.dersigma22.st^2+der2h.derp1p2*-der2p2.dersigma22.st2)*c.copula2.be1be2 - derc.dersigma22.st^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dersigma22.st^2 + c.copula.be1^-1 * der2h.derp1p2 * derp2.dersigma22.st^2 + c.copula.be1^-1 * c.copula2.be1be2 *
-der2p2.dersigma22.st2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dersigma22.st^2 + c.copula.be2^-1 * der2h.derp2p2 * derp2.dersigma22.st^2 + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dersigma22.st2 +
der2pdf2.dersigma22.st2 * pdf2^-1 + derpdf2.dersigma22.st^2*-pdf2^-2 ) +
VC$c00*( (bit1.s2s2*p00 - (-c.copula.be2*derp2.dersigma22.st)^2)/p00^2 )
)
d2l.be1.be2 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dereta1*derp2.dereta2*c.copula2.be1be2 - derc.dereta1*derc.dereta2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dereta1 * derp2.dereta2 + c.copula.be1^-1 * der2h.derp1p1 * derp1.dereta1 * derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dereta1 * derp2.dereta2 + c.copula.be2^-1 * der2h.derp1p2 * derp1.dereta1 * derp2.dereta2 ) +
VC$c00*( (bit1.b1b2*p00 - (c.copula.be1*derp1.dereta1*c.copula.be2*derp2.dereta2))/p00^2 )
)
d2l.be1.rho <- -VC$weights*(
VC$c11*( (der2c.derp1.derrho *-derp1.dereta1*derteta.derteta.st* c.copula2.be1be2 - -derc.dereta1*der2h.derp1teta*derteta.derteta.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1 * - derp1.dereta1 + c.copula.be1^-1 * der3C.p1p1teta *derteta.derteta.st*- derp1.dereta1) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be1be2 * - derp1.dereta1 + c.copula.be2^-1 * der2h.derp1teta *derteta.derteta.st*- derp1.dereta1 ) +
VC$c00*( (bit1.b1th*p00 - (-c.copula.be1*derp1.dereta1*c.copula.theta))/p00^2 )
)
d2l.be2.rho <- -VC$weights*(
VC$c11*( (der2c.derp2.derrho *-derp2.dereta2*derteta.derteta.st* c.copula2.be1be2 - -derc.dereta2*der2h.derp1teta*derteta.derteta.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1be2 * - derp2.dereta2 + c.copula.be1^-1 * der2h.derp1teta *derteta.derteta.st*- derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be2 * - derp2.dereta2 + c.copula.be2^-1 * der2h.derp2teta *derteta.derteta.st*- derp2.dereta2 ) +
VC$c00*( (bit1.b2th*p00 - (-c.copula.be2*derp2.dereta2*c.copula.theta))/p00^2 )
)
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$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1^2 + c.copula.be1^-1 * c.copula2.be1 * - der2p1.dereta1eta1 +
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1eta1 ) +
VC$c00*( (bit1.b1b1*p00 - (-c.copula.be1*derp1.dereta1)^2)/p00^2 )
)
d2l.be1.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1*derp1.dersigma21.st + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1*derp1.dersigma21.st + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1dersigma21.st ) +
VC$c00*( (bit1.b1s1*p00 - c.copula.be1^2*derp1.dereta1*derp1.dersigma21.st)/p00^2 )
)
d2l.be2.sigma22 <- -VC$weights*(
VC$c11*( (der2pdf2.dereta2dersigma22.st * pdf2 - derpdf2.dereta2*derpdf2.dersigma22.st) / pdf2^2 +
((der2c.derp2.derp2 * derp2.dereta2* derp2.dersigma22.st+der2h.derp1p2*-der2p2.dereta2dersigma22.st) * c.copula2.be1be2 - derc.dereta2*derc.dersigma22.st) /c.copula2.be1be2^2 ) +
VC$c10*(-(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be1^-1 * c.copula2.be1be2 * -der2p2.dereta2dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp2p2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dereta2dersigma22.st +
der2pdf2.dereta2dersigma22.st * pdf2^-1 + derpdf2.dereta2*derpdf2.dersigma22.st*-pdf2^-2 ) +
VC$c00*( (bit1.b2s2*p00 - c.copula.be2^2*derp2.dereta2*derp2.dersigma22.st)/p00^2 )
)
d2l.be2.sigma21 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp2.dereta2*derp1.dersigma21.st* c.copula2.be1be2 - derc.dereta2*derc.dersigma21.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dersigma21.st * derp2.dereta2 + c.copula.be1^-1 * der2h.derp1p1 * derp1.dersigma21.st * derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dersigma21.st * derp2.dereta2 + c.copula.be2^-1 * der2h.derp1p2 * derp1.dersigma21.st * derp2.dereta2 ) +
VC$c00*( (bit1.b2s1*p00 - (c.copula.be2*derp2.dereta2*c.copula.be1*derp1.dersigma21.st))/p00^2 )
)
