Nothing
R/bdiscrcont13.R
In JRM: Joint Regression Modelling
Defines functions
bdiscrcont13
Documented in
bdiscrcont13
bdiscrcont13 <- function(params, respvec, VC, ps, AT = FALSE){
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 <- etan1 <- etan2 <- l.ln <- NULL
epsilon <- 0.0000001
max.p <- 0.9999999
if(is.null(VC$X3)){
sigma21.st <- etas1 <- 0
sigma22.st <- etas2 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
nu2.st <- etan2 <- params[(VC$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 <- 0
sigma22.st <- etas2 <- VC$X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
nu2.st <- etan2 <- 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 <- 0
sstr2 <- esp.tr(sigma22.st, VC$margins[2])
sigma21.st <- 0
sigma22.st <- sstr2$vrb.st
sigma21 <- 0
sigma22 <- sstr2$vrb
sstr2 <- esp.tr(nu2.st, VC$margins[2])
nu2.st <- sstr2$vrb.st
nu2 <- sstr2$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$BivD
teta.ind1 <- as.logical(c(1,0,round(runif(VC$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[1:4]) 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
}
##################
dHs1 <- distrHsDiscr(respvec$y1, eta1, sigma21, sigma21.st, nu = 1, nu.st = 1, margin2=VC$margins[1], naive = FALSE, y2m = VC$y1m)
dHs2 <- distrHs(respvec$y2, eta2, sigma22, sigma22.st, nu2, nu2.st, margin2=VC$margins[2], naive = FALSE)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH11 <- copgHs(p1[teta.ind1], p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof)
if( length(teta2) != 0) dH12 <- copgHs(p1[teta.ind2], p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof)
h1 <- NA
if( length(teta1) != 0) h1[teta.ind1] <- dH11$c.copula.be2
if( length(teta2) != 0) h1[teta.ind2] <- dH12$c.copula.be2
if( length(teta1) != 0) dH21 <- copgHs(mm(p1[teta.ind1]-pdf1[teta.ind1]), p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof)
if( length(teta2) != 0) dH22 <- copgHs(mm(p1[teta.ind2]-pdf1[teta.ind2]), p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof)
h2 <- NA
if( length(teta1) != 0) h2[teta.ind1] <- dH21$c.copula.be2
if( length(teta2) != 0) h2[teta.ind2] <- dH22$c.copula.be2
diffh1.h2 <- h1 - h2
diffh1.h2 <- ifelse(diffh1.h2 < epsilon, epsilon, diffh1.h2)
l.par <- VC$weights*( log(pdf2) + log(diffh1.h2) )
##################
c.copula2.be1be2H1 <- NA
if( length(teta1) != 0) c.copula2.be1be2H1[teta.ind1] <- dH11$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2H1[teta.ind2] <- dH12$c.copula2.be1be2
c.copula2.be1be2H2 <- NA
if( length(teta1) != 0) c.copula2.be1be2H2[teta.ind1] <- dH21$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2H2[teta.ind2] <- dH22$c.copula2.be1be2
c.copula2.be2H1 <- NA
if( length(teta1) != 0) c.copula2.be2H1[teta.ind1] <- dH11$c.copula2.be2
if( length(teta2) != 0) c.copula2.be2H1[teta.ind2] <- dH12$c.copula2.be2
c.copula2.be2H2 <- NA
if( length(teta1) != 0) c.copula2.be2H2[teta.ind1] <- dH21$c.copula2.be2
if( length(teta2) != 0) c.copula2.be2H2[teta.ind2] <- dH22$c.copula2.be2
c.copula2.be2thH1 <- NA
if( length(teta1) != 0) c.copula2.be2thH1[teta.ind1] <- dH11$c.copula2.be2th
if( length(teta2) != 0) c.copula2.be2thH1[teta.ind2] <- dH12$c.copula2.be2th
c.copula2.be2thH2 <- NA
if( length(teta1) != 0) c.copula2.be2thH2[teta.ind1] <- dH21$c.copula2.be2th
if( length(teta2) != 0) c.copula2.be2thH2[teta.ind2] <- dH22$c.copula2.be2th
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derp1.dereta1 <- dHs1$derp2.dereta2
derp1m1.dereta1 <- derp1.dereta1 - derpdf1.dereta1
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derp1m1.dersigma21.st <- derp1.dersigma21.st - derpdf1.dersigma21.st
derpdf2.dereta2 <- dHs2$derpdf2.dereta2
derp2.dereta2 <- dHs2$derp2.dereta2
derpdf2.dersigma22.st <- dHs2$derpdf2.dersigma2.st
derp2.dersigma22.st <- dHs2$derp2.dersigma.st
derpdf2.dernu2.st <- dHs2$derpdf2.dernu.st
derp2.dernu2.st <- dHs2$derp2.nu.st
####################
