R/bprobgHsCont.r
In KironmoyDas/KD-STAT0035-GMupdate: Generalised Joint Regression Modelling
Defines functions
bprobgHsCont
Documented in
bprobgHsCont
bprobgHsCont <- 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 <- etas <- l.ln <- NULL
if(is.null(VC$X3)){
sigma2.st <- etas <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
}
if(!is.null(VC$X3)){
sigma2.st <- etas <- VC$X3%*%params[(VC$X1.d2+VC$X2.d2+1):(VC$X1.d2+VC$X2.d2+VC$X3.d2)]
teta.st <- etad <- 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)]
}
sstr1 <- esp.tr(sigma2.st, VC$margins[2])
sigma2.st <- sstr1$vrb.st
sigma2 <- sstr1$vrb
eta2 <- eta.tr(eta2, VC$margins[2])
dHs <- distrHs(respvec$y2, eta2, sigma2, sigma2.st, nu = 1, nu.st = 1, margin2=VC$margins[2], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf2 <- dHs$pdf2
p2 <- dHs$p2
derpdf2.dereta2 <- dHs$derpdf2.dereta2
derpdf2.dersigma2.st <- dHs$derpdf2.dersigma2.st
derp2.dersigma.st <- dHs$derp2.dersigma.st
derp2.dereta2 <- dHs$derp2.dereta2
der2p2.dereta2eta2 <- dHs$der2p2.dereta2eta2
der2pdf2.dereta2 <- dHs$der2pdf2.dereta2
der2p2.dersigma2.st2 <- dHs$der2p2.dersigma2.st2
der2pdf2.dersigma2.st2 <- dHs$der2pdf2.dersigma2.st2
der2p2.dereta2dersigma2.st <- dHs$der2p2.dereta2dersigma2.st
der2pdf2.dereta2dersigma2.st <- dHs$der2pdf2.dereta2dersigma2.st
pd1 <- probm(eta1, VC$margins[1], bc = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
p1 <- 1 - pd1$pr # pnorm(-eta1)
########################################################################################################
resT <- teta.tr(VC, teta.st)
teta.st1 <- teta.st2 <- teta.st <- resT$teta.st
teta1 <- teta2 <- teta <- resT$teta
########################################################################################################
Cop1 <- Cop2 <- VC$BivD
teta.ind1 <- as.logical(c(1,0,round(runif(VC$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
}
########################################################################################################
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)
h <- NA
if( length(teta1) != 0) h[teta.ind1] <- dH1$c.copula.be2
if( length(teta2) != 0) h[teta.ind2] <- dH2$c.copula.be2
l.par <- VC$weights*( respvec$cy*log(h) + respvec$y1*log(1 - h) + log(pdf2) )
########################################################################################################
c.copula2.be2 <- c.copula2.be1be2 <- c.copula2.be2th <- NA
if( length(teta1) != 0){
c.copula2.be2[teta.ind1] <- dH1$c.copula2.be2
c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula2.be2th[teta.ind1] <- dH1$c.copula2.be2th
}
if( length(teta2) != 0){
c.copula2.be2[teta.ind2] <- dH2$c.copula2.be2
c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula2.be2th[teta.ind2] <- dH2$c.copula2.be2th
}
derp1.dereta1 <- pd1$derp1.dereta1 # -dnorm(-eta1)
derh.dereta1 <- c.copula2.be1be2 * derp1.dereta1
derh.dereta2 <- c.copula2.be2 * derp2.dereta2
dl.dbe1 <- VC$weights*( derh.dereta1 *(respvec$cy/h - respvec$y1/(1-h)) )
dl.dbe2 <- VC$weights*( derh.dereta2 * (respvec$cy/h - respvec$y1/(1-h)) + derpdf2.dereta2/pdf2 )
dl.dsigma.st <- VC$weights*( c.copula2.be2 * derp2.dersigma.st *(respvec$cy/h - respvec$y1/(1-h)) + derpdf2.dersigma2.st/pdf2 )
dl.dteta.st <- VC$weights*( c.copula2.be2th*(respvec$cy/h - respvec$y1/(1-h)) )
########################################################################################################
