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-#####################################################################################################
-## Modele ln-lineaire generalise                                                                   ##
-## Gestion donnees en DataTable - Optimisation Nelder-Mead en fonction                             ##
-## 2020-01-20                                                                                      ##
-## source("ANC/GlnLM-EffLocDisp-DT-fctNM.R")                                                       ##
-#####################################################################################################
-
-options(width=100);
-ok <-1;
-if (ok == 1) {
-  rm(list = ls());
-}
-
-library(data.table);
-library(numDeriv);
-
-## Repertoire de travail ##
-chem <- "/Users/eva.falipou/Documents/Eva/ANC/ln_linaire/";
-
-#####################################################################################################
-## Lecture donnees - Exemple : analyse NTK avec loq=1                                              ##
-#####################################################################################################
-ok <-1;
-if (ok == 1) {
-  fin <- paste(chem,"BDD_exemple_ln-lineaire.csv",sep="");
-  don <- fread(fin,dec=",",sep=";");
-  don[,y:=NTK]; # choix de la variable dependante
-  ## Libelle variable dependante pour documenter affichages ##
-  labvdep <- "NTK";
-  ## Left-censoring ##
-  loq <- 1.0; # LQ correspondant a la variable dependante 
-  don[,lb:=y];
-  don[y<=loq,lb:=0];
-  don[,ub:=y];
-  don[y<=loq,ub:=loq];
-  ## Variables explicatives ##
-  don[,D0:=ifelse(Dispositif=="D0",1,0)];
-  don[,D2:=ifelse(Dispositif=="D2",1,0)];
-  don[,inf2ans:=ifelse(classe_age=="< 2 ans",1,0)];
-  don[,inf70pct:=ifelse(classe_charge=="< 70%",1,0)];
-  ## Nettoyage ##
-  don <- don[,.(y,lb,ub,D0,D2,inf2ans,inf70pct)];
-  don <- na.omit(don);
-  ## Effects on location (median) ##
-  zm <- c("D0");
-  #zm <- c();## No effect on location ##
-  nbzm <- length(zm);
-  ## Effects on dispersion ##
-  zd <- c();
-  #zd <- c("D1","D2","inf2ans","inf70pct");## No effect on dispersion ##
-  nbzd <- length(zd);
-}
-
-#####################################################################################################
-## Log-Likelihood calculation - Based on log-normal distribution                                   ##
-#####################################################################################################
-funk <- function(theta) {## theta : parameter vector (beta0,beta1,gamma0,gamma1) ##
-  n <- don[,.N];
-  ## Regression - Effects on median ##
-  if (nbzm > 0) {
-    Zm <- cbind(array(1, dim=c(n,1)), as.matrix(don[,zm,with=F]));
-  } else {
-    Zm <- array(1, dim=c(n,1));
-  }
-  zbm <- Zm%*%theta[1:(1+nbzm)];
-  ## Regression - Effects on dispersion ##
-  if (nbzd > 0) {
-    Zd <- cbind(array(1, dim=c(n,1)), as.matrix(don[,zd,with=F]));
-  } else {
-    Zd <- array(1, dim=c(n,1));
-  }
-  zbd <- Zd%*%theta[(2+nbzm):(2+nbzm+nbzd)];
-  s <- exp(zbd);
-  ## Log-Likelihood calculation ##
-  ll <- 0;
-  li <- don[, which(lb == 0)];
-  if (length(li) > 0) {
-    ll <- sum(log(plnorm(q=don[li, ub],meanlog=zbm[li],sdlog=s[li])));
-  }
-  li <- don[, which(lb > 0 & ub > lb)];