if( length(teta1) != 0) BITS.H11 <- 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) BITS.H12 <- copgHsCont(p1[teta.ind2], p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta1) != 0) BITS.H21 <- copgHsCont(mm(p1[teta.ind1]-pdf1[teta.ind1]), p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta2) != 0) BITS.H22 <- copgHsCont(mm(p1[teta.ind2]-pdf1[teta.ind2]), p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
der2h.derp1p1.H1 <- NA
if( length(teta1) != 0) der2h.derp1p1.H1[teta.ind1] <- BITS.H11$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1.H1[teta.ind2] <- BITS.H12$der2h.derp1p1
der2h.derp1p1.H2 <- NA
if( length(teta1) != 0) der2h.derp1p1.H2[teta.ind1] <- BITS.H21$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1.H2[teta.ind2] <- BITS.H22$der2h.derp1p1
der2h.derp1p2.H1 <- NA
if( length(teta1) != 0) der2h.derp1p2.H1[teta.ind1] <- BITS.H11$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2.H1[teta.ind2] <- BITS.H12$der2h.derp1p2
der2h.derp1p2.H2 <- NA
if( length(teta1) != 0) der2h.derp1p2.H2[teta.ind1] <- BITS.H21$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2.H2[teta.ind2] <- BITS.H22$der2h.derp1p2
derteta.derteta.st.H1 <- NA
if( length(teta1) != 0) derteta.derteta.st.H1[teta.ind1] <- BITS.H11$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st.H1[teta.ind2] <- BITS.H12$derteta.derteta.st
der2h.derp1teta.H1 <- NA
if( length(teta1) != 0) der2h.derp1teta.H1[teta.ind1] <- BITS.H11$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta.H1[teta.ind2] <- BITS.H12$der2h.derp1teta
derteta.derteta.st.H2 <- NA
if( length(teta1) != 0) derteta.derteta.st.H2[teta.ind1] <- BITS.H21$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st.H2[teta.ind2] <- BITS.H22$derteta.derteta.st
der2h.derp1teta.H2 <- NA
if( length(teta1) != 0) der2h.derp1teta.H2[teta.ind1] <- BITS.H21$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta.H2[teta.ind2] <- BITS.H22$der2h.derp1teta
der2h.derp2teta.H1 <- NA
if( length(teta1) != 0) der2h.derp2teta.H1[teta.ind1] <- BITS.H11$der2h.derp2teta
if( length(teta2) != 0) der2h.derp2teta.H1[teta.ind2] <- BITS.H12$der2h.derp2teta
der2h.derp2teta.H2 <- NA
if( length(teta1) != 0) der2h.derp2teta.H2[teta.ind1] <- BITS.H21$der2h.derp2teta
if( length(teta2) != 0) der2h.derp2teta.H2[teta.ind2] <- BITS.H22$der2h.derp2teta
der2h.derp1teta.st.H1 <- der2h.derp1teta.H1 * derteta.derteta.st.H1
der2h.derp1teta.st.H2 <- der2h.derp1teta.H2 * derteta.derteta.st.H2
der2h.derp2teta.st.H1 <- der2h.derp2teta.H1 * derteta.derteta.st.H1
der2h.derp2teta.st.H2 <- der2h.derp2teta.H2 * derteta.derteta.st.H2
####################
BITdl.dbe1 <- 1/diffh1.h2*(c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 )
dl.dbe1 <- VC$weights*( BITdl.dbe1 )
dl.dbe2 <- VC$weights*( derpdf2.dereta2/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2 ) )
dl.dsigma22.st <- VC$weights*( derpdf2.dersigma22.st/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st ) )
dl.dnu2.st <- VC$weights*( derpdf2.dernu2.st/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st ) )
dl.dteta.st <- VC$weights*( 1/diffh1.h2*(c.copula2.be2thH1-c.copula2.be2thH2) )
#################################################################################################
der2h.derp2p2.H1 <- NA
if( length(teta1) != 0) der2h.derp2p2.H1[teta.ind1] <- BITS.H11$der2h.derp2p2
if( length(teta2) != 0) der2h.derp2p2.H1[teta.ind2] <- BITS.H12$der2h.derp2p2
der2h.derp2p2.H2 <- NA
if( length(teta1) != 0) der2h.derp2p2.H2[teta.ind1] <- BITS.H21$der2h.derp2p2
if( length(teta2) != 0) der2h.derp2p2.H2[teta.ind2] <- BITS.H22$der2h.derp2p2
derteta.derteta.st <- NA
if( length(teta1) != 0) derteta.derteta.st[teta.ind1] <- BITS.H11$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st[teta.ind2] <- BITS.H12$derteta.derteta.st
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0) der2teta.derteta.stteta.st[teta.ind1] <- BITS.H11$der2teta.derteta.stteta.st
if( length(teta2) != 0) der2teta.derteta.stteta.st[teta.ind2] <- BITS.H12$der2teta.derteta.stteta.st
der2h.derteta.teta.st.H1 <- NA