der2h.derp2p2 <- der2h.derteta.teta.st <- derteta.derteta.st <- der2teta.derteta.stteta.st <- der2h.derp1p2 <- der2h.derp1teta <- der2h.derp2teta <- der2h.derp1p1 <- NA
if( length(teta1) != 0) BITS1 <- copgHsCont(p1[teta.ind1], p2[teta.ind1], teta1, teta.st1, Cop1, 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, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta1) != 0){
der2h.derp2p2[teta.ind1] <- BITS1$der2h.derp2p2
der2h.derteta.teta.st[teta.ind1] <- BITS1$der2h.derteta.teta.st
derteta.derteta.st[teta.ind1] <- BITS1$derteta.derteta.st
der2teta.derteta.stteta.st[teta.ind1] <- BITS1$der2teta.derteta.stteta.st
der2h.derp1p2[teta.ind1] <- BITS1$der2h.derp1p2
der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
der2h.derp2teta[teta.ind1] <- BITS1$der2h.derp2teta
der2h.derp1p1[teta.ind1] <- BITS1$der2h.derp1p1
}
if( length(teta2) != 0){
der2h.derp2p2[teta.ind2] <- BITS2$der2h.derp2p2
der2h.derteta.teta.st[teta.ind2] <- BITS2$der2h.derteta.teta.st
derteta.derteta.st[teta.ind2] <- BITS2$derteta.derteta.st
der2teta.derteta.stteta.st[teta.ind2] <- BITS2$der2teta.derteta.stteta.st
der2h.derp1p2[teta.ind2] <- BITS2$der2h.derp1p2
der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
der2h.derp2teta[teta.ind2] <- BITS2$der2h.derp2teta
der2h.derp1p1[teta.ind2] <- BITS2$der2h.derp1p1
}
der2p1.dereta1eta1 <- pd1$der2p1.dereta1eta1 #####eta1 * dnorm(-eta1)
der2h.dereta2.dereta2 <- der2h.derp2p2*derp2.dereta2^2 + c.copula2.be2*der2p2.dereta2eta2
der2h.derteta.st2 <- der2h.derteta.teta.st*derteta.derteta.st^2 + c.copula2.be2th/derteta.derteta.st* der2teta.derteta.stteta.st
der2h.derp2dersigma2.st <- der2h.derp2p2*derp2.dersigma.st
der2h.dersigma2.st2 <- der2h.derp2dersigma2.st*derp2.dersigma.st + c.copula2.be2*der2p2.dersigma2.st2
derh.dersigma2.st <- c.copula2.be2 * derp2.dersigma.st
der2h.dereta1.dereta2 <- der2h.derp1p2*derp1.dereta1*derp2.dereta2
der2h.dereta1.derteta.st <- der2h.derp1teta*derp1.dereta1*derteta.derteta.st
der2h.dereta1.dersigma2.st <- der2h.derp1p2 * derp2.dersigma.st*derp1.dereta1
der2h.dereta2.derteta.st <- der2h.derp2teta*derp2.dereta2*derteta.derteta.st
der2h.derteta.st.dersigma2.st <- der2h.derp2teta* derteta.derteta.st*derp2.dersigma.st
der2h.dereta2.dersigma2.st <- der2h.derp2dersigma2.st*derp2.dereta2 + c.copula2.be2*der2p2.dereta2dersigma2.st
der2h.dereta1.dereta1 <- der2h.derp1p1*derp1.dereta1^2 + c.copula2.be1be2*der2p1.dereta1eta1
d2l.be1.be1 <- -VC$weights*(der2h.dereta1.dereta1 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.be2 <- -VC$weights*(der2h.dereta2.dereta2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dereta2*pdf2-(derpdf2.dereta2)^2)/(pdf2)^2 )
d2l.rho.rho <- -VC$weights*(der2h.derteta.st2*(respvec$cy/h - respvec$y1/(1-h)) - c.copula2.be2th^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.sigma.sigma <- -VC$weights*(der2h.dersigma2.st2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dersigma2.st^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dersigma2.st2*pdf2-(derpdf2.dersigma2.st)^2)/(pdf2)^2 )