-  if (length(li) > 0) {
-    Fu <- plnorm(don[li, ub],meanlog=zbm[li],sdlog=s[li]);
-    Fl <- plnorm(don[li, lb],meanlog=zbm[li],sdlog=s[li]);
-    ll <- ll + sum(log(Fu - Fl));
-  }
-  li <- don[, which(lb > 0 & ub == lb)];
-  if (length(li) > 0) {
-    f <- dlnorm(don[li, ub],meanlog=zbm[li],sdlog=s[li]);
-    ll <- ll + sum(log(f));
-  }
-  if(is.na(ll) | is.infinite(ll)) {
-    ll <- -1.0e200;
-    ## Checking calculation in case of data problem ##
-    #cat("theta = ", theta, " - ll = ", -ll, "\n");
-  }
-  -ll; ## minimize -ll <=> maximize ll ##
-}
-
-## Amotry Function ###########################################################################
-amotry <- function(p, y, psum, ndim, ihi, fac) {
-  ptry <- numeric();
-  fac1 <- (1 - fac) / ndim;
-  fac2 <- fac1 - fac;
-  for(j in 1:ndim) ptry[j] <- psum[j] * fac1 - p[ihi,j] * fac2;
-  ptry <- pmin(pmax(ptry, lowb), uppb); ## Bounds
-  ytry <- funk(ptry);
-  if(ytry < y[ihi]) {
-    y[ihi] <- ytry;
-    for(j in 1:ndim) {
-      psum[j] <- psum[j] + ptry[j] - p[ihi,j];
-      p[ihi,j] <- ptry[j];
-    }
-  }
-  list(ytry, p, y, psum);
-}
-
-## Nelder-Mead calibration ##
-NMcal <- function(NMpar) {
-  ## Libelle variable dependante ##
-  labvdep <- NMpar[[1]];
-  ## Libelle parametres ##
-  labtheta <- NMpar[[2]];
-  ## Nb parametres a estimer ##
-  nbp <- length(labtheta);
-  ## Valeurs de reference des parametres pour test H0 ##
-  thref <- NMpar[[3]];
-  ## Valeurs initiales des parametres et bornes ##
-  theta <- NMpar[[4]];print(theta);
-  lowb <- NMpar[[5]];
-  uppb <- NMpar[[6]];
-  ## Pas de recherche initial ##
-  lbd <- NMpar[[7]];
-  ## Initialisation simplex ####################################################################
-  ndim <- length(theta);
-  mpts <- ndim + 1;
-  p <- array(0, c(mpts, ndim));
-  p[1,] <- theta;
-  for(i in 2:mpts) {
-    p[i,] <- p[1,];
-    p[i,i-1] <- p[i,i-1] + lbd[i-1];
-  }
-  #print(p);
-  psum <- numeric();
-  y <- numeric();
-  yr <- numeric();
-  for(i in 1:mpts) y[i] <- funk(p[i,]);
-  ftol <- 1e-8;
-  maxiter <- 5000;
-  #maxiter <- 1;
-  maxcycle <- 0;
-  tiny <- 1e-10;
-  ##############################################################################################
-  iter <- 0;
-  cycle <- 0;
-  for(j in 1:ndim) psum[j] <- sum(p[,j]);
-  swap <- numeric();
-  repeat {
-    iter <- iter + 1;
-    if (iter == 1 | round(iter / 100) == iter / 100) {
-      cat("Iteration", iter, "\n");
-      print(cbind(p, y));
-    }
-    ## Rank points of simplex ##################################################################
-    yr <- rank(y, ties.method="first");
-    for(i in 1:mpts) {
-      if(yr[i] == 1) ilo <- i;
-      if(yr[i] == ndim) inhi <- i;
-      if(yr[i] == mpts) {ihi <- i;yhi <- y[i];}
-    }
-    ## Test whether convergence achieved #######################################################
-    rtol <- 2 * abs(y[ihi] - y[ilo]) / (abs(y[ihi]) + abs(y[ilo]) + tiny);
-    if(rtol < ftol){
-      print("precision reached");
-      converge <- 1;
-    }
-    if(iter >= maxiter){ 
-      print("maxiter reached");
-      converge <- 0;
-    }
-    if(rtol < ftol || iter >= maxiter) {
-      swap[1] <- y[1];y[1] <- y[ilo];y[ilo] <- swap[1];
-      swap <- p[1,];p[1,] <- p[ilo,];p[ilo,] <- swap;