if( length(teta1) != 0) der2h.derteta.teta.st.H1[teta.ind1] <- BITS.H11$der2h.derteta.teta.st
if( length(teta2) != 0) der2h.derteta.teta.st.H1[teta.ind2] <- BITS.H12$der2h.derteta.teta.st
der2h.derteta.teta.st.H2 <- NA
if( length(teta1) != 0) der2h.derteta.teta.st.H2[teta.ind1] <- BITS.H21$der2h.derteta.teta.st
if( length(teta2) != 0) der2h.derteta.teta.st.H2[teta.ind2] <- BITS.H22$der2h.derteta.teta.st
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p1m1.dereta1eta1 <- der2p1.dereta1eta1 - dHs1$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2p1m1.dersigma21.st2 <- der2p1.dersigma21.st2 - der2pdf1.dersigma21.st2
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
der2p1m1.dereta1dersigma21.st <- der2p1.dereta1dersigma21.st - dHs1$der2pdf2.dereta2dersigma2.st
der2pdf2.dereta2 <- dHs2$der2pdf2.dereta2
der2p2.dereta2eta2 <- dHs2$der2p2.dereta2eta2
der2pdf2.dersigma22.st2 <- dHs2$der2pdf2.dersigma2.st2
der2p2.dersigma22.st2 <- dHs2$der2p2.dersigma2.st2
der2pdf2.dereta2dersigma22.st <- dHs2$der2pdf2.dereta2dersigma2.st
der2p2.dereta2dersigma22.st <- dHs2$der2p2.dereta2dersigma2.st
der2pdf2.dernu2.st2 <- dHs2$der2pdf2.dernu.st2
der2p2.dernu2.st2 <- dHs2$der2p2.dernu.st2
der2pdf2.dereta2dernu2.st <- dHs2$der2pdf2.dereta2dernu.st
der2p2.dereta2dernu2.st <- dHs2$der2p2.dereta2dernu.st
der2pdf2.dersigma22.stdernu2.st <- dHs2$der2pdf2.sigma2.st2dernu.st
der2p2.dersigma22.stdernu2.st <- dHs2$der2p2.dersigma2.stdernu.st
d2l.be1.be1 <- -VC$weights*( - BITdl.dbe1^2 + 1/diffh1.h2*( (der2h.derp1p1.H1*derp1.dereta1^2 + c.copula2.be1be2H1*der2p1.dereta1eta1) - (der2h.derp1p1.H2*derp1m1.dereta1^2 + c.copula2.be1be2H2*der2p1m1.dereta1eta1) ) )
d2l.be2.be2 <- -VC$weights*( (der2pdf2.dereta2*pdf2 - derpdf2.dereta2^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dereta2^2/diffh1.h2^2 +1/diffh1.h2*( der2h.derp2p2.H1*derp2.dereta2^2 + c.copula2.be2H1*der2p2.dereta2eta2 -(der2h.derp2p2.H2*derp2.dereta2^2 + c.copula2.be2H2*der2p2.dereta2eta2 ) ) )
d2l.sigma22.sigma22 <- -VC$weights*( (der2pdf2.dersigma22.st2*pdf2 - derpdf2.dersigma22.st^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dersigma22.st^2/diffh1.h2^2+1/diffh1.h2*( der2h.derp2p2.H1*derp2.dersigma22.st^2 + c.copula2.be2H1*der2p2.dersigma22.st2-(der2h.derp2p2.H2*derp2.dersigma22.st^2 + c.copula2.be2H2*der2p2.dersigma22.st2) ) )
d2l.be1.be2 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dereta2/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dereta2 )
d2l.be1.sigma22 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dersigma22.st/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dersigma22.st )
d2l.be1.rho <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*(c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1teta.st.H1*derp1.dereta1 - der2h.derp1teta.st.H2*derp1m1.dereta1 ) )
d2l.be2.rho <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2 ) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dereta2 )
d2l.rho.sigma22 <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st ) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dersigma22.st )
d2l.be2.sigma22 <- -VC$weights*( (der2pdf2.dereta2dersigma22.st*pdf2 - derpdf2.dereta2*derpdf2.dersigma22.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dereta2*derp2.dersigma22.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dereta2dersigma22.st) )
d2l.rho.rho <- -VC$weights*( - (c.copula2.be2thH1 - c.copula2.be2thH2)^2/diffh1.h2^2 + diffh1.h2^-1*(der2h.derteta.teta.st.H1*derteta.derteta.st^2 - (c.copula2.be2thH1/derteta.derteta.st)*der2teta.derteta.stteta.st - (der2h.derteta.teta.st.H2*derteta.derteta.st^2 - (c.copula2.be2thH2/derteta.derteta.st)*der2teta.derteta.stteta.st) ) )
d2l.nu2.nu2 <- -VC$weights*( (der2pdf2.dernu2.st2*pdf2 - derpdf2.dernu2.st^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dernu2.st^2/diffh1.h2^2+1/diffh1.h2*( der2h.derp2p2.H1*derp2.dernu2.st^2 + c.copula2.be2H1*der2p2.dernu2.st2-(der2h.derp2p2.H2*derp2.dernu2.st^2 + c.copula2.be2H2*der2p2.dernu2.st2) ) )