d2l.be1.be2 <- -VC$weights*(der2h.dereta1.dereta2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1*derh.dereta2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be1.rho <- -VC$weights*(der2h.dereta1.derteta.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1 * c.copula2.be2th* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be1.sigma <- -VC$weights*(der2h.dereta1.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1 * derh.dersigma2.st* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.rho <- -VC$weights*(der2h.dereta2.derteta.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2*c.copula2.be2th * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.sigma <- -VC$weights*(der2h.dereta2.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2*derh.dersigma2.st * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dereta2dersigma2.st*pdf2-(derpdf2.dereta2*derpdf2.dersigma2.st))/(pdf2)^2 )
d2l.rho.sigma <- -VC$weights*(der2h.derteta.st.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dersigma2.st * c.copula2.be2th* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
if( is.null(VC$X3) ){
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$X1*c(d2l.be1.rho)))))
be1.sigma <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma, be2.rho ),
cbind( t(be1.sigma), t(be2.sigma), sum(d2l.sigma.sigma), sum(d2l.rho.sigma) ),
cbind( t(be1.rho) , t(be2.rho), sum(d2l.rho.sigma), sum(d2l.rho.rho) )
)
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
sum( dl.dsigma.st ),
sum( dl.dteta.st ) )
}
if( !is.null(VC$X3) ){
be1.be1 <- crossprod(VC$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$X4)
be1.sigma <- crossprod(VC$X1*c(d2l.be1.sigma),VC$X3)
be2.rho <- crossprod(VC$X2*c(d2l.be2.rho), VC$X4)
be2.sigma <- crossprod(VC$X2*c(d2l.be2.sigma),VC$X3)
sigma.sigma <- crossprod(VC$X3*c(d2l.sigma.sigma),VC$X3)
sigma.rho <- crossprod(VC$X3*c(d2l.rho.sigma),VC$X4)
rho.rho <- crossprod(VC$X4*c(d2l.rho.rho), VC$X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma , be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma , be2.rho ),
cbind( t(be1.sigma), t(be2.sigma), sigma.sigma , sigma.rho ),
cbind( t(be1.rho) , t(be2.rho) , t(sigma.rho), rho.rho )
)
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums( c(dl.dsigma.st)*VC$X3 ) ,
colSums( c(dl.dteta.st)*VC$X4 ) )
}
res <- -sum(l.par)
if(VC$extra.regI == "pC") H <- regH(H, type = 1)
S.h <- ps$S.h
if( length(S.h) != 1){
S.h1 <- 0.5*crossprod(params,S.h)%*%params
S.h2 <- S.h%*%params
} else S.h <- S.h1 <- S.h2 <- 0
S.res <- res
res <- S.res + S.h1
G <- G + S.h2
H <- H + S.h
if(VC$extra.regI == "sED") H <- regH(H, type = 2)
if(VC$margins[2] == "LN"){
dHs <- distrHsAT(exp(respvec$y2), eta2, sigma2, 1, margin2 = VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf2 <- dHs$pdf2
p2 <- dHs$p2
if( length(teta1) != 0) dH1 <- copgHsAT(p1[teta.ind1], p2[teta.ind1], teta1, Cop1, 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, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
h <- NA
if( length(teta1) != 0) h[teta.ind1] <- dH1$c.copula.be2
if( length(teta2) != 0) h[teta.ind2] <- dH2$c.copula.be2
l.ln <- -sum(VC$weights*( respvec$cy*log(h) + respvec$y1*log(1 - h) + log(pdf2) ))
}
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2, l=S.res, l.ln=l.ln, l.par=l.par, ps = ps, etas = etas,
eta1=eta1, eta2=eta2, etad=etad,
dl.dbe1=dl.dbe1, dl.dbe2=dl.dbe2, dl.dsigma.st = dl.dsigma.st, dl.dteta.st = dl.dteta.st,
BivD=VC$BivD, theta.star = teta.st,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
p1 = 1-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,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
KironmoyDas/KD-STAT0035-GMupdate documentation built on Feb. 15, 2021, 12:17 a.m.