-      print("Iteration", quote=FALSE);print(iter, quote=FALSE);
-      print(cbind(p, y));
-      print("", quote=FALSE);
-      ## Display Calibration Results ########################################################
-      print("Final", quote=FALSE);print(c(p[1,], y[1]));
-      ## Covariance matrix ##
-      covmat <- tryCatch(expr={solve(hessian(funk,p[1,]))},error=function(e){hinv <- 0;return(array(NA,dim=c(nbp,nbp)))});
-      hinv <- ifelse(sum(is.na(covmat))>0,0,1);
-      cat("Covariance matrix :\n");
-      print(covmat);
-      cat("\n");
-      cat("Dependent variable : ",labvdep,"\n");
-      ## Table of estimates ##
-      cat(format("Label", width=15));
-      cat(format("Estimate", width=15, justify="right"));
-      cat(format("Std. Dev.", width=15, justify="right"));
-      cat(format("Ref", width=7, justify="right"));
-      cat(format("Chi2", width=15, justify="right"));
-      cat(format("DF", width=4, justify="right"));
-      cat(format("Pval", width=11, justify="right"), "\n");
-      for (j in 1:length(theta)) {
-        thtest <- p[1,];
-        thtest[j] <- thref[j];
-        #chi2 <- 2 * abs(y[1] - funk(thtest));
-        #stdev <- abs(p[1,j] - thref[j]) / sqrt(chi2);
-        stdev <- sqrt(covmat[j,j]);
-        chi2 <- ((p[1,j] - thref[j])^2/covmat[j,j]);
-        df <- 1;
-        pval <- pchisq(chi2, df, lower.tail=FALSE);
-        cat(format(labtheta[j], width=15));
-        cat(formatC(p[1,j], digits=4, format="e", width=15));
-        cat(formatC(stdev, digits=4, format="e", width=15));
-        cat(format(thref[j], digits=2, width=7));
-        cat(formatC(chi2, digits=4, format="e", width=15));
-        cat(format(df, digits=1, width=4));
-        cat(formatC(pval, digits=4, format="f", width=11), "\n");
-      }
-      if (cycle < maxcycle) {
-        for(i in 2:mpts) {
-          p[i,] <- p[1,];
-          p[i,i-1] <- p[i,i-1] + lbd[i-1];
-        }
-        for(i in 1:mpts) y[i] <- funk(p[i,]);
-        iter <- 0;
-        cycle <- cycle + 1;
-      }
-      else break;
-    }
-    ## New iteration ###########################################################################
-    lamo <- amotry(p, y, psum, ndim, ihi, -1);
-    ytry <- lamo[[1]];p <- lamo[[2]];y <- lamo[[3]];psum <- lamo[[4]];
-    ##print("Factor -1");
-    ##print(cbind(p, y));
-    if(ytry <= y[ilo]) {
-      lamo <- amotry(p, y, psum, ndim, ihi, 2);
-      ytry <- lamo[[1]];p <- lamo[[2]];y <- lamo[[3]];psum <- lamo[[4]];
-      ##print("Factor 2");
-      ##print(cbind(p, y));
-    }
-    else if(ytry >= y[inhi]) {
-      ysave <- y[ihi];
-      lamo <- amotry(p, y, psum, ndim, ihi, .5);
-      ytry <- lamo[[1]];p <- lamo[[2]];y <- lamo[[3]];psum <- lamo[[4]];
-      ##print("Factor .5");
-      ##print(cbind(p, y));
-      if(ytry >= ysave) {
-        for(i in 1:mpts) {
-          if(i != ilo) {
-            for(j in 1:ndim) p[i,j] <- 0.5 * (p[i,j] + p[ilo,j]);
-            y[i] <- funk(p[i,]);
-          }
-        }
-        for(j in 1:ndim) psum[j] <- sum(p[,j]);
-      }
-    }
-  }
-  list(p[1,],converge,hinv,covmat);
-}
-
-#####################################################################################################
-## Variance of theoretical percent-quantile                                                          ##