d2l.be2.nu2 <- -VC$weights*( (der2pdf2.dereta2dernu2.st*pdf2 - derpdf2.dereta2*derpdf2.dernu2.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dereta2*derp2.dernu2.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dereta2dernu2.st) )
d2l.be1.nu2 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dernu2.st/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dernu2.st )
d2l.rho.nu2 <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dernu2.st )
d2l.sigma22.nu2 <- -VC$weights*( (der2pdf2.dersigma22.stdernu2.st*pdf2 - derpdf2.dersigma22.st*derpdf2.dernu2.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dersigma22.st*derp2.dernu2.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dersigma22.stdernu2.st) )
if( is.null(VC$X3) ){
G <- -c(colSums( c(dl.dbe1)*VC$X1 ),
colSums( c(dl.dbe2)*VC$X2 ),
sum( dl.dsigma22.st ),
sum( dl.dnu2.st ),
sum( dl.dteta.st ) )
be1.be1 <- crossprod(VC$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.sigma22 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma22)))))
be1.nu2 <- t(t(rowSums(t(VC$X1*c(d2l.be1.nu2)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma22 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma22)))))
be2.nu2 <- t(t(rowSums(t(VC$X2*c(d2l.be2.nu2)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma22, be1.nu2, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma22, be2.nu2, be2.rho ),
cbind( t(be1.sigma22) , t(be2.sigma22) , sum(d2l.sigma22.sigma22), sum(d2l.sigma22.nu2), sum(d2l.rho.sigma22)),
cbind( t(be1.nu2) , t(be2.nu2) , sum(d2l.sigma22.nu2), sum(d2l.nu2.nu2), sum(d2l.rho.nu2)),
cbind( t(be1.rho) , t(be2.rho) , sum(d2l.rho.sigma22), sum(d2l.rho.nu2), sum(d2l.rho.rho) )
)
}
if( !is.null(VC$X3) ){
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums(c(dl.dsigma22.st)*VC$X3 ) ,
colSums(c(dl.dnu2.st)*VC$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$X5)
be1.sigma22 <- crossprod(VC$X1*c(d2l.be1.sigma22),VC$X3)
be1.nu2 <- crossprod(VC$X1*c(d2l.be1.nu2),VC$X4)
be2.nu2 <- crossprod(VC$X2*c(d2l.be2.nu2),VC$X4)
be2.sigma22 <- crossprod(VC$X2*c(d2l.be2.sigma22),VC$X3)
nu2.nu2 <- crossprod(VC$X4*c(d2l.nu2.nu2),VC$X4)
rho.nu2 <- crossprod(VC$X4*c(d2l.rho.nu2),VC$X5)
sigma22.sigma22 <- crossprod(VC$X3*c(d2l.sigma22.sigma22),VC$X3)
rho.sigma22 <- crossprod(VC$X3*c(d2l.rho.sigma22),VC$X5)
rho.rho <- crossprod(VC$X5*c(d2l.rho.rho),VC$X5)
sigma22.nu2 <- crossprod(VC$X3*c(d2l.sigma22.nu2),VC$X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma22, be1.nu2, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma22, be2.nu2, be2.rho ),
cbind( t(be1.sigma22) , t(be2.sigma22), sigma22.sigma22, sigma22.nu2, rho.sigma22),
cbind( t(be1.nu2) , t(be2.nu2) , t(sigma22.nu2), nu2.nu2, rho.nu2),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma22), t(rho.nu2), rho.rho ) )
}
res <- -sum(l.par)
if(VC$extra.regI == "pC") H <- regH(H, type = 1)
S.h <- ps$S.h
if( length(S.h) != 1){
S.h1 <- 0.5*crossprod(params,S.h)%*%params
S.h2 <- S.h%*%params
} else S.h <- S.h1 <- S.h2 <- 0
S.res <- res
res <- S.res + S.h1
G <- G + S.h2
H <- H + S.h
if(VC$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 = etas1, etas2 = etas2, etan1 = etan1, etan2 = etan2,
BivD=VC$BivD, p1 = p1, p2 = p2,
dl.dbe1 =dl.dbe1,
dl.dbe2 =dl.dbe2,
dl.dsigma21.st =0,
dl.dsigma22.st =dl.dsigma22.st,
dl.dnu2.st =dl.dnu2.st,
dl.dteta.st =dl.dteta.st,
teta.ind2 = teta.ind2, teta.ind1 = teta.ind1,
Cop1 = Cop1, Cop2 = Cop2, teta1 = teta1, teta2 = teta2)
}
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Defines functions bdiscrcont13
Documented in bdiscrcont13
bdiscrcont13 <- function(params, respvec, VC, ps, AT = FALSE){
eta1 <- VC$X1%*%params[1:VC$X1.d2]
eta2 <- VC$X2%*%params[(VC$X1.d2 + 1):(VC$X1.d2 + VC$X2.d2)]
etad <- etas1 <- etas2 <- etan1 <- etan2 <- l.ln <- NULL
epsilon <- 0.0000001
max.p <- 0.9999999
if(is.null(VC$X3)){
sigma21.st <- etas1 <- 0
