R/HTE3.R

In OnofriAndreaPG/drcSeedGerm: Utilities for Data Analyses in Seed Germination/Emergence Assays

#HT-to-event. With shifted exponential + GR50polynomial (convex up)
HTE3.fun <- function(time, Psi, G, Psib, sigmaPsib, thetaH, b){
  Pmax <- PmaxPsi1.fun(Psi, G, Psib, sigmaPsib)
  GR50 <- GRPsiPol.fun(Psi, Psib, thetaH)
  plogis(b * (log(time) - log(1/GR50)))*Pmax
}
"HTE3" <- function(fixed = c(NA, NA, NA, NA, NA),
                   names = c("G", "Psib", "sigmaPsib", "thetaH", "b")){
  numParm <- 5
  if (!is.character(names) | !(length(names) == numParm)) {stop("Not correct 'names' argument")}
  if ( !(length(fixed) == numParm) ) {stop("Not correct 'fixed' argument")}
  # Only G can be constrained
  if (any(!is.na(fixed[2:5]))) {stop("Only the G parameter can be constrained, at the moment")}

  ## Handling 'fixed' argument
  notFixed <- is.na(fixed)
  parmVec <- rep(0, numParm)
  parmVec[!notFixed] <- fixed[!notFixed]

  fct <- function(x, parm){
    parmMat <- matrix(parmVec, nrow(parm), numParm, byrow = TRUE)
    parmMat[, notFixed] <- parm
    parm <- parmMat

    S <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                  parm[,4], parm[,5])
    return(S)
  }

  names <- names[notFixed]
  name <- "HTE3"

  ss <- function(data){
    data <- subset(data, is.finite(data[,1])==T)
    result <- c()
    PsiF <- factor(data[,2])
    for(i in 1:length(levels(PsiF))){
      temp <- subset(data, data[,2] == levels(PsiF)[i])
      x <- temp[,1] + 0.0001; y <- temp[,3]

      # self-start
      d <- max(y) * 1.05
      pseudoY <- log((d - y)/(y + 0.00001)  + 1e-06 )
      coefs <- coef( lm(pseudoY ~ log(x+0.000001)))
      k <- -coefs[1]; b <- coefs[2]
      ED50 <- exp(k/b)
      modT <- try(nls(y ~ d/(1 + exp(b * (log(x + 0.000001) - log(ED50)))),
                      start = list(d = d, b = b, ED50 = ED50)), silent=T)
      if(inherits(modT, "try-error")) {
        res <- as.numeric(levels(PsiF)[i])
      result <- c(result, res)}
    }
    result
    dataset_cum <- subset(data, is.finite(data[,1])==T)

    if(is.null(result)!=T){
      for(i in 1:length(result)) dataset_cum <- subset(dataset_cum, dataset_cum[,2] != result[i])}
    PsiF <- factor(dataset_cum[,2])
    x1 <- dataset_cum[,1]
    x2 <- dataset_cum[,2]
    y <- dataset_cum[,3]

    modI <- drm(y ~ x1, fct=LL.3(), curveid=PsiF, pmodels=list(~1,~PsiF-1,~PsiF-1), data=dataset_cum)
    psiLevels <- as.numeric(levels(PsiF))
    b <- - coef(modI)[1]
    Pmax <- coef(modI)[2:(length(psiLevels)+1)]
    modPmax <- drm(Pmax ~ psiLevels, fct=PmaxPsi1())
    if(is.na(fixed[1])){
      G <- coef(modPmax)[1]; Psib <- coef(modPmax)[2]; sigmaPsib <- coef(modPmax)[3]
    } else {
      G <- fixed[1]; Psib <- coef(modPmax)[1]; sigmaPsib <- coef(modPmax)[2]
    }
    # G <- coef(modPmax)[3]; Psib <- coef(modPmax)[1]; sigmaPsib <- coef(modPmax)[2]