-#####################################################################################################
-delt <- function(tab,percent,covm) {
-  n <- tab[,.N];
-  if (nbzm > 0) {
-    Zm <- cbind(array(1, dim=c(n,1)), as.matrix(tab[,zm,with=F]));
-  } else {
-    Zm <- array(1, dim=c(n,1));
-  }
-  if (nbzd > 0) {
-    Zd <- cbind(array(1, dim=c(n,1)), as.matrix(tab[,zd,with=F]));
-  } else {
-    Zd <- array(1, dim=c(n,1));
-  }
-  zbd <- Zd%*%theta[(2+nbzm):(2+nbzm+nbzd)];
-  Zmd <- Zm;
-  for(j in 1:(nbzd+1)) Zmd <- cbind(Zmd, Zd[,j] * exp(zbd) * qnorm(percent));
-  diag(Zmd%*%covm%*%t(Zmd));
-}
-
-###################################################################################################
-## Model parameter estimation                                                                    ##
-###################################################################################################
-ok <- 1;
-if (ok == 1) {
-  ## Libelle parametres ##
-  labtheta <- c("beta0",zm,"gamma0",zd);
-  ## Nb parametres a estimer ##
-  nbp <- length(labtheta);
-  ## Valeurs de reference des parametres pour test H0 ##
-  thref <- rep(0,nbp);
-  ## Valeurs initiales des parametres et bornes ##
-  theta <- rep(0,nbp);
-  lowb <-  rep(-Inf,nbp);
-  uppb <-  rep(+Inf,nbp);
-  ## Pas de recherche initial ##
-  lbd <- rep(0.5,nbp);
-  NMpar <- list(labvdep,labtheta,theta,thref,lowb,uppb,lbd);
-  calage <- NMcal(NMpar);
-  thopt <- calage[[1]];
-  converge <- calage[[2]];
-  hinv <- calage[[3]];
-  covmat <- calage[[4]];
-  #####################################################################################################
-  ## Quantile estimation                                                                             ##
-  #####################################################################################################
-  percent <- 0.5;## Quantile probability ##
-  ## Quantiles are estimated by fac variables ##
-  fac <- unique(c(zm,zd));
-  ## Empirical (observed) quantiles ##
-  qua <- don[,.(qobs=quantile(ub,probs=percent,na.rm=T),nbobs=.N),by=fac];
-  n <- qua[,.N];
-  ## Regression - Effects on median ##
-  if (nbzm > 0) {
-    Zm <- cbind(array(1,dim=c(n,1)),as.matrix(qua[,zm,with=F]));
-  } else {
-    Zm <- array(1,dim=c(n,1));
-  }
-  zbm <- Zm%*%thopt[1:(1+nbzm)];
-  ## Regression - Effects on dispersion ##
-  if (nbzd > 0) {
-    Zd <- cbind(array(1,dim=c(n,1)),as.matrix(qua[,zd,with=F]));
-  } else {
-    Zd <- array(1,dim=c(n,1));
-  }
-  zbd <- Zd%*%thopt[(2+nbzm):(2+nbzm+nbzd)];
-  #s <- exp(zbd);
-  qua[,qcal:=exp(zbm+exp(zbd)*qnorm(percent))];
-  ## Left-censored counts ##
-  lce <- don[lb<ub,.(nblce=.N),by=fac];
-  qua <- merge(qua,lce,by=fac,all=TRUE);
-  qua[is.na(nblce),nblce:=0];
-  ## Variance of theoretical quantile ##
-  qua[,vqc:=delt(qua,percent,covmat)];
-  ## Lower and upper bounds of theoretical quantile ##
-  qua[,lbqc:=qcal*exp(-1.96*vqc^0.5)];
-  qua[,ubqc:=qcal*exp(+1.96*vqc^0.5)];
-  ## Displaying observed and theoretical quantile ##
-  cat("\n");
-  cat("Dependent variable : ",labvdep," - Table of observed and theoretical ",percent*100,"%-quantiles:\n",sep="");
-  #print(qua[, .(Z1,Z2,nbobs,nblce,qobs,qcal,vqc,lbqc,ubqc)]);
-  print(qua[,c(fac,"nbobs","nblce","qobs","qcal","vqc","lbqc","ubqc"),with=F]);
-}