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Defines functions bprobgHsCont
Documented in bprobgHsCont
bprobgHsCont <- 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 <- etas <- l.ln <- NULL
if(is.null(VC$X3)){
sigma2.st <- etas <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
}
if(!is.null(VC$X3)){
sigma2.st <- etas <- VC$X3%*%params[(VC$X1.d2+VC$X2.d2+1):(VC$X1.d2+VC$X2.d2+VC$X3.d2)]
teta.st <- etad <- 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)]
}
sstr1 <- esp.tr(sigma2.st, VC$margins[2])
sigma2.st <- sstr1$vrb.st
sigma2 <- sstr1$vrb
eta2 <- eta.tr(eta2, VC$margins[2])
dHs <- distrHs(respvec$y2, eta2, sigma2, sigma2.st, nu = 1, nu.st = 1, margin2=VC$margins[2], naive = FALSE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf2 <- dHs$pdf2
p2 <- dHs$p2
derpdf2.dereta2 <- dHs$derpdf2.dereta2
derpdf2.dersigma2.st <- dHs$derpdf2.dersigma2.st
derp2.dersigma.st <- dHs$derp2.dersigma.st
derp2.dereta2 <- dHs$derp2.dereta2
der2p2.dereta2eta2 <- dHs$der2p2.dereta2eta2
der2pdf2.dereta2 <- dHs$der2pdf2.dereta2
der2p2.dersigma2.st2 <- dHs$der2p2.dersigma2.st2
der2pdf2.dersigma2.st2 <- dHs$der2pdf2.dersigma2.st2
der2p2.dereta2dersigma2.st <- dHs$der2p2.dereta2dersigma2.st
der2pdf2.dereta2dersigma2.st <- dHs$der2pdf2.dereta2dersigma2.st
pd1 <- probm(eta1, VC$margins[1], bc = TRUE, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
p1 <- 1 - pd1$pr # pnorm(-eta1)
########################################################################################################
resT <- teta.tr(VC, teta.st)
teta.st1 <- teta.st2 <- teta.st <- resT$teta.st
teta1 <- teta2 <- teta <- resT$teta
########################################################################################################
Cop1 <- Cop2 <- VC$BivD
teta.ind1 <- as.logical(c(1,0,round(runif(VC$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
}
########################################################################################################
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)
h <- NA
if( length(teta1) != 0) h[teta.ind1] <- dH1$c.copula.be2
if( length(teta2) != 0) h[teta.ind2] <- dH2$c.copula.be2
l.par <- VC$weights*( respvec$cy*log(h) + respvec$y1*log(1 - h) + log(pdf2) )
########################################################################################################
c.copula2.be2 <- c.copula2.be1be2 <- c.copula2.be2th <- NA
if( length(teta1) != 0){
c.copula2.be2[teta.ind1] <- dH1$c.copula2.be2
c.copula2.be1be2[teta.ind1] <- dH1$c.copula2.be1be2
c.copula2.be2th[teta.ind1] <- dH1$c.copula2.be2th
}
if( length(teta2) != 0){
c.copula2.be2[teta.ind2] <- dH2$c.copula2.be2
c.copula2.be1be2[teta.ind2] <- dH2$c.copula2.be1be2
c.copula2.be2th[teta.ind2] <- dH2$c.copula2.be2th
}
derp1.dereta1 <- pd1$derp1.dereta1 # -dnorm(-eta1)
derh.dereta1 <- c.copula2.be1be2 * derp1.dereta1
derh.dereta2 <- c.copula2.be2 * derp2.dereta2
dl.dbe1 <- VC$weights*( derh.dereta1 *(respvec$cy/h - respvec$y1/(1-h)) )
dl.dbe2 <- VC$weights*( derh.dereta2 * (respvec$cy/h - respvec$y1/(1-h)) + derpdf2.dereta2/pdf2 )
dl.dsigma.st <- VC$weights*( c.copula2.be2 * derp2.dersigma.st *(respvec$cy/h - respvec$y1/(1-h)) + derpdf2.dersigma2.st/pdf2 )
dl.dteta.st <- VC$weights*( c.copula2.be2th*(respvec$cy/h - respvec$y1/(1-h)) )
########################################################################################################