d2l.be1.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dereta1*derp2.dersigma22.st* c.copula2.be1be2 - derc.dereta1*derc.dersigma22.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dereta1 * derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p1 * derp1.dereta1 * derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dereta1 * derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp1p2 * derp1.dereta1 * derp2.dersigma22.st ) +
VC$c00*( (bit1.b1s2*p00 - (c.copula.be1*derp1.dereta1*c.copula.be2*derp2.dersigma22.st))/p00^2 )
)
d2l.rho.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be1be2 * - derp1.dersigma21.st + c.copula.be2^-1 * der2h.derp1teta *derteta.derteta.st*- derp1.dersigma21.st ) +
VC$c00*( (bit1.s1th*p00 - (-c.copula.be1*derp1.dersigma21.st*c.copula.theta))/p00^2 )
)
d2l.rho.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp2.derrho*-derp2.dersigma22.st*derteta.derteta.st*c.copula2.be1be2 - -derc.dersigma22.st*der2h.derp1teta *derteta.derteta.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1be2 * - derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1teta *derteta.derteta.st*- derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be2 * - derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp2teta *derteta.derteta.st*- derp2.dersigma22.st ) +
VC$c00*( (bit1.s2th*p00 - (-c.copula.be2*derp2.dersigma22.st*c.copula.theta))/p00^2 )
)
d2l.sigma21.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dersigma21.st*derp2.dersigma22.st* c.copula2.be1be2 - derc.dersigma21.st*derc.dersigma22.st ) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dersigma21.st * derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p1 * derp1.dersigma21.st * derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dersigma21.st * derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp1p2 * derp1.dersigma21.st * derp2.dersigma22.st ) +
VC$c00*( (bit1.s1s2*p00 - (c.copula.be1*derp1.dersigma21.st*c.copula.be2*derp2.dersigma22.st))/p00^2 )
)
if( is.null(VC$X3) ){
G <- -c(colSums( c(dl.dbe1)*VC$X1 ),
colSums( c(dl.dbe2)*VC$X2 ),
sum( dl.dsigma21.st ),
sum( dl.dsigma22.st ),
sum( dl.dteta.st ) )
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1),VC$X1)
be2.be2 <- crossprod(VC$X2*c(d2l.be2.be2),VC$X2)
be1.be2 <- crossprod(VC$X1*c(d2l.be1.be2),VC$X2)
be1.rho <- t(t(rowSums(t(VC$X1*c(d2l.be1.rho)))))
be1.sigma21 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma21)))))
be1.sigma22 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma22)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma21 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma21)))))
be2.sigma22 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma22)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.sigma22, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.sigma22, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sum(d2l.sigma21.sigma21), sum(d2l.sigma21.sigma22), sum(d2l.rho.sigma21)),
cbind( t(be1.sigma22) , t(be2.sigma22) , sum(d2l.sigma21.sigma22), sum(d2l.sigma22.sigma22), sum(d2l.rho.sigma22)),
cbind( t(be1.rho) , t(be2.rho) , sum(d2l.rho.sigma21), sum(d2l.rho.sigma22), sum(d2l.rho.rho) )
)
}
if( !is.null(VC$X3) ){
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums(c(dl.dsigma21.st)*VC$X3 ) ,
colSums(c(dl.dsigma22.st)*VC$X4 ) ,
colSums( c(dl.dteta.st)*VC$X5 ) )
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1),VC$X1)
be2.be2 <- crossprod(VC$X2*c(d2l.be2.be2),VC$X2)
be1.be2 <- crossprod(VC$X1*c(d2l.be1.be2),VC$X2)
be1.rho <- crossprod(VC$X1*c(d2l.be1.rho),VC$X5)
be2.rho <- crossprod(VC$X2*c(d2l.be2.rho),VC$X5)
be1.sigma21 <- crossprod(VC$X1*c(d2l.be1.sigma21),VC$X3)
be1.sigma22 <- crossprod(VC$X1*c(d2l.be1.sigma22),VC$X4)
be2.sigma21 <- crossprod(VC$X2*c(d2l.be2.sigma21),VC$X3)
be2.sigma22 <- crossprod(VC$X2*c(d2l.be2.sigma22),VC$X4)
sigma21.sigma21 <- crossprod(VC$X3*c(d2l.sigma21.sigma21),VC$X3)
sigma21.sigma22 <- crossprod(VC$X3*c(d2l.sigma21.sigma22),VC$X4)
rho.sigma21 <- crossprod(VC$X3*c(d2l.rho.sigma21),VC$X5)
sigma22.sigma22 <- crossprod(VC$X4*c(d2l.sigma22.sigma22),VC$X4)
rho.sigma22 <- crossprod(VC$X4*c(d2l.rho.sigma22),VC$X5)