sigma22.st <- etas2 <- params[(VC$X1.d2 + VC$X2.d2 + 1)]
nu2.st <- etan2 <- params[(VC$X1.d2 + VC$X2.d2 + 2)]
teta.st <- etad <- params[(VC$X1.d2 + VC$X2.d2 + 3)]
}
if(!is.null(VC$X3)){
sigma21.st <- etas1 <- 0
sigma22.st <- etas2 <- VC$X3%*%params[(VC$X1.d2 + VC$X2.d2 + 1):(VC$X1.d2 + VC$X2.d2 + VC$X3.d2)]
nu2.st <- etan2 <- VC$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$X5.d2)]
}
##################
## Transformations
##################
sstr1 <- 0
sstr2 <- esp.tr(sigma22.st, VC$margins[2])
sigma21.st <- 0
sigma22.st <- sstr2$vrb.st
sigma21 <- 0
sigma22 <- sstr2$vrb
sstr2 <- esp.tr(nu2.st, VC$margins[2])
nu2.st <- sstr2$vrb.st
nu2 <- 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
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$BivD2[1:4]) teta.ind1 <- ifelse(VC$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$Cop2
}
##################
dHs1 <- distrHsDiscr(respvec$y1, eta1, sigma21, sigma21.st, nu = 1, nu.st = 1, margin2=VC$margins[1], naive = FALSE, y2m = VC$y1m)
dHs2 <- distrHs(respvec$y2, eta2, sigma22, sigma22.st, nu2, nu2.st, margin2=VC$margins[2], naive = FALSE)
pdf1 <- dHs1$pdf2
pdf2 <- dHs2$pdf2
p1 <- dHs1$p2
p2 <- dHs2$p2
if( length(teta1) != 0) dH11 <- copgHs(p1[teta.ind1], p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof)
if( length(teta2) != 0) dH12 <- copgHs(p1[teta.ind2], p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof)
h1 <- NA
if( length(teta1) != 0) h1[teta.ind1] <- dH11$c.copula.be2
if( length(teta2) != 0) h1[teta.ind2] <- dH12$c.copula.be2
if( length(teta1) != 0) dH21 <- copgHs(mm(p1[teta.ind1]-pdf1[teta.ind1]), p2[teta.ind1], eta1=NULL, eta2=NULL, teta1, teta.st1, Cop1, VC$dof)
if( length(teta2) != 0) dH22 <- copgHs(mm(p1[teta.ind2]-pdf1[teta.ind2]), p2[teta.ind2], eta1=NULL, eta2=NULL, teta2, teta.st2, Cop2, VC$dof)
h2 <- NA
if( length(teta1) != 0) h2[teta.ind1] <- dH21$c.copula.be2
if( length(teta2) != 0) h2[teta.ind2] <- dH22$c.copula.be2
diffh1.h2 <- h1 - h2
diffh1.h2 <- ifelse(diffh1.h2 < epsilon, epsilon, diffh1.h2)
l.par <- VC$weights*( log(pdf2) + log(diffh1.h2) )
##################
c.copula2.be1be2H1 <- NA
if( length(teta1) != 0) c.copula2.be1be2H1[teta.ind1] <- dH11$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2H1[teta.ind2] <- dH12$c.copula2.be1be2
c.copula2.be1be2H2 <- NA
if( length(teta1) != 0) c.copula2.be1be2H2[teta.ind1] <- dH21$c.copula2.be1be2
if( length(teta2) != 0) c.copula2.be1be2H2[teta.ind2] <- dH22$c.copula2.be1be2
c.copula2.be2H1 <- NA
if( length(teta1) != 0) c.copula2.be2H1[teta.ind1] <- dH11$c.copula2.be2
if( length(teta2) != 0) c.copula2.be2H1[teta.ind2] <- dH12$c.copula2.be2
c.copula2.be2H2 <- NA
if( length(teta1) != 0) c.copula2.be2H2[teta.ind1] <- dH21$c.copula2.be2
if( length(teta2) != 0) c.copula2.be2H2[teta.ind2] <- dH22$c.copula2.be2
c.copula2.be2thH1 <- NA
if( length(teta1) != 0) c.copula2.be2thH1[teta.ind1] <- dH11$c.copula2.be2th
if( length(teta2) != 0) c.copula2.be2thH1[teta.ind2] <- dH12$c.copula2.be2th
c.copula2.be2thH2 <- NA
if( length(teta1) != 0) c.copula2.be2thH2[teta.ind1] <- dH21$c.copula2.be2th
if( length(teta2) != 0) c.copula2.be2thH2[teta.ind2] <- dH22$c.copula2.be2th
derpdf1.dereta1 <- dHs1$derpdf2.dereta2
derp1.dereta1 <- dHs1$derp2.dereta2
derp1m1.dereta1 <- derp1.dereta1 - derpdf1.dereta1
derpdf1.dersigma21.st <- dHs1$derpdf2.dersigma2.st
derp1.dersigma21.st <- dHs1$derp2.dersigma.st
derp1m1.dersigma21.st <- derp1.dersigma21.st - derpdf1.dersigma21.st
derpdf2.dereta2 <- dHs2$derpdf2.dereta2
derp2.dereta2 <- dHs2$derp2.dereta2
derpdf2.dersigma22.st <- dHs2$derpdf2.dersigma2.st
derp2.dersigma22.st <- dHs2$derp2.dersigma.st
derpdf2.dernu2.st <- dHs2$derpdf2.dernu.st
derp2.dernu2.st <- dHs2$derp2.nu.st
####################
if( length(teta1) != 0) BITS.H11 <- copgHsCont(p1[teta.ind1], p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta2) != 0) BITS.H12 <- copgHsCont(p1[teta.ind2], p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta1) != 0) BITS.H21 <- copgHsCont(mm(p1[teta.ind1]-pdf1[teta.ind1]), p2[teta.ind1], teta1, teta.st1, Cop1, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
