R/jags_3mlqmm_f.R

In AntoineBbi/BQt: BQt: Bayesian Quantile regression for joint modeling

jags_3mlqmm_f <-
  function (...) {
    for(q in 1:Q){
      c1[q] <- (1-2*tau[q])/(tau[q]*(1-tau[q]))
      c2[q] <- 2/(tau[q]*(1-tau[q]))
    }
  # likelihood
  for (i in 1:I){
    # longitudinal part
    for(j in offset[i]:(offset[i+1]-1)){
      # define object
      W[j, 1] ~ dexp(1/sigma[1])
      W[j, 2] ~ dexp(1/sigma[2])
      W[j, 3] ~ dexp(1/sigma[3])
      V11[j] <- W[j, 1]*sigma[1]*c2[1]
      V22[j] <- W[j, 2]*sigma[2]*c2[2]
      V33[j] <- W[j, 3]*sigma[3]*c2[3]
      V12[j] <- sqrt(V11[j]*V22[j])*rho12
      V13[j] <- sqrt(V11[j]*V33[j])*rho13
      V23[j] <- sqrt(V22[j]*V33[j])*rho23
      # first quantile distribution
      y[j, 1] ~ dnorm(mu1[j], prec1[j])
      mu1[j] <- inprod(beta[1, 1:ncX], X[j, 1:ncX]) + inprod(b[i, 1:ncU], U[j, 1:ncU]) + c1[1]*W[j, 1]
      prec1[j] <- 1/V11[j]
      # conditional distrubtion for second quantile given y[j, 1]
      y[j, 2] ~ dnorm(mu2.knowing.y1[j], prec2[j])
      mu2[j] <- inprod(beta[2, 1:ncX], X[j, 1:ncX]) + inprod(b[i, (ncU+1):(2*ncU)], U[j, 1:ncU]) + c1[2]*W[j, 2]
      mu2.knowing.y1[j] <- mu2[j] + rho12*sqrt(V22[j]/V11[j])*(y[j, 1]-mu1[j])
      prec2[j] <- 1/(V22[j]*(1-pow(rho12, 2)) )
      # # Conditional normal distribution for third quantile, conditional on both first and second quantile
      y[j, 3] ~ dnorm(mu3.knowing.y1.y2[j], prec3[j])
      mu3[j] <- inprod(beta[3, 1:ncX], X[j, 1:ncX]) + inprod(b[i, (ncU*2+1):(3*ncU)], U[j, 1:ncU]) + c1[3]*W[j, 3]
      mu3.knowing.y1.y2[j] <- mu3[j] + sqrt(V33[j]/V11[j])*(rho13-rho12*rho23)*(y[j, 1]-mu1[j]) + sqrt(V33[j]/V22[j])*(rho23-rho12*rho13)*(y[j, 2]-mu2[j])
      prec3[j] <- 1/(V33[j]*(1 - (pow(rho13, 2)+pow(rho23, 2)-2*rho12*rho13*rho23)/(1-pow(rho12, 2))))
    }#end of j loop
    # random effects
    b[i, 1:(ncU*Q)] ~ dmnorm(mu0[], prec.Sigma2[, ])
  }#end of i loop
  # priors for parameters
  prec.Sigma2[1:(ncU*Q), 1:(ncU*Q)] ~ dwish(priorR.Sigma2[, ], priorK.Sigma2)
  covariance.b <- inverse(prec.Sigma2[, ])
  for(qqq in 1:Q){
    beta[qqq, 1:ncX] ~ dmnorm(priorMean.beta[qqq, ], priorTau.beta[, ])
    sigma[qqq] ~ dgamma(priorA.sigma, priorB.sigma)
  }
  rho12 ~ dunif(-1,1)
  rho13 ~ dunif(-1,1)
  rho23 ~ dunif(-1,1)
}