rho.rho <- crossprod(VC$X5*c(d2l.rho.rho),VC$X5)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.sigma22, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.sigma22, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sigma21.sigma21, sigma21.sigma22, rho.sigma21),
cbind( t(be1.sigma22) , t(be2.sigma22) , t(sigma21.sigma22), sigma22.sigma22, rho.sigma22),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma21), t(rho.sigma22), rho.rho ) )
}
res <- -sum(l.par)
if(VC$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)
if( VC$margins[1] == "LN" || VC$margins[2] == "LN"){
if(VC$margins[1] == "LN") dHs1 <- distrHsAT(exp(respvec$y1), eta1, sigma21, 1, margin2=VC$margins[1], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if(VC$margins[2] == "LN") dHs2 <- distrHsAT(exp(respvec$y2), eta2, sigma22, 1, margin2=VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH1 <- copgHsAT(p1[teta.ind1], p2[teta.ind1], teta1, Cop1, Ln = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
if( length(teta2) != 0) dH2 <- copgHsAT(p1[teta.ind2], p2[teta.ind2], teta2, Cop2, Ln = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
c.copula2.be1be2 <- NA
if( length(teta1) != 0) c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
l.ln <- -sum( VC$weights*( log(pdf1) + log(pdf2) + log(c.copula2.be1be2) ) )
}
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2,
l=S.res, l.ln = l.ln, l.par=l.par, ps = ps,
eta1=eta1, eta2=eta2, etad=etad, etas1 = etas1, etas2 = etas2,
BivD=VC$BivD, p1 = p1, p2 = p2, pdf1 = pdf1, pdf2 = pdf2,
c.copula.be2 = c.copula.be2,
c.copula.be1 = c.copula.be1,
c.copula2.be1be2 = c.copula2.be1be2,
dl.dbe1 =dl.dbe1,
dl.dbe2 =dl.dbe2,
dl.dsigma21.st =dl.dsigma21.st,
dl.dsigma22.st =dl.dsigma22.st,
dl.dteta.st =dl.dteta.st,
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 bcontSurv
bcontSurv <- function(params, respvec, VC, ps, AT = FALSE){
p1 <- p2 <- pdf1 <- pdf2 <- c.copula.be2 <- c.copula.be1 <- c.copula2.be1be2 <- NA
eta1 <- VC$X1%*%params[1:VC$X1.d2]
eta2 <- VC$X2%*%params[(VC$X1.d2 + 1):(VC$X1.d2 + VC$X2.d2)]
etad <- etas1 <- etas2 <- l.ln <- NULL
if(is.null(VC$X3)){
sigma21.st <- etas1 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
sigma22.st <- etas2 <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 3)]
}
if(!is.null(VC$X3)){
sigma21.st <- etas1 <- VC$X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
sigma22.st <- etas2 <- VC$X4%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2)]
teta.st <- etad <- VC$X5%*%params[(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2 + VC$X4.d2 + VC$X5.d2)]
}
##################
## Transformations
##################
sstr1 <- esp.tr(sigma21.st, VC$margins[1])
sstr2 <- esp.tr(sigma22.st, VC$margins[2])
sigma21.st <- sstr1$vrb.st
sigma22.st <- sstr2$vrb.st
sigma21 <- sstr1$vrb
sigma22 <- sstr2$vrb
eta1 <- eta.tr(eta1, VC$margins[1])
eta2 <- eta.tr(eta2, VC$margins[2])
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)
dHs2 <- distrHs(respvec$y2, eta2, sigma22, sigma22.st, nu = 1, nu.st = 1, margin2=VC$margins[2], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH1 <- copgHs(1-p1[teta.ind1], 1-p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if( length(teta2) != 0) dH2 <- copgHs(1-p1[teta.ind2], 1-p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof, VC$dof, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
c.copula2.be1be2 <- c.copula.be1 <- c.copula.be2 <- p00 <- c.copula.theta <- NA
if( length(teta1) != 0){ c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula.be1[teta.ind1] <- dH1$c.copula.be1
c.copula.be2[teta.ind1] <- dH1$c.copula.be2
c.copula.theta[teta.ind1] <- dH1$c.copula.theta
p00[teta.ind1] <- mm(BiCDF(1-p1[teta.ind1], 1-p2[teta.ind1], nC1, teta1, VC$dof), min.pr = VC$min.pr, max.pr = VC$max.pr )
}
if( length(teta2) != 0){ c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula.be1[teta.ind2] <- dH2$c.copula.be1
c.copula.be2[teta.ind2] <- dH2$c.copula.be2
c.copula.theta[teta.ind2] <- dH2$c.copula.theta
p00[teta.ind2] <- mm(BiCDF(1-p1[teta.ind2], 1-p2[teta.ind2], nC2, teta2, VC$dof), min.pr = VC$min.pr, max.pr = VC$max.pr )
}
l.par <- VC$weights*( VC$c11*( log(c.copula2.be1be2) + log(pdf1) + log(pdf2) ) +
VC$c10*( log(c.copula.be1) + log(pdf1) ) +
VC$c01*( log(c.copula.be2) + log(pdf2) ) +
