R/loglik_cragg_MG_intR.R

In jackiemauro/hurdleIV:

### This function returns the negative log-likelihood (so that it can be minimized)
### The math follows Max G'Sell's derivation.
### Using integrateR

loglik_MG_intR = function(params){
  require(Rmpfr)
  sig_v = params[1]
  sig_u = params[2]
  tau1 = params[3]
  tau0 = params[4]
  rho = params[5]
  beta11 = params[6]
  beta12 = params[7]
  beta2 = params[8]
  gamma11 = params[9]
  gamma12 = params[10]
  gamma2 = params[11]
  pi11 = params[12]
  pi12 = params[13]
  pi2 = params[14]
  tm0 = proc.time()[1]

  censored = y1<=0

  pre = matrix( c(1, rho,    tau0,
                  0,     sig_u^2,    tau1,
                  0,  0, sig_v^2),
                ncol = 3, byrow = T)
  Sig_err = t(pre)%*%pre / ((t(pre)%*%pre)[1,1])
  if(min(eigen(Sig_err)$values)<=0){return(Inf)}
  if((sig_u<=0)|(sig_v<=0)){return(Inf)}

  #Transformation matrix from (eta, u, v) to (y0*, log y1*, x2) (without the mean)
  A = rbind(
    c(1,0,gamma2),
    c(0,1,beta2),
    c(0,0,1)
  )
  #Covariance of (y0*, log y1*, x2)
  Sig = A%*%Sig_err%*%t(A)
  if(min(eigen(Sig)$values)<=0){return(Inf)}

  #Means for (y0^*, y1*, x2).
  mu_y0 = gamma11 + gamma12*x1 + gamma2*(pi11 + pi12*x1 + pi2*z)
  mu_y1 = beta11 + beta12*x1 + beta2*(pi11 + pi12*x1 + pi2*z)
  mu_x2 = pi11 + x1*pi12 + z*pi2

  #Parameters for x2
  sig2_x2 = Sig[3,3]

  #Parameters for y0star given x2
  mu_y0_x2 = mu_y0 + Sig[1,3]/Sig[3,3]*(x2-mu_x2)
  sig2_y0_x2 = Sig[1,1] - Sig[1,3]^2/Sig[3,3]

  #Parameters for log(y1star) given x2
  mu_y1_x2 = mu_y1 + Sig[2,3]/Sig[3,3]*(x2-mu_x2)
  sig2_y1_x2 = Sig[2,2] - Sig[2,3]^2/Sig[3,3]

  #Parameters for y0star given y1star and x2
  mu_y0_y1x2 = c(mu_y0 + Sig[1,2:3,drop=FALSE]%*%solve(Sig[2:3,2:3])%*%rbind(y1-mu_y1,x2-mu_x2))
  sig2_y0_y1x2 = Sig[1,1] - Sig[1,2:3,drop=FALSE]%*%solve(Sig[2:3,2:3])%*%Sig[2:3,1,drop=FALSE]

  #Parameters for y0star and y1star given x2
  #mu_y1y0_x2 = c(t(t(cbind(mu_y0,mu_y1)) + Sig[1:2,3]%*%solve(sig2_x2)%*%t(x2-mu_x2)))
  sig2_y1y0_x2 = Sig[1:2,1:2] - Sig[1:2,3]%*%solve(sig2_x2)%*%Sig[3,1:2]
  sig2_y1y0_x2[upper.tri(sig2_y1y0_x2)] <- sig2_y1y0_x2[lower.tri(sig2_y1y0_x2)]
  if(any(eigen(sig2_y1y0_x2)$value<0)){return(-Inf)}

  #Parameters for y1star and y0star given x2
  Sig_02 = Sig[-2,-2]
  sig2_y1_y0x2 = Sig[2,2] - Sig[2,c(1,3),drop=FALSE]%*%solve(Sig_02)%*%Sig[c(1,3),2,drop=FALSE]


  ###Calculate the contributions to the log likelihood.
  dat = data.frame(y1=y1,x2=x2
                   ,mu_y0_y1x2=mu_y0_y1x2
                   ,mu_y1_x2=mu_y1_x2,mu_y0_x2=mu_y0_x2
                   ,mu_x2=mu_x2,mu_y1=mu_y1,mu_y0=mu_y0)
  dat0 = dat[y1==0,]
  dat1 = dat[y1>0,]


  # ll0
  f0 <- function(dat){
    dat = as.list(dat)
    pnorm(0,mean=dat$mu_y0_x2,sd=sqrt(sig2_y0_x2),log.p = TRUE) +
      dnorm(dat$x2,mean=dat$mu_x2,sd=sqrt(sig2_x2),log = TRUE)
  }

  ll0 = sum( apply(dat0,1,f0) )


  #ll1
  f1 <- function(dat){
    dat = as.list(dat)
    constants = log(1/(2*pi*det(sig2_y1y0_x2)))

    integrand <- function(u){
      # why is u sometimes 1x2 and sometimes 1x1?
      top = diag(exp(-0.5*cbind(u-dat$mu_y0,dat$y1-dat$mu_y1)%*%solve(sig2_y1y0_x2)%*%rbind(u-dat$mu_y0,dat$y1-dat$mu_y1)))
      bmean = dat$mu_y1 + Sig[2,c(1,3),drop=FALSE]%*%solve(Sig_02)%*%rbind(u-dat$mu_y0,dat$x2-dat$mu_x2)
      ratio = top/pnorm(mpfr(0,20),mean=bmean[1,],sd=sqrt(sig2_y1_y0x2)[1,1],lower.tail = F)
      return(ratio)
    }

    int_result = integrateR(integrand,0,2000,ord = 14)
    assign("JMcounter",JMcounter+1,envir = .GlobalEnv)
    print(paste("round:",JMcounter))

    dnorm(dat$x2,mean=dat$mu_x2,sd=sqrt(sig2_x2),log = TRUE) +
      constants +
      log(int_result$value)
  }

  tosum = apply(dat1,1,f1)
  ll1 = as.numeric(Reduce("+",tosum))

  print(paste("likelihood=",-(ll0+ll1)))
  print(paste('total time:',proc.time()[1] -tm0))

  #Return the negative log-likelihood, since I will be using optim (which minimizes instead of maximizing)
  -(ll0+ll1)
}