R/g.tri.r

In JRM: Joint Regression Modelling

g.tri <- function (respvec, VC, TIn) 
{
  mean1 <- TIn$theta12 * TIn$mar1
  mean2 <- TIn$theta13 * TIn$mar1
  mean3 <- TIn$theta12 * TIn$mar2
  mean4 <- TIn$theta23 * TIn$mar2
  mean5 <- TIn$theta13 * TIn$mar3
  mean6 <- TIn$theta23 * TIn$mar3
  var1 <- 1 - TIn$theta12^2
  var2 <- 1 - TIn$theta13^2
  var3 <- 1 - TIn$theta23^2
  cov1 <- TIn$theta23 - TIn$theta12 * TIn$theta13
  cov2 <- TIn$theta13 - TIn$theta12 * TIn$theta23
  cov3 <- TIn$theta12 - TIn$theta13 * TIn$theta23
  
  cov1 <- mmf(cov1)
  cov2 <- mmf(cov2)
  cov3 <- mmf(cov3)
  
  d.1 <- dnorm(TIn$mar1)
  d.2 <- dnorm(TIn$mar2)
  d.3 <- dnorm(TIn$mar3)
  p.1.11 <- mm(pbinorm(TIn$mar2, TIn$mar3, mean1 = mean1, mean2 = mean2, 
                       var1 = var1, var2 = var2, cov12 = cov1))
  p.1.10 <- mm(pbinorm(TIn$mar2, -TIn$mar3, mean1 = mean1, 
                       mean2 = -mean2, var1 = var1, var2 = var2, cov12 = -cov1))
  p.1.00 <- mm(pbinorm(-TIn$mar2, -TIn$mar3, mean1 = -mean1, 
                       mean2 = -mean2, var1 = var1, var2 = var2, cov12 = cov1))
  p.1.01 <- mm(pbinorm(-TIn$mar2, TIn$mar3, mean1 = -mean1, 
                       mean2 = mean2, var1 = var1, var2 = var2, cov12 = -cov1))
  p.2.11 <- mm(pbinorm(TIn$mar1, TIn$mar3, mean1 = mean3, mean2 = mean4, 
                       var1 = var1, var2 = var3, cov12 = cov2))
  p.2.10 <- mm(pbinorm(TIn$mar1, -TIn$mar3, mean1 = mean3, 
                       mean2 = -mean4, var1 = var1, var2 = var3, cov12 = -cov2))
  p.2.00 <- mm(pbinorm(-TIn$mar1, -TIn$mar3, mean1 = -mean3, 
                       mean2 = -mean4, var1 = var1, var2 = var3, cov12 = cov2))
  p.2.01 <- mm(pbinorm(-TIn$mar1, TIn$mar3, mean1 = -mean3, 
                       mean2 = mean4, var1 = var1, var2 = var3, cov12 = -cov2))
  p.3.11 <- mm(pbinorm(TIn$mar1, TIn$mar2, mean1 = mean5, mean2 = mean6, 
                       var1 = var2, var2 = var3, cov12 = cov3))
  p.3.10 <- mm(pbinorm(TIn$mar1, -TIn$mar2, mean1 = mean5, 
                       mean2 = -mean6, var1 = var2, var2 = var3, cov12 = -cov3))
  p.3.00 <- mm(pbinorm(-TIn$mar1, -TIn$mar2, mean1 = -mean5, 
                       mean2 = -mean6, var1 = var2, var2 = var3, cov12 = cov3))
  p.3.01 <- mm(pbinorm(-TIn$mar1, TIn$mar2, mean1 = -mean5, 
                       mean2 = mean6, var1 = var2, var2 = var3, cov12 = -cov3))
  dmar1 <- probm(TIn$eta1, VC$margins[1], only.pr = FALSE)$d.n
  dmar2 <- probm(TIn$eta2, VC$margins[2], only.pr = FALSE)$d.n
  dmar3 <- probm(TIn$eta3, VC$margins[3], only.pr = FALSE)$d.n
  dF1.de1 <- (1/d.1) * dmar1
  dF2.de2 <- (1/d.2) * dmar2
  dF3.de3 <- (1/d.3) * dmar3
  dl.dF1 <- respvec$y1.y2.y3/TIn$p111 * d.1 * p.1.11 + respvec$y1.y2.cy3/TIn$p110 * 
    d.1 * p.1.10 - respvec$cy1.y2.y3/TIn$p011 * d.1 * p.1.11 - 
    respvec$cy1.y2.cy3/TIn$p010 * d.1 * p.1.10 - respvec$cy1.cy2.cy3/TIn$p000 * 
    d.1 * p.1.00 - respvec$cy1.cy2.y3/TIn$p001 * d.1 * p.1.01 + 
    respvec$y1.cy2.cy3/TIn$p100 * d.1 * p.1.00 + respvec$y1.cy2.y3/TIn$p101 * 
    d.1 * p.1.01
  dl.de1 <- dl.dF1 * dF1.de1
  dl.dF2 <- respvec$y1.y2.y3/TIn$p111 * d.2 * p.2.11 + respvec$y1.y2.cy3/TIn$p110 * 
    d.2 * p.2.10 + respvec$cy1.y2.y3/TIn$p011 * d.2 * p.2.01 + 
    respvec$cy1.y2.cy3/TIn$p010 * d.2 * p.2.00 - respvec$cy1.cy2.cy3/TIn$p000 * 
    d.2 * p.2.00 - respvec$cy1.cy2.y3/TIn$p001 * d.2 * p.2.01 - 
    respvec$y1.cy2.cy3/TIn$p100 * d.2 * p.2.10 - respvec$y1.cy2.y3/TIn$p101 * 
    d.2 * p.2.11
  dl.de2 <- dl.dF2 * dF2.de2
  dl.dF3 <- respvec$y1.y2.y3/TIn$p111 * d.3 * p.3.11 - respvec$y1.y2.cy3/TIn$p110 * 
    d.3 * p.3.11 + respvec$cy1.y2.y3/TIn$p011 * d.3 * p.3.01 - 
