R/fMP_CorrGxM.R

In GxM: Maximum Likelihood Estimation for Gene-by-Measured Environment Interaction Models

fMP_CorrGxM <-
function(listdata, param, PointsW) {

  ## model 6

  m = c(listdata$M1,listdata$M2); 
  p1 = listdata$P1;  p2 = listdata$P2; 
  rG = listdata$rG;

  muM = param$muM;  muP = param$muP;
  aM = param$aM;  cM = param$cM;  eM = param$eM;

  aP = param$aP;  cP = param$cP;  eP = param$eP;
  rA = param$rA;  rC = param$rC;  rE = param$rE;
  alphaP = param$alphaP;
  kappaP = param$kappaP;
  epsilonP = param$epsilonP;

  aC = rA*aP;  cC = rC*cP;  eC = rE*eP;
  aU = sqrt(1-rA^2)*aP;  cU = sqrt(1-rC^2)*cP;  eU = sqrt(1-rE^2)*eP;
  alphaC = rA*alphaP;
  alphaU = sqrt(1-rA^2)*alphaP;
  kappaC = rC*kappaP;
  kappaU = sqrt(1-rC^2)*kappaP;
  epsilonC = rE*epsilonP;
  epsilonU = sqrt(1-rE^2)*epsilonP;

  Points = PointsW$Points;
  W=PointsW$W;
  K3 = length(W);

  entry1 = aM^2 + cM^2 + eM^2;   
  entry2 = aM^2*rG + cM^2; 
  SigmaM = matrix(c(entry1, entry2, 
                    entry2, entry1),2,2);
  invSigmaM = solve(SigmaM);
  fm = log(2*pi) + 0.5*log(det(SigmaM)) + 0.5*(m-muM)%*%invSigmaM%*%(m-muM); 

  SigmaAC = matrix(c( 1, rG, 0,
                     rG,  1, 0,
                      0,  0, 1), 3,3)
  SigmaACM = matrix(c( aM, aM*rG, cM, aM*rG, aM, cM), 3,2)
  covAC_M = SigmaAC - SigmaACM %*%invSigmaM%*%t(SigmaACM);
  trans = sqrt(2)*t(chol(covAC_M));
  tmpA = SigmaACM %*% invSigmaM; 
  tmpB = tmpA %*% c(muM,muM);
  tmpC = tmpA %*% m - tmpB;  
  tmpD = matrix(rep(tmpC,K3),3,K3)
  AC = tmpD + trans %*% Points;
  CC = t(matrix(rep(AC[3,],2),K3,2))

  tmpA = matrix(rep(m-muM,K3),2,K3)    
  E = (tmpA - aM*AC[1:2,] - cM*CC) / eM;    
  muP_ACM = muP+(aC+alphaC*m)*AC[1:2,]+(cC+kappaC*m)*CC+(eC+epsilonC*m)*E; 

  entry11 = (aU+alphaU*m[1])^2+(cU+kappaU*m[1])^2+(eU+epsilonU*m[1])^2;
  entry12 = (aU+alphaU*m[1])*(aU+alphaU*m[2])*rG+(cU+kappaU*m[1])*(cU+kappaU*m[2]);
  entry22 = (aU+alphaU*m[2])^2+(cU+kappaU*m[2])^2+(eU+epsilonU*m[2])^2;

  det_covP_ACM = entry11*entry22 - entry12^2;
  infind = det_covP_ACM < 1e-6;
  entry11[infind] = 1e-3;
  entry12[infind] = 0;
  entry22[infind] = 1e-3;

  tmpA = (p1-muP_ACM[1,])*entry22 - (p2-muP_ACM[2,])*entry12;  
  tmpB = -(p1-muP_ACM[1,])*entry12 + (p2-muP_ACM[2,])*entry11;  
  tmpC = (tmpA*(p1-muP_ACM[1,]) + tmpB*(p2-muP_ACM[2,])) / det_covP_ACM;
  inversevalue = 2*pi*sqrt(det_covP_ACM)*exp(0.5*tmpC);

  fp_M = -log(sum(W/inversevalue)) + 1.5*log(pi);

  return(fm+fp_M);
}