der2h.derp2p2 <- der2h.derteta.teta.st <- derteta.derteta.st <- der2teta.derteta.stteta.st <- der2h.derp1p2 <- der2h.derp1teta <- der2h.derp2teta <- der2h.derp1p1 <- NA
if( length(teta1) != 0) BITS1 <- copgHsCont(p1[teta.ind1], p2[teta.ind1], teta1, teta.st1, Cop1, 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, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta1) != 0){
der2h.derp2p2[teta.ind1] <- BITS1$der2h.derp2p2
der2h.derteta.teta.st[teta.ind1] <- BITS1$der2h.derteta.teta.st
derteta.derteta.st[teta.ind1] <- BITS1$derteta.derteta.st
der2teta.derteta.stteta.st[teta.ind1] <- BITS1$der2teta.derteta.stteta.st
der2h.derp1p2[teta.ind1] <- BITS1$der2h.derp1p2
der2h.derp1teta[teta.ind1] <- BITS1$der2h.derp1teta
der2h.derp2teta[teta.ind1] <- BITS1$der2h.derp2teta
der2h.derp1p1[teta.ind1] <- BITS1$der2h.derp1p1
}
if( length(teta2) != 0){
der2h.derp2p2[teta.ind2] <- BITS2$der2h.derp2p2
der2h.derteta.teta.st[teta.ind2] <- BITS2$der2h.derteta.teta.st
derteta.derteta.st[teta.ind2] <- BITS2$derteta.derteta.st
der2teta.derteta.stteta.st[teta.ind2] <- BITS2$der2teta.derteta.stteta.st
der2h.derp1p2[teta.ind2] <- BITS2$der2h.derp1p2
der2h.derp1teta[teta.ind2] <- BITS2$der2h.derp1teta
der2h.derp2teta[teta.ind2] <- BITS2$der2h.derp2teta
der2h.derp1p1[teta.ind2] <- BITS2$der2h.derp1p1
}
der2p1.dereta1eta1 <- pd1$der2p1.dereta1eta1 #####eta1 * dnorm(-eta1)
der2h.dereta2.dereta2 <- der2h.derp2p2*derp2.dereta2^2 + c.copula2.be2*der2p2.dereta2eta2
der2h.derteta.st2 <- der2h.derteta.teta.st*derteta.derteta.st^2 + c.copula2.be2th/derteta.derteta.st* der2teta.derteta.stteta.st
der2h.derp2dersigma2.st <- der2h.derp2p2*derp2.dersigma.st
der2h.dersigma2.st2 <- der2h.derp2dersigma2.st*derp2.dersigma.st + c.copula2.be2*der2p2.dersigma2.st2
derh.dersigma2.st <- c.copula2.be2 * derp2.dersigma.st
der2h.dereta1.dereta2 <- der2h.derp1p2*derp1.dereta1*derp2.dereta2
der2h.dereta1.derteta.st <- der2h.derp1teta*derp1.dereta1*derteta.derteta.st
der2h.dereta1.dersigma2.st <- der2h.derp1p2 * derp2.dersigma.st*derp1.dereta1
der2h.dereta2.derteta.st <- der2h.derp2teta*derp2.dereta2*derteta.derteta.st
der2h.derteta.st.dersigma2.st <- der2h.derp2teta* derteta.derteta.st*derp2.dersigma.st
der2h.dereta2.dersigma2.st <- der2h.derp2dersigma2.st*derp2.dereta2 + c.copula2.be2*der2p2.dereta2dersigma2.st
der2h.dereta1.dereta1 <- der2h.derp1p1*derp1.dereta1^2 + c.copula2.be1be2*der2p1.dereta1eta1
d2l.be1.be1 <- -VC$weights*(der2h.dereta1.dereta1 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.be2 <- -VC$weights*(der2h.dereta2.dereta2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dereta2*pdf2-(derpdf2.dereta2)^2)/(pdf2)^2 )
d2l.rho.rho <- -VC$weights*(der2h.derteta.st2*(respvec$cy/h - respvec$y1/(1-h)) - c.copula2.be2th^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.sigma.sigma <- -VC$weights*(der2h.dersigma2.st2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dersigma2.st^2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dersigma2.st2*pdf2-(derpdf2.dersigma2.st)^2)/(pdf2)^2 )
d2l.be1.be2 <- -VC$weights*(der2h.dereta1.dereta2 *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1*derh.dereta2 * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be1.rho <- -VC$weights*(der2h.dereta1.derteta.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1 * c.copula2.be2th* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be1.sigma <- -VC$weights*(der2h.dereta1.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta1 * derh.dersigma2.st* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.rho <- -VC$weights*(der2h.dereta2.derteta.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2*c.copula2.be2th * (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