    respvec$cy1.y2.cy3/TIn$p010 * d.3 * p.3.01 - respvec$cy1.cy2.cy3/TIn$p000 * 
    d.3 * p.3.00 + respvec$cy1.cy2.y3/TIn$p001 * d.3 * p.3.00 - 
    respvec$y1.cy2.cy3/TIn$p100 * d.3 * p.3.10 + respvec$y1.cy2.y3/TIn$p101 * 
    d.3 * p.3.10
  dl.de3 <- dl.dF3 * dF3.de3
  mean.12 <- (TIn$mar1 * (TIn$theta13 - TIn$theta12 * TIn$theta23) + 
                TIn$mar2 * (TIn$theta23 - TIn$theta12 * TIn$theta13))/(1 - 
                                                                         TIn$theta12^2)
  mean.13 <- (TIn$mar1 * (TIn$theta12 - TIn$theta13 * TIn$theta23) + 
                TIn$mar3 * (TIn$theta23 - TIn$theta12 * TIn$theta13))/(1 - 
                                                                         TIn$theta13^2)
  mean.23 <- (TIn$mar2 * (TIn$theta12 - TIn$theta13 * TIn$theta23) + 
                TIn$mar3 * (TIn$theta13 - TIn$theta12 * TIn$theta23))/(1 - 
                                                                         TIn$theta23^2)
  deno <- 1 - TIn$theta12^2 - TIn$theta13^2 - TIn$theta23^2 + 
    2 * TIn$theta12 * TIn$theta13 * TIn$theta23
  sd.12 <- sqrt(deno/(1 - TIn$theta12^2))
  sd.13 <- sqrt(deno/(1 - TIn$theta13^2))
  sd.23 <- sqrt(deno/(1 - TIn$theta23^2))
  p12.g <- mm(pnorm((TIn$mar3 - mean.12)/sd.12))
  p13.g <- mm(pnorm((TIn$mar2 - mean.13)/sd.13))
  p23.g <- mm(pnorm((TIn$mar1 - mean.23)/sd.23))
  p12.g.c <- mm(1 - p12.g)
  p13.g.c <- mm(1 - p13.g)
  p23.g.c <- mm(1 - p23.g)
  d11.12 <- dbinorm(TIn$mar1, TIn$mar2, cov12 = TIn$theta12)
  d11.13 <- dbinorm(TIn$mar1, TIn$mar3, cov12 = TIn$theta13)
  d11.23 <- dbinorm(TIn$mar2, TIn$mar3, cov12 = TIn$theta23)
  dl.dtheta12 <- respvec$y1.y2.y3/TIn$p111 * d11.12 * p12.g + 
    respvec$y1.y2.cy3/TIn$p110 * d11.12 * p12.g.c - respvec$cy1.y2.y3/TIn$p011 * 
    d11.12 * p12.g - respvec$cy1.y2.cy3/TIn$p010 * d11.12 * 
    p12.g.c + respvec$cy1.cy2.cy3/TIn$p000 * d11.12 * p12.g.c + 
    respvec$cy1.cy2.y3/TIn$p001 * d11.12 * p12.g - respvec$y1.cy2.cy3/TIn$p100 * 
    d11.12 * p12.g.c - respvec$y1.cy2.y3/TIn$p101 * d11.12 * 
    p12.g
  dl.dtheta13 <- respvec$y1.y2.y3/TIn$p111 * d11.13 * p13.g - 
    respvec$y1.y2.cy3/TIn$p110 * d11.13 * p13.g - respvec$cy1.y2.y3/TIn$p011 * 
    d11.13 * p13.g + respvec$cy1.y2.cy3/TIn$p010 * d11.13 * 
    p13.g + respvec$cy1.cy2.cy3/TIn$p000 * d11.13 * p13.g.c - 
    respvec$cy1.cy2.y3/TIn$p001 * d11.13 * p13.g.c - respvec$y1.cy2.cy3/TIn$p100 * 
    d11.13 * p13.g.c + respvec$y1.cy2.y3/TIn$p101 * d11.13 * 
    p13.g.c
  dl.dtheta23 <- respvec$y1.y2.y3/TIn$p111 * d11.23 * p23.g - 
    respvec$y1.y2.cy3/TIn$p110 * d11.23 * p23.g + respvec$cy1.y2.y3/TIn$p011 * 
    d11.23 * p23.g.c - respvec$cy1.y2.cy3/TIn$p010 * d11.23 * 
    p23.g.c + respvec$cy1.cy2.cy3/TIn$p000 * d11.23 * p23.g.c - 
    respvec$cy1.cy2.y3/TIn$p001 * d11.23 * p23.g.c + respvec$y1.cy2.cy3/TIn$p100 * 
    d11.23 * p23.g - respvec$y1.cy2.y3/TIn$p101 * d11.23 * 
    p23.g
  if (VC$Chol == FALSE) {
    dtheta12.dtheta12.st <- 4 * exp(2 * TIn$theta12.st)/(exp(2 * 
                                                               TIn$theta12.st) + 1)^2
    dtheta13.dtheta13.st <- 4 * exp(2 * TIn$theta13.st)/(exp(2 * 
                                                               TIn$theta13.st) + 1)^2
    dtheta23.dtheta23.st <- 4 * exp(2 * TIn$theta23.st)/(exp(2 * 
                                                               TIn$theta23.st) + 1)^2
    dl.dtheta12.st <- dl.dtheta12 * dtheta12.dtheta12.st
    dl.dtheta13.st <- dl.dtheta13 * dtheta13.dtheta13.st
    dl.dtheta23.st <- dl.dtheta23 * dtheta23.dtheta23.st
  }
  if (VC$Chol == TRUE) {
    