if( length(teta2) != 0) BITS.H22 <- copgHsCont(mm(p1[teta.ind2]-pdf1[teta.ind2]), p2[teta.ind2], teta2, teta.st2, Cop2, Cont = TRUE, par2 = VC$dof, nu.st = log(VC$dof-2))
der2h.derp1p1.H1 <- NA
if( length(teta1) != 0) der2h.derp1p1.H1[teta.ind1] <- BITS.H11$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1.H1[teta.ind2] <- BITS.H12$der2h.derp1p1
der2h.derp1p1.H2 <- NA
if( length(teta1) != 0) der2h.derp1p1.H2[teta.ind1] <- BITS.H21$der2h.derp1p1
if( length(teta2) != 0) der2h.derp1p1.H2[teta.ind2] <- BITS.H22$der2h.derp1p1
der2h.derp1p2.H1 <- NA
if( length(teta1) != 0) der2h.derp1p2.H1[teta.ind1] <- BITS.H11$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2.H1[teta.ind2] <- BITS.H12$der2h.derp1p2
der2h.derp1p2.H2 <- NA
if( length(teta1) != 0) der2h.derp1p2.H2[teta.ind1] <- BITS.H21$der2h.derp1p2
if( length(teta2) != 0) der2h.derp1p2.H2[teta.ind2] <- BITS.H22$der2h.derp1p2
derteta.derteta.st.H1 <- NA
if( length(teta1) != 0) derteta.derteta.st.H1[teta.ind1] <- BITS.H11$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st.H1[teta.ind2] <- BITS.H12$derteta.derteta.st
der2h.derp1teta.H1 <- NA
if( length(teta1) != 0) der2h.derp1teta.H1[teta.ind1] <- BITS.H11$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta.H1[teta.ind2] <- BITS.H12$der2h.derp1teta
derteta.derteta.st.H2 <- NA
if( length(teta1) != 0) derteta.derteta.st.H2[teta.ind1] <- BITS.H21$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st.H2[teta.ind2] <- BITS.H22$derteta.derteta.st
der2h.derp1teta.H2 <- NA
if( length(teta1) != 0) der2h.derp1teta.H2[teta.ind1] <- BITS.H21$der2h.derp1teta
if( length(teta2) != 0) der2h.derp1teta.H2[teta.ind2] <- BITS.H22$der2h.derp1teta
der2h.derp2teta.H1 <- NA
if( length(teta1) != 0) der2h.derp2teta.H1[teta.ind1] <- BITS.H11$der2h.derp2teta
if( length(teta2) != 0) der2h.derp2teta.H1[teta.ind2] <- BITS.H12$der2h.derp2teta
der2h.derp2teta.H2 <- NA
if( length(teta1) != 0) der2h.derp2teta.H2[teta.ind1] <- BITS.H21$der2h.derp2teta
if( length(teta2) != 0) der2h.derp2teta.H2[teta.ind2] <- BITS.H22$der2h.derp2teta
der2h.derp1teta.st.H1 <- der2h.derp1teta.H1 * derteta.derteta.st.H1
der2h.derp1teta.st.H2 <- der2h.derp1teta.H2 * derteta.derteta.st.H2
der2h.derp2teta.st.H1 <- der2h.derp2teta.H1 * derteta.derteta.st.H1
der2h.derp2teta.st.H2 <- der2h.derp2teta.H2 * derteta.derteta.st.H2
####################
BITdl.dbe1 <- 1/diffh1.h2*(c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 )
dl.dbe1 <- VC$weights*( BITdl.dbe1 )
dl.dbe2 <- VC$weights*( derpdf2.dereta2/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2 ) )
dl.dsigma22.st <- VC$weights*( derpdf2.dersigma22.st/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st ) )
dl.dnu2.st <- VC$weights*( derpdf2.dernu2.st/pdf2 + 1/diffh1.h2*( (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st ) )
dl.dteta.st <- VC$weights*( 1/diffh1.h2*(c.copula2.be2thH1-c.copula2.be2thH2) )
#################################################################################################
der2h.derp2p2.H1 <- NA
if( length(teta1) != 0) der2h.derp2p2.H1[teta.ind1] <- BITS.H11$der2h.derp2p2
if( length(teta2) != 0) der2h.derp2p2.H1[teta.ind2] <- BITS.H12$der2h.derp2p2
der2h.derp2p2.H2 <- NA
if( length(teta1) != 0) der2h.derp2p2.H2[teta.ind1] <- BITS.H21$der2h.derp2p2
if( length(teta2) != 0) der2h.derp2p2.H2[teta.ind2] <- BITS.H22$der2h.derp2p2
derteta.derteta.st <- NA
if( length(teta1) != 0) derteta.derteta.st[teta.ind1] <- BITS.H11$derteta.derteta.st
if( length(teta2) != 0) derteta.derteta.st[teta.ind2] <- BITS.H12$derteta.derteta.st
der2teta.derteta.stteta.st <- NA
if( length(teta1) != 0) der2teta.derteta.stteta.st[teta.ind1] <- BITS.H11$der2teta.derteta.stteta.st
if( length(teta2) != 0) der2teta.derteta.stteta.st[teta.ind2] <- BITS.H12$der2teta.derteta.stteta.st
der2h.derteta.teta.st.H1 <- NA