VC$c00*log(p00)
)
##################
##################
# cont-cont
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
derpdf2.dereta2 <- dHs2$derpdf2.dereta2
derpdf2.dersigma22.st <- dHs2$derpdf2.dersigma2.st
derp1.dereta1 <- dHs1$derp2.dereta2
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derp2.dereta2 <- dHs2$derp2.dereta2
derp2.dersigma22.st <- dHs2$derp2.dersigma.st
if( length(teta1) != 0) BITS1 <- copgHsCont(1-p1[teta.ind1], 1-p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, VC$dof, VC$dof)
if( length(teta2) != 0) BITS2 <- copgHsCont(1-p1[teta.ind2], 1-p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, VC$dof, VC$dof)
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
derc.dereta1 <- der2h.derp1p1 * derp1.dereta1
derc.dersigma21.st <- der2h.derp1p1 * derp1.dersigma21.st
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
derc.dereta2 <- der2h.derp1p2 * derp2.dereta2
derc.dersigma22.st <- der2h.derp1p2 * derp2.dersigma22.st
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
#################
#################
c.copula2.be1 <- c.copula2.be2 <- c.copula2.be1th <- c.copula2.be2th <- bit1.th2 <- c.copula2.be1t <- c.copula2.be2t <- NA
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 <- VC$weights*(
VC$c11*( derpdf1.dereta1/pdf1 + -derc.dereta1/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1 * derp1.dereta1 + derpdf1.dereta1 * pdf1^-1) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be1be2 * derp1.dereta1 ) +
VC$c00*( -derp1.dereta1*c.copula.be1/p00 )
)
dl.dbe2 <- VC$weights*(
VC$c11*( derpdf2.dereta2/pdf2 + -derc.dereta2/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1be2 * derp2.dereta2 ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be2 * derp2.dereta2 + derpdf2.dereta2 * pdf2^-1 ) +
VC$c00*( -derp2.dereta2*c.copula.be2/p00 )
)
dl.dsigma21.st <- VC$weights*(
VC$c11*( derpdf1.dersigma21.st/pdf1 + -derc.dersigma21.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1 * derp1.dersigma21.st + derpdf1.dersigma21.st * pdf1^-1 ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be1be2 * derp1.dersigma21.st ) +
VC$c00*( -derp1.dersigma21.st*c.copula.be1/p00 )
)
dl.dsigma22.st <- VC$weights*(
VC$c11*( derpdf2.dersigma22.st/pdf2 + -derc.dersigma22.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * -c.copula2.be1be2 * derp2.dersigma22.st ) +
VC$c01*( c.copula.be2^-1 * -c.copula2.be2 * derp2.dersigma22.st + derpdf2.dersigma22.st * pdf2^-1 ) +
VC$c00*( -derp2.dersigma22.st*c.copula.be2/p00 )
)
dl.dteta.st <- VC$weights*(
VC$c11*( der2h.derp1teta.st/c.copula2.be1be2 ) +
VC$c10*( c.copula.be1^-1 * c.copula2.be1th ) +
VC$c01*( c.copula.be2^-1 * c.copula2.be2th ) +
VC$c00*( c.copula.theta/p00 )
)
#################################################################################################
# cont-cont
der2c.derrho.derrho <- NA
der2c.derp1.derp1 <- NA
der2c.derp2.derp2 <- NA
der2c.derp1.derp2 <- NA
der2c.derp1.derrho <- NA
der2c.derp2.derrho <- NA
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0){ der2c.derrho.derrho[teta.ind1] <- BITS1$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$der2teta.derteta.stteta.st
der2pdf1.dereta1 <- dHs1$der2pdf2.dereta2
der2pdf2.dereta2 <- dHs2$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2pdf2.dersigma22.st2 <- dHs2$der2pdf2.dersigma2.st2
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p2.dereta2eta2 <- dHs2$der2p2.dereta2eta2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2p2.dersigma22.st2 <- dHs2$der2p2.dersigma2.st2
der2pdf1.dereta1dersigma21.st <- dHs1$der2pdf2.dereta2dersigma2.st
der2pdf2.dereta2dersigma22.st <- dHs2$der2pdf2.dereta2dersigma2.st
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
der2p2.dereta2dersigma22.st <- dHs2$der2p2.dereta2dersigma2.st
########################
########################
bit1.b1b1 <- c.copula2.be1*derp1.dereta1^2 + -c.copula.be1*der2p1.dereta1eta1
bit1.s1s1 <- c.copula2.be1*derp1.dersigma21.st^2 + -c.copula.be1*der2p1.dersigma21.st2
bit1.b1s1 <- c.copula2.be1*derp1.dereta1*derp1.dersigma21.st + -c.copula.be1*der2p1.dereta1dersigma21.st
bit1.b2s1 <- c.copula2.be1be2*derp2.dereta2*derp1.dersigma21.st