    # #### When I compare corrs with regressors and corrs without regressors: ####
# TIn$theta12.st <- rep(TIn$theta12.st, VC$n)
# TIn$theta13.st <- rep(TIn$theta13.st, VC$n)
# TIn$theta23.st <- rep(TIn$theta23.st, VC$n)

    # TIn$theta12.st <- theta12.st
    # TIn$theta13.st <- theta13.st
    # TIn$theta23.st <- theta23.st
 ########################################################
    
    dth12.dth12.st <- 1/(1 + TIn$theta12.st^2)^(3/2)
    dth13.dth13.st <- (1 + TIn$theta23.st^2)/(1 + TIn$theta13.st^2 + TIn$theta23.st^2)^(3/2)
    dth13.dth23.st <- -(TIn$theta13.st * TIn$theta23.st)/(1 + TIn$theta13.st^2 + TIn$theta23.st^2)^(3/2)
    dth23.dth12.st <- TIn$theta13.st/sqrt((1 + TIn$theta12.st^2) * (1 + TIn$theta13.st^2 + TIn$theta23.st^2)) - (TIn$theta12.st * (TIn$theta12.st * TIn$theta13.st + TIn$theta23.st))/((1 + TIn$theta12.st^2)^(3/2) * sqrt(1 + TIn$theta13.st^2 + TIn$theta23.st^2))
    dth23.dth13.st <- TIn$theta12.st/sqrt((1 + TIn$theta12.st^2) * 
                                            (1 + TIn$theta13.st^2 + TIn$theta23.st^2)) - (TIn$theta13.st * 
                                                                                            (TIn$theta12.st * TIn$theta13.st + TIn$theta23.st))/(sqrt(1 + 
                                                                                                                                                        TIn$theta12.st^2) * (1 + TIn$theta13.st^2 + TIn$theta23.st^2)^(3/2))
    dth23.dth23.st <- 1/sqrt((1 + TIn$theta12.st^2) * (1 + TIn$theta13.st^2 + TIn$theta23.st^2)) - (TIn$theta23.st * (TIn$theta12.st * TIn$theta13.st + TIn$theta23.st))/(sqrt(1 + 
                                                                                                                                                                                 TIn$theta12.st^2) * (1 + TIn$theta13.st^2 + TIn$theta23.st^2)^(3/2))
    