if( length(teta1) != 0) der2h.derteta.teta.st.H1[teta.ind1] <- BITS.H11$der2h.derteta.teta.st
if( length(teta2) != 0) der2h.derteta.teta.st.H1[teta.ind2] <- BITS.H12$der2h.derteta.teta.st
der2h.derteta.teta.st.H2 <- NA
if( length(teta1) != 0) der2h.derteta.teta.st.H2[teta.ind1] <- BITS.H21$der2h.derteta.teta.st
if( length(teta2) != 0) der2h.derteta.teta.st.H2[teta.ind2] <- BITS.H22$der2h.derteta.teta.st
der2p1.dereta1eta1 <- dHs1$der2p2.dereta2eta2
der2p1m1.dereta1eta1 <- der2p1.dereta1eta1 - dHs1$der2pdf2.dereta2
der2pdf1.dersigma21.st2 <- dHs1$der2pdf2.dersigma2.st2
der2p1.dersigma21.st2 <- dHs1$der2p2.dersigma2.st2
der2p1m1.dersigma21.st2 <- der2p1.dersigma21.st2 - der2pdf1.dersigma21.st2
der2p1.dereta1dersigma21.st <- dHs1$der2p2.dereta2dersigma2.st
der2p1m1.dereta1dersigma21.st <- der2p1.dereta1dersigma21.st - dHs1$der2pdf2.dereta2dersigma2.st
der2pdf2.dereta2 <- dHs2$der2pdf2.dereta2
der2p2.dereta2eta2 <- dHs2$der2p2.dereta2eta2
der2pdf2.dersigma22.st2 <- dHs2$der2pdf2.dersigma2.st2
der2p2.dersigma22.st2 <- dHs2$der2p2.dersigma2.st2
der2pdf2.dereta2dersigma22.st <- dHs2$der2pdf2.dereta2dersigma2.st
der2p2.dereta2dersigma22.st <- dHs2$der2p2.dereta2dersigma2.st
der2pdf2.dernu2.st2 <- dHs2$der2pdf2.dernu.st2
der2p2.dernu2.st2 <- dHs2$der2p2.dernu.st2
der2pdf2.dereta2dernu2.st <- dHs2$der2pdf2.dereta2dernu.st
der2p2.dereta2dernu2.st <- dHs2$der2p2.dereta2dernu.st
der2pdf2.dersigma22.stdernu2.st <- dHs2$der2pdf2.sigma2.st2dernu.st
der2p2.dersigma22.stdernu2.st <- dHs2$der2p2.dersigma2.stdernu.st
d2l.be1.be1 <- -VC$weights*( - BITdl.dbe1^2 + 1/diffh1.h2*( (der2h.derp1p1.H1*derp1.dereta1^2 + c.copula2.be1be2H1*der2p1.dereta1eta1) - (der2h.derp1p1.H2*derp1m1.dereta1^2 + c.copula2.be1be2H2*der2p1m1.dereta1eta1) ) )
d2l.be2.be2 <- -VC$weights*( (der2pdf2.dereta2*pdf2 - derpdf2.dereta2^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dereta2^2/diffh1.h2^2 +1/diffh1.h2*( der2h.derp2p2.H1*derp2.dereta2^2 + c.copula2.be2H1*der2p2.dereta2eta2 -(der2h.derp2p2.H2*derp2.dereta2^2 + c.copula2.be2H2*der2p2.dereta2eta2 ) ) )
d2l.sigma22.sigma22 <- -VC$weights*( (der2pdf2.dersigma22.st2*pdf2 - derpdf2.dersigma22.st^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dersigma22.st^2/diffh1.h2^2+1/diffh1.h2*( der2h.derp2p2.H1*derp2.dersigma22.st^2 + c.copula2.be2H1*der2p2.dersigma22.st2-(der2h.derp2p2.H2*derp2.dersigma22.st^2 + c.copula2.be2H2*der2p2.dersigma22.st2) ) )
d2l.be1.be2 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dereta2/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dereta2 )
d2l.be1.sigma22 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dersigma22.st/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dersigma22.st )
d2l.be1.rho <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*(c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1teta.st.H1*derp1.dereta1 - der2h.derp1teta.st.H2*derp1m1.dereta1 ) )
d2l.be2.rho <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2 ) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dereta2 )
d2l.rho.sigma22 <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st ) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dersigma22.st )
d2l.be2.sigma22 <- -VC$weights*( (der2pdf2.dereta2dersigma22.st*pdf2 - derpdf2.dereta2*derpdf2.dersigma22.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dereta2*derp2.dersigma22.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dereta2dersigma22.st) )
d2l.rho.rho <- -VC$weights*( - (c.copula2.be2thH1 - c.copula2.be2thH2)^2/diffh1.h2^2 + diffh1.h2^-1*(der2h.derteta.teta.st.H1*derteta.derteta.st^2 - (c.copula2.be2thH1/derteta.derteta.st)*der2teta.derteta.stteta.st - (der2h.derteta.teta.st.H2*derteta.derteta.st^2 - (c.copula2.be2thH2/derteta.derteta.st)*der2teta.derteta.stteta.st) ) )
d2l.nu2.nu2 <- -VC$weights*( (der2pdf2.dernu2.st2*pdf2 - derpdf2.dernu2.st^2)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)^2*derp2.dernu2.st^2/diffh1.h2^2+1/diffh1.h2*( der2h.derp2p2.H1*derp2.dernu2.st^2 + c.copula2.be2H1*der2p2.dernu2.st2-(der2h.derp2p2.H2*derp2.dernu2.st^2 + c.copula2.be2H2*der2p2.dernu2.st2) ) )