bit1.b1s2 <- c.copula2.be1be2*derp1.dereta1*derp2.dersigma22.st
bit1.b2b2 <- c.copula2.be2*derp2.dereta2^2 + -c.copula.be2*der2p2.dereta2eta2
bit1.s2s2 <- c.copula2.be2*derp2.dersigma22.st^2 + -c.copula.be2*der2p2.dersigma22.st2
bit1.b2s2 <- c.copula2.be2*derp2.dereta2*derp2.dersigma22.st + -c.copula.be2*der2p2.dereta2dersigma22.st
bit1.b1b2 <- c.copula2.be1be2*derp1.dereta1*derp2.dereta2
bit1.b1th <- -c.copula2.be1th*derp1.dereta1
bit1.b2th <- -c.copula2.be2th*derp2.dereta2
bit1.s1th <- -c.copula2.be1th*derp1.dersigma21.st
bit1.s2th <- -c.copula2.be2th*derp2.dersigma22.st
bit1.s1s2 <- c.copula2.be1be2*derp1.dersigma21.st*derp2.dersigma22.st
########################
########################
der3C.derp1p1p1 <- der3C.derp1tetateta <- der2h.derteta.teta.st <- der3C.p1p1teta <- der2h.derp2teta <- der2h.derp2p2 <- NA
if( length(teta1) != 0){der3C.derp1p1p1[teta.ind1] <- BITS1$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$der2h.derp2p2
}
if( length(teta2) != 0){der3C.derp1p1p1[teta.ind2] <- BITS2$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$der2h.derp2p2
}
########################
######################## der2h.derp1p1 * derp1.dereta1
d2l.be1.be1 <- -VC$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 +
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1eta1 ) +
VC$c00*( (bit1.b1b1*p00 - (-c.copula.be1*derp1.dereta1)^2)/p00^2 )
)
d2l.be2.be2 <- -VC$weights*(
VC$c11*( (der2pdf2.dereta2 * pdf2 - derpdf2.dereta2^2) / pdf2^2 +
((der2c.derp2.derp2 * derp2.dereta2^2 + der2h.derp1p2 * -der2p2.dereta2eta2) * c.copula2.be1be2 - derc.dereta2^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dereta2^2 + c.copula.be1^-1 * der2h.derp1p2 * derp2.dereta2^2 + c.copula.be1^-1 * c.copula2.be1be2 * -der2p2.dereta2eta2) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dereta2^2 + c.copula.be2^-1 * der2h.derp2p2 * derp2.dereta2^2 + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dereta2eta2 +
der2pdf2.dereta2 * pdf2^-1 + derpdf2.dereta2^2*-pdf2^-2 ) +
VC$c00*( (bit1.b2b2*p00 - (-c.copula.be2*derp2.dereta2)^2)/p00^2 )
)
####################################################
####################################################
if( !(VC$BivD %in% VC$BivD2) ){
if(VC$BivD %in% c("GAL90","C90","GAL180","C180","GAL270","C270","J90","J180","J270","G90","G180","G270")){
bit2rho <- VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th^2 + c.copula.be1^-1 * der3C.derp1tetateta * derteta.derteta.st^2 - c.copula.be1^-1 * c.copula2.be1t * der2teta.derteta.stteta.st)
bit3rho <- VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th^2 + c.copula.be2^-1 * der2h.derteta.teta.st * derteta.derteta.st^2 - c.copula.be2^-1 * c.copula2.be2t * der2teta.derteta.stteta.st)
}else{
bit2rho <- VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th^2 + c.copula.be1^-1 * der3C.derp1tetateta * derteta.derteta.st^2 + c.copula.be1^-1 * c.copula2.be1t * der2teta.derteta.stteta.st)
bit3rho <- VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th^2 + c.copula.be2^-1 * der2h.derteta.teta.st * derteta.derteta.st^2 + c.copula.be2^-1 * c.copula2.be2t * der2teta.derteta.stteta.st)
}
}
if( VC$BivD %in% VC$BivD2 ){
bit2rho <- bit3rho <- NA
if(Cop1 %in% c("GAL0","C0","J0","G0")){
bit2rho[teta.ind1] <- VC$c10[teta.ind1]*( -(c.copula.be1[teta.ind1])^-2 * c.copula2.be1th[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * der3C.derp1tetateta[teta.ind1] * derteta.derteta.st[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * c.copula2.be1t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
bit3rho[teta.ind1] <- VC$c01[teta.ind1]*( -(c.copula.be2[teta.ind1])^-2 * c.copula2.be2th[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * der2h.derteta.teta.st[teta.ind1] * derteta.derteta.st[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * c.copula2.be2t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
}
if(Cop1 %in% c("GAL180","C180","J180","G180")){
bit2rho[teta.ind1] <- VC$c10[teta.ind1]*( -(c.copula.be1[teta.ind1])^-2 * c.copula2.be1th[teta.ind1]^2 + c.copula.be1[teta.ind1]^-1 * der3C.derp1tetateta[teta.ind1] * derteta.derteta.st[teta.ind1]^2 - c.copula.be1[teta.ind1]^-1 * c.copula2.be1t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