    if(is.null(VC$X4)){ 
      
      dth12.dth13.st <- 0
      dth12.dth23.st <- 0
      dth13.dth12.st <- 0
                      
      dl.dtheta       <- cbind(dl.dtheta12, dl.dtheta13, dl.dtheta23)
      dtheta.theta.st <- matrix(c(dth12.dth12.st, dth13.dth12.st, 
                                  dth23.dth12.st, dth12.dth13.st, dth13.dth13.st, dth23.dth13.st, 
                                  dth12.dth23.st, dth13.dth23.st, dth23.dth23.st), 
                                3, 3)
      dl.dtheta.st <- dl.dtheta %*% dtheta.theta.st
      dl.dtheta12.st <- dl.dtheta.st[, 1]
      dl.dtheta13.st <- dl.dtheta.st[, 2]
      dl.dtheta23.st <- dl.dtheta.st[, 3]
    }
    
    if(!is.null(VC$X4)){  

    dth12.dth13.st <- rep(0, VC$n)
    dth12.dth23.st <- rep(0, VC$n)
    dth13.dth12.st <- rep(0, VC$n)
   

    dl.dtheta <- c(dl.dtheta12, dl.dtheta13, dl.dtheta23)
    
    dl.dtheta12.st <- dl.dtheta * c(dth12.dth12.st, dth13.dth12.st, dth23.dth12.st)
    dl.dtheta13.st <- dl.dtheta * c(dth12.dth13.st, dth13.dth13.st, dth23.dth13.st)
    dl.dtheta23.st <- dl.dtheta * c(dth12.dth23.st, dth13.dth23.st, dth23.dth23.st)
    }
    
  }
  GTRIVec <- list(p12.g = p12.g, p13.g = p13.g, p23.g = p23.g, 
                  p12.g.c = p12.g.c, p13.g.c = p13.g.c, p23.g.c = p23.g.c, 
                  d.1 = d.1, d.2 = d.2, d.3 = d.3, dmar1 = dmar1, dmar2 = dmar2, 
                  dmar3 = dmar3, d11.12 = d11.12, d11.13 = d11.13, d11.23 = d11.23, 
                  p.1.11 = p.1.11, p.1.10 = p.1.10, p.1.00 = p.1.00, p.1.01 = p.1.01, 
                  p.2.11 = p.2.11, p.2.10 = p.2.10, p.2.00 = p.2.00, p.2.01 = p.2.01, 
                  p.3.11 = p.3.11, p.3.10 = p.3.10, p.3.00 = p.3.00, p.3.01 = p.3.01, 
                  dF1.de1 = dF1.de1, dF2.de2 = dF2.de2, dF3.de3 = dF3.de3, 
                  dl.dF1 = dl.dF1, dl.dF2 = dl.dF2, dl.dF3 = dl.dF3, dl.de1 = VC$weights * 
                    dl.de1, dl.de2 = VC$weights * dl.de2, dl.de3 = VC$weights * 
                    dl.de3, dl.dtheta12.st = VC$weights * dl.dtheta12.st, 
                  dl.dtheta13.st = VC$weights * dl.dtheta13.st, dl.dtheta23.st = VC$weights * 
                    dl.dtheta23.st, mean.12 = mean.12, mean.13 = mean.13, 
                  mean.23 = mean.23, sd.12 = sd.12, sd.13 = sd.13, sd.23 = sd.23, 
                  dl.dtheta12 = dl.dtheta12, dl.dtheta13 = dl.dtheta13, 
                  dl.dtheta23 = dl.dtheta23)
  GTRIVec
}