d2l.be2.nu2 <- -VC$weights*( (der2pdf2.dereta2dernu2.st*pdf2 - derpdf2.dereta2*derpdf2.dernu2.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dereta2/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dereta2*derp2.dernu2.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dereta2dernu2.st) )
d2l.be1.nu2 <- -VC$weights*( - (c.copula2.be2H1 - c.copula2.be2H2)*(derp2.dernu2.st/diffh1.h2^2)*( c.copula2.be1be2H1*derp1.dereta1 - c.copula2.be1be2H2*derp1m1.dereta1 ) + diffh1.h2^-1*( der2h.derp1p2.H1*derp1.dereta1 - der2h.derp1p2.H2*derp1m1.dereta1 )*derp2.dernu2.st )
d2l.rho.nu2 <- -VC$weights*( -(c.copula2.be2thH1 - c.copula2.be2thH2)/diffh1.h2^2*((c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st) + diffh1.h2^-1*( der2h.derp2teta.st.H1 - der2h.derp2teta.st.H2 )*derp2.dernu2.st )
d2l.sigma22.nu2 <- -VC$weights*( (der2pdf2.dersigma22.stdernu2.st*pdf2 - derpdf2.dersigma22.st*derpdf2.dernu2.st)/pdf2^2 - (c.copula2.be2H1 - c.copula2.be2H2)*derp2.dernu2.st*(c.copula2.be2H1 - c.copula2.be2H2)*derp2.dersigma22.st/diffh1.h2^2 + diffh1.h2^-1*( (der2h.derp2p2.H1-der2h.derp2p2.H2)*derp2.dersigma22.st*derp2.dernu2.st + (c.copula2.be2H1-c.copula2.be2H2)*der2p2.dersigma22.stdernu2.st) )
if( is.null(VC$X3) ){
G <- -c(colSums( c(dl.dbe1)*VC$X1 ),
colSums( c(dl.dbe2)*VC$X2 ),
sum( dl.dsigma22.st ),
sum( dl.dnu2.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$X1*c(d2l.be1.rho)))))
be1.sigma22 <- t(t(rowSums(t(VC$X1*c(d2l.be1.sigma22)))))
be1.nu2 <- t(t(rowSums(t(VC$X1*c(d2l.be1.nu2)))))
be2.rho <- t(t(rowSums(t(VC$X2*c(d2l.be2.rho)))))
be2.sigma22 <- t(t(rowSums(t(VC$X2*c(d2l.be2.sigma22)))))
be2.nu2 <- t(t(rowSums(t(VC$X2*c(d2l.be2.nu2)))))
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma22, be1.nu2, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma22, be2.nu2, be2.rho ),
cbind( t(be1.sigma22) , t(be2.sigma22) , sum(d2l.sigma22.sigma22), sum(d2l.sigma22.nu2), sum(d2l.rho.sigma22)),
cbind( t(be1.nu2) , t(be2.nu2) , sum(d2l.sigma22.nu2), sum(d2l.nu2.nu2), sum(d2l.rho.nu2)),
cbind( t(be1.rho) , t(be2.rho) , sum(d2l.rho.sigma22), sum(d2l.rho.nu2), sum(d2l.rho.rho) )
)
}
if( !is.null(VC$X3) ){
G <- -c( colSums( c(dl.dbe1)*VC$X1 ) ,
colSums( c(dl.dbe2)*VC$X2 ) ,
colSums(c(dl.dsigma22.st)*VC$X3 ) ,
colSums(c(dl.dnu2.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.sigma22 <- crossprod(VC$X1*c(d2l.be1.sigma22),VC$X3)
be1.nu2 <- crossprod(VC$X1*c(d2l.be1.nu2),VC$X4)
be2.nu2 <- crossprod(VC$X2*c(d2l.be2.nu2),VC$X4)
be2.sigma22 <- crossprod(VC$X2*c(d2l.be2.sigma22),VC$X3)
nu2.nu2 <- crossprod(VC$X4*c(d2l.nu2.nu2),VC$X4)
rho.nu2 <- crossprod(VC$X4*c(d2l.rho.nu2),VC$X5)
sigma22.sigma22 <- crossprod(VC$X3*c(d2l.sigma22.sigma22),VC$X3)
rho.sigma22 <- crossprod(VC$X3*c(d2l.rho.sigma22),VC$X5)
rho.rho <- crossprod(VC$X5*c(d2l.rho.rho),VC$X5)
sigma22.nu2 <- crossprod(VC$X3*c(d2l.sigma22.nu2),VC$X4)
H <- rbind( cbind( be1.be1 , be1.be2 , be1.sigma22, be1.nu2, be1.rho ),
cbind( t(be1.be2) , be2.be2 , be2.sigma22, be2.nu2, be2.rho ),
cbind( t(be1.sigma22) , t(be2.sigma22), sigma22.sigma22, sigma22.nu2, rho.sigma22),
cbind( t(be1.nu2) , t(be2.nu2) , t(sigma22.nu2), nu2.nu2, rho.nu2),
cbind( t(be1.rho) , t(be2.rho) , t(rho.sigma22), t(rho.nu2), 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
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$extra.regI == "sED") H <- regH(H, type = 2)
list(value=res, gradient=G, hessian=H, S.h=S.h, S.h1=S.h1, S.h2=S.h2, l=S.res, l.ln = l.ln, l.par=l.par, ps = ps,
eta1=eta1, eta2=eta2, etad=etad, etas1 = etas1, etas2 = etas2, etan1 = etan1, etan2 = etan2,
BivD=VC$BivD, p1 = p1, p2 = p2,
dl.dbe1 =dl.dbe1,
dl.dbe2 =dl.dbe2,
dl.dsigma21.st =0,
dl.dsigma22.st =dl.dsigma22.st,
dl.dnu2.st =dl.dnu2.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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