bit3rho[teta.ind1] <- VC$c01[teta.ind1]*( -(c.copula.be2[teta.ind1])^-2 * c.copula2.be2th[teta.ind1]^2 + c.copula.be2[teta.ind1]^-1 * der2h.derteta.teta.st[teta.ind1] * derteta.derteta.st[teta.ind1]^2 - c.copula.be2[teta.ind1]^-1 * c.copula2.be2t[teta.ind1] * der2teta.derteta.stteta.st[teta.ind1])
}
if(Cop2 %in% c("GAL90","C90","J90","G90","GAL270","C270","J270","G270")){
bit2rho[teta.ind2] <- VC$c10[teta.ind2]*( -(c.copula.be1[teta.ind2])^-2 * c.copula2.be1th[teta.ind2]^2 + c.copula.be1[teta.ind2]^-1 * der3C.derp1tetateta[teta.ind2] * derteta.derteta.st[teta.ind2]^2 - c.copula.be1[teta.ind2]^-1 * c.copula2.be1t[teta.ind2] * der2teta.derteta.stteta.st[teta.ind2])
bit3rho[teta.ind2] <- VC$c01[teta.ind2]*( -(c.copula.be2[teta.ind2])^-2 * c.copula2.be2th[teta.ind2]^2 + c.copula.be2[teta.ind2]^-1 * der2h.derteta.teta.st[teta.ind2] * derteta.derteta.st[teta.ind2]^2 - c.copula.be2[teta.ind2]^-1 * c.copula2.be2t[teta.ind2] * der2teta.derteta.stteta.st[teta.ind2])
}
}
############################
d2l.rho.rho <- -VC$weights*(
VC$c11*( ((der2c.derrho.derrho*derteta.derteta.st^2 + der2h.derp1teta *der2teta.derteta.stteta.st)*c.copula2.be1be2 - der2h.derp1teta.st^2) /c.copula2.be1be2^2 ) +
bit2rho +
bit3rho +
VC$c00*( (bit1.th2*p00 - (c.copula.theta)^2)/p00^2 )
)
###################################################
###################################################
d2l.sigma21.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dersigma21.st^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dersigma21.st^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dersigma21.st2 ) +
VC$c00*( (bit1.s1s1*p00 - (-c.copula.be1*derp1.dersigma21.st)^2)/p00^2 )
)
d2l.sigma22.sigma22 <- -VC$weights*(
VC$c11*( (der2pdf2.dersigma22.st2 * pdf2 - derpdf2.dersigma22.st^2) / pdf2^2 +
((der2c.derp2.derp2*derp2.dersigma22.st^2+der2h.derp1p2*-der2p2.dersigma22.st2)*c.copula2.be1be2 - derc.dersigma22.st^2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dersigma22.st^2 + c.copula.be1^-1 * der2h.derp1p2 * derp2.dersigma22.st^2 + c.copula.be1^-1 * c.copula2.be1be2 *
-der2p2.dersigma22.st2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dersigma22.st^2 + c.copula.be2^-1 * der2h.derp2p2 * derp2.dersigma22.st^2 + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dersigma22.st2 +
der2pdf2.dersigma22.st2 * pdf2^-1 + derpdf2.dersigma22.st^2*-pdf2^-2 ) +
VC$c00*( (bit1.s2s2*p00 - (-c.copula.be2*derp2.dersigma22.st)^2)/p00^2 )
)
d2l.be1.be2 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dereta1*derp2.dereta2*c.copula2.be1be2 - derc.dereta1*derc.dereta2) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dereta1 * derp2.dereta2 + c.copula.be1^-1 * der2h.derp1p1 * derp1.dereta1 * derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dereta1 * derp2.dereta2 + c.copula.be2^-1 * der2h.derp1p2 * derp1.dereta1 * derp2.dereta2 ) +
VC$c00*( (bit1.b1b2*p00 - (c.copula.be1*derp1.dereta1*c.copula.be2*derp2.dereta2))/p00^2 )
)
d2l.be1.rho <- -VC$weights*(
VC$c11*( (der2c.derp1.derrho *-derp1.dereta1*derteta.derteta.st* c.copula2.be1be2 - -derc.dereta1*der2h.derp1teta*derteta.derteta.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1 * - derp1.dereta1 + c.copula.be1^-1 * der3C.p1p1teta *derteta.derteta.st*- derp1.dereta1) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be1be2 * - derp1.dereta1 + c.copula.be2^-1 * der2h.derp1teta *derteta.derteta.st*- derp1.dereta1 ) +
VC$c00*( (bit1.b1th*p00 - (-c.copula.be1*derp1.dereta1*c.copula.theta))/p00^2 )
)
d2l.be2.rho <- -VC$weights*(
VC$c11*( (der2c.derp2.derrho *-derp2.dereta2*derteta.derteta.st* c.copula2.be1be2 - -derc.dereta2*der2h.derp1teta*derteta.derteta.st) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1be2 * - derp2.dereta2 + c.copula.be1^-1 * der2h.derp1teta *derteta.derteta.st*- derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be2 * - derp2.dereta2 + c.copula.be2^-1 * der2h.derp2teta *derteta.derteta.st*- derp2.dereta2 ) +
VC$c00*( (bit1.b2th*p00 - (-c.copula.be2*derp2.dereta2*c.copula.theta))/p00^2 )
)
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$c10*( -(c.copula.be1)^-2 * c.copula2.be1^2 * derp1.dereta1^2 + c.copula.be1^-1 * der3C.derp1p1p1 * derp1.dereta1^2 + c.copula.be1^-1 * c.copula2.be1 * - der2p1.dereta1eta1 +