d2l.be2.sigma <- -VC$weights*(der2h.dereta2.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dereta2*derh.dersigma2.st * (respvec$cy/h^2 + respvec$y1/(1-h)^2) + (der2pdf2.dereta2dersigma2.st*pdf2-(derpdf2.dereta2*derpdf2.dersigma2.st))/(pdf2)^2 )
d2l.rho.sigma <- -VC$weights*(der2h.derteta.st.dersigma2.st *(respvec$cy/h - respvec$y1/(1-h)) - derh.dersigma2.st * c.copula2.be2th* (respvec$cy/h^2 + respvec$y1/(1-h)^2) )
if( is.null(VC$X3) ){
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$X1*c(d2l.be1.rho)))))
be1.sigma <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma, be2.rho ),
cbind( t(be1.sigma), t(be2.sigma), sum(d2l.sigma.sigma), sum(d2l.rho.sigma) ),
cbind( t(be1.rho) , t(be2.rho), sum(d2l.rho.sigma), sum(d2l.rho.rho) )
)
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
sum( dl.dsigma.st ),
sum( dl.dteta.st ) )
}
if( !is.null(VC$X3) ){
be1.be1 <- crossprod(VC$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$X4)
be1.sigma <- crossprod(VC$X1*c(d2l.be1.sigma),VC$X3)
be2.rho <- crossprod(VC$X2*c(d2l.be2.rho), VC$X4)
be2.sigma <- crossprod(VC$X2*c(d2l.be2.sigma),VC$X3)
sigma.sigma <- crossprod(VC$X3*c(d2l.sigma.sigma),VC$X3)
sigma.rho <- crossprod(VC$X3*c(d2l.rho.sigma),VC$X4)
rho.rho <- crossprod(VC$X4*c(d2l.rho.rho), VC$X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma , be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma , be2.rho ),
cbind( t(be1.sigma), t(be2.sigma), sigma.sigma , sigma.rho ),
cbind( t(be1.rho) , t(be2.rho) , t(sigma.rho), rho.rho )
)
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums( c(dl.dsigma.st)*VC$X3 ) ,
colSums( c(dl.dteta.st)*VC$X4 ) )
}
res <- -sum(l.par)
if(VC$extra.regI == "pC") H <- regH(H, type = 1)
S.h <- ps$S.h
if( length(S.h) != 1){
S.h1 <- 0.5*crossprod(params,S.h)%*%params
S.h2 <- S.h%*%params
} else S.h <- S.h1 <- S.h2 <- 0
S.res <- res
res <- S.res + S.h1
G <- G + S.h2
H <- H + S.h
if(VC$extra.regI == "sED") H <- regH(H, type = 2)
if(VC$margins[2] == "LN"){
dHs <- distrHsAT(exp(respvec$y2), eta2, sigma2, 1, margin2 = VC$margins[2], min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr)
pdf2 <- dHs$pdf2
p2 <- dHs$p2
if( length(teta1) != 0) dH1 <- copgHsAT(p1[teta.ind1], p2[teta.ind1], teta1, Cop1, 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, min.dn = VC$min.dn, min.pr = VC$min.pr, max.pr = VC$max.pr, par2 = VC$dof)
h <- NA
if( length(teta1) != 0) h[teta.ind1] <- dH1$c.copula.be2
if( length(teta2) != 0) h[teta.ind2] <- dH2$c.copula.be2
l.ln <- -sum(VC$weights*( respvec$cy*log(h) + respvec$y1*log(1 - h) + log(pdf2) ))
}
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2, l=S.res, l.ln=l.ln, l.par=l.par, ps = ps, etas = etas,
eta1=eta1, eta2=eta2, etad=etad,
dl.dbe1=dl.dbe1, dl.dbe2=dl.dbe2, dl.dsigma.st = dl.dsigma.st, dl.dteta.st = dl.dteta.st,
BivD=VC$BivD, theta.star = teta.st,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
p1 = 1-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,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
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