der2pdf1.dereta1 * pdf1^-1 + derpdf1.dereta1^2*-pdf1^-2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1^2 + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1^2 + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1eta1 ) +
VC$c00*( (bit1.b1b1*p00 - (-c.copula.be1*derp1.dereta1)^2)/p00^2 )
)
d2l.be1.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2^2 * derp1.dereta1*derp1.dersigma21.st + c.copula.be2^-1 * der2h.derp1p1 * derp1.dereta1*derp1.dersigma21.st + c.copula.be2^-1 * c.copula2.be1be2 * -der2p1.dereta1dersigma21.st ) +
VC$c00*( (bit1.b1s1*p00 - c.copula.be1^2*derp1.dereta1*derp1.dersigma21.st)/p00^2 )
)
d2l.be2.sigma22 <- -VC$weights*(
VC$c11*( (der2pdf2.dereta2dersigma22.st * pdf2 - derpdf2.dereta2*derpdf2.dersigma22.st) / pdf2^2 +
((der2c.derp2.derp2 * derp2.dereta2* derp2.dersigma22.st+der2h.derp1p2*-der2p2.dereta2dersigma22.st) * c.copula2.be1be2 - derc.dereta2*derc.dersigma22.st) /c.copula2.be1be2^2 ) +
VC$c10*(-(c.copula.be1)^-2 * c.copula2.be1be2^2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be1^-1 * c.copula2.be1be2 * -der2p2.dereta2dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2^2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp2p2 * derp2.dereta2*derp2.dersigma22.st + c.copula.be2^-1 * c.copula2.be2 * - der2p2.dereta2dersigma22.st +
der2pdf2.dereta2dersigma22.st * pdf2^-1 + derpdf2.dereta2*derpdf2.dersigma22.st*-pdf2^-2 ) +
VC$c00*( (bit1.b2s2*p00 - c.copula.be2^2*derp2.dereta2*derp2.dersigma22.st)/p00^2 )
)
d2l.be2.sigma21 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp2.dereta2*derp1.dersigma21.st* c.copula2.be1be2 - derc.dereta2*derc.dersigma21.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dersigma21.st * derp2.dereta2 + c.copula.be1^-1 * der2h.derp1p1 * derp1.dersigma21.st * derp2.dereta2 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dersigma21.st * derp2.dereta2 + c.copula.be2^-1 * der2h.derp1p2 * derp1.dersigma21.st * derp2.dereta2 ) +
VC$c00*( (bit1.b2s1*p00 - (c.copula.be2*derp2.dereta2*c.copula.be1*derp1.dersigma21.st))/p00^2 )
)
d2l.be1.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dereta1*derp2.dersigma22.st* c.copula2.be1be2 - derc.dereta1*derc.dersigma22.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dereta1 * derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p1 * derp1.dereta1 * derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dereta1 * derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp1p2 * derp1.dereta1 * derp2.dersigma22.st ) +
VC$c00*( (bit1.b1s2*p00 - (c.copula.be1*derp1.dereta1*c.copula.be2*derp2.dersigma22.st))/p00^2 )
)
d2l.rho.sigma21 <- -VC$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 ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be1be2 * - derp1.dersigma21.st + c.copula.be2^-1 * der2h.derp1teta *derteta.derteta.st*- derp1.dersigma21.st ) +
VC$c00*( (bit1.s1th*p00 - (-c.copula.be1*derp1.dersigma21.st*c.copula.theta))/p00^2 )
)
d2l.rho.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp2.derrho*-derp2.dersigma22.st*derteta.derteta.st*c.copula2.be1be2 - -derc.dersigma22.st*der2h.derp1teta *derteta.derteta.st)/c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1th * c.copula2.be1be2 * - derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1teta *derteta.derteta.st*- derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be2th * c.copula2.be2 * - derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp2teta *derteta.derteta.st*- derp2.dersigma22.st ) +
VC$c00*( (bit1.s2th*p00 - (-c.copula.be2*derp2.dersigma22.st*c.copula.theta))/p00^2 )
)
d2l.sigma21.sigma22 <- -VC$weights*(
VC$c11*( (der2c.derp1.derp2*derp1.dersigma21.st*derp2.dersigma22.st* c.copula2.be1be2 - derc.dersigma21.st*derc.dersigma22.st ) /c.copula2.be1be2^2 ) +
VC$c10*( -(c.copula.be1)^-2 * c.copula2.be1be2 * c.copula2.be1 * derp1.dersigma21.st * derp2.dersigma22.st + c.copula.be1^-1 * der2h.derp1p1 * derp1.dersigma21.st * derp2.dersigma22.st ) +
VC$c01*( -(c.copula.be2)^-2 * c.copula2.be1be2 * c.copula2.be2 * derp1.dersigma21.st * derp2.dersigma22.st + c.copula.be2^-1 * der2h.derp1p2 * derp1.dersigma21.st * derp2.dersigma22.st ) +
VC$c00*( (bit1.s1s2*p00 - (c.copula.be1*derp1.dersigma21.st*c.copula.be2*derp2.dersigma22.st))/p00^2 )
)
if( is.null(VC$X3) ){
G <- -c(colSums( c(dl.dbe1)*VC$X1 ),
colSums( c(dl.dbe2)*VC$X2 ),
sum( dl.dsigma21.st ),
sum( dl.dsigma22.st ),
sum( dl.dteta.st ) )
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1),VC$X1)
be2.be2 <- crossprod(VC$X2*c(d2l.be2.be2),VC$X2)
be1.be2 <- crossprod(VC$X1*c(d2l.be1.be2),VC$X2)
be1.rho <- t(t(rowSums(t(VC$X1*c(d2l.be1.rho)))))
be1.sigma21 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma21)))))
be1.sigma22 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma22)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma21 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma21)))))
be2.sigma22 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma22)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.sigma22, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.sigma22, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sum(d2l.sigma21.sigma21), sum(d2l.sigma21.sigma22), sum(d2l.rho.sigma21)),
cbind( t(be1.sigma22) , t(be2.sigma22) , sum(d2l.sigma21.sigma22), sum(d2l.sigma22.sigma22), sum(d2l.rho.sigma22)),
cbind( t(be1.rho) , t(be2.rho) , sum(d2l.rho.sigma21), sum(d2l.rho.sigma22), sum(d2l.rho.rho) )
)
}
if( !is.null(VC$X3) ){
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums(c(dl.dsigma21.st)*VC$X3 ) ,
colSums(c(dl.dsigma22.st)*VC$X4 ) ,
colSums( c(dl.dteta.st)*VC$X5 ) )
be1.be1 <- crossprod(VC$X1*c(d2l.be1.be1),VC$X1)
be2.be2 <- crossprod(VC$X2*c(d2l.be2.be2),VC$X2)
be1.be2 <- crossprod(VC$X1*c(d2l.be1.be2),VC$X2)
be1.rho <- crossprod(VC$X1*c(d2l.be1.rho),VC$X5)
be2.rho <- crossprod(VC$X2*c(d2l.be2.rho),VC$X5)
be1.sigma21 <- crossprod(VC$X1*c(d2l.be1.sigma21),VC$X3)
be1.sigma22 <- crossprod(VC$X1*c(d2l.be1.sigma22),VC$X4)
be2.sigma21 <- crossprod(VC$X2*c(d2l.be2.sigma21),VC$X3)
be2.sigma22 <- crossprod(VC$X2*c(d2l.be2.sigma22),VC$X4)
sigma21.sigma21 <- crossprod(VC$X3*c(d2l.sigma21.sigma21),VC$X3)
sigma21.sigma22 <- crossprod(VC$X3*c(d2l.sigma21.sigma22),VC$X4)
rho.sigma21 <- crossprod(VC$X3*c(d2l.rho.sigma21),VC$X5)
sigma22.sigma22 <- crossprod(VC$X4*c(d2l.sigma22.sigma22),VC$X4)
rho.sigma22 <- crossprod(VC$X4*c(d2l.rho.sigma22),VC$X5)
rho.rho <- crossprod(VC$X5*c(d2l.rho.rho),VC$X5)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma21, be1.sigma22, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma21, be2.sigma22, be2.rho ),
cbind( t(be1.sigma21) , t(be2.sigma21) , sigma21.sigma21, sigma21.sigma22, rho.sigma21),
cbind( t(be1.sigma22) , t(be2.sigma22) , t(sigma21.sigma22), sigma22.sigma22, rho.sigma22),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma21), t(rho.sigma22), rho.rho ) )
}
res <- -sum(l.par)
if(VC$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)
if( VC$margins[1] == "LN" || VC$margins[2] == "LN"){
if(VC$margins[1] == "LN") dHs1 <- distrHsAT(exp(respvec$y1), eta1, sigma21, 1, margin2=VC$margins[1], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
if(VC$margins[2] == "LN") dHs2 <- distrHsAT(exp(respvec$y2), eta2, sigma22, 1, margin2=VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH1 <- copgHsAT(p1[teta.ind1], p2[teta.ind1], teta1, Cop1, Ln = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
if( length(teta2) != 0) dH2 <- copgHsAT(p1[teta.ind2], p2[teta.ind2], teta2, Cop2, Ln = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
c.copula2.be1be2 <- NA
if( length(teta1) != 0) c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
l.ln <- -sum( VC$weights*( log(pdf1) + log(pdf2) + log(c.copula2.be1be2) ) )
}
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2,
l=S.res, l.ln = l.ln, l.par=l.par, ps = ps,
eta1=eta1, eta2=eta2, etad=etad, etas1 = etas1, etas2 = etas2,
BivD=VC$BivD, p1 = p1, p2 = p2, pdf1 = pdf1, pdf2 = pdf2,
c.copula.be2 = c.copula.be2,
c.copula.be1 = c.copula.be1,
c.copula2.be1be2 = c.copula2.be1be2,
dl.dbe1 =dl.dbe1,
dl.dbe2 =dl.dbe2,
dl.dsigma21.st =dl.dsigma21.st,
dl.dsigma22.st =dl.dsigma22.st,
dl.dteta.st =dl.dteta.st,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
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