    GR50 <- 1/coef(modI)[(length(psiLevels)+2):length(coef(modI))]
    modGR <- drm(GR50 ~ psiLevels, fct=GRPsiPol())
    thetaH <- coef(modGR)[2]; Psib2 <- coef(modGR)[1]
    psib <- mean(Psib, Psib2)
    return(c(G, Psib, sigmaPsib, thetaH, b)[is.na(fixed)]) }

  GR <- function(parms, respl, reference="control", type="relative", Psi){
       G <- as.numeric(parms[1]); Psib<- as.numeric(parms[2])
       sigmaPsib<- as.numeric(parms[3]); thetaH<- as.numeric(parms[4])
       b <- as.numeric(parms[5])
       g <- respl/100
      if(type=="absolute"){
        .Pmax <- PmaxPsi1.fun(Psi, G, Psib, sigmaPsib)
        .Pmax <- ifelse(.Pmax > 0, .Pmax, 0)
        .temp2 <- (.Pmax - g)/g
        .temp2 <- ifelse(.temp2 < 0, 0, .temp2)
        .GR50 <- GRPsiPol.fun(Psi, Psib, thetaH)
        .GR50 <- ifelse(.GR50>0, .GR50, 0)
         res <- as.numeric( exp( - (1/b)*log(.temp2) + log(1/.GR50) ) )
         EDp <- 1/res
        .GR <- EDp
         gra <- function(G, Psib, sigmaPsib, thetaH, b)  1/exp( - (1/b)*log( (1/g)* (G * (1 - exp( - (Psi - Psib) * (1/sigmaPsib)))  - g)) + log( thetaH/(-(Psi^2 - Psib^2))) )

        #Beginning of derivatives (finite differences) ###########################
        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G + 10e-6, Psib, sigmaPsib, thetaH, b)
        d1 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib + 10e-6, sigmaPsib, thetaH, b)
        d2 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib + 10e-6, thetaH, b)
        d3 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib, thetaH + 10e-6, b)
        d4 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib, thetaH, b + 10e-6)
        d5 <- (d1.2 - d1.1)/10e-6
        #End of derivatives #########################
        EDder <- c(d1,d2,d3,d4,d5)
      } else{ if(type=="relative") {
        .Pmax <- PmaxPsi1.fun(Psi, G, Psib, sigmaPsib)
        .Pmax <- ifelse(.Pmax > 0, .Pmax, 0)
        .temp2 <- (1 - g)/g
        .GR50 <- GRPsiPol.fun(Psi, Psib, thetaH)
        .GR50 <- ifelse(.GR50>0, .GR50, 0)
        res <- as.numeric( exp( - (1/b)*log(.temp2) + log(1/.GR50) ) )
        EDp <- 1/res
        .GR <- EDp
        gra <- function(G, Psib, sigmaPsib, thetaH, b)  1/exp( - (1/b)*log( (1/g)* (G * (1 - exp( - (Psi - Psib) * (1/sigmaPsib)))  - g)) + log( thetaH/(-(Psi^2 - Psib^2))) )

        #Beginning of derivatives (finite differences) ###########################
        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G + 10e-6, Psib, sigmaPsib, thetaH, b)
        d1 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib + 10e-6, sigmaPsib, thetaH, b)
        d2 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib + 10e-6, thetaH, b)
        d3 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib, thetaH + 10e-6, b)
        d4 <- (d1.2 - d1.1)/10e-6

        d1.1 <- gra(G, Psib, sigmaPsib, thetaH, b)
        d1.2 <- gra(G, Psib, sigmaPsib, thetaH, b + 10e-6)
        d5 <- (d1.2 - d1.1)/10e-6
        #End of derivatives #########################

        EDder <- c(d1,d2,d3,d4,d5)
      } }
    return(list(EDp, EDder))
}

  deriv1 <- function(x, parm){
    parmMat <- matrix(parmVec, nrow(parm),
                        numParm, byrow = TRUE)
    parmMat[, notFixed] <- parm
    parm <- parmMat

    #Approximation by using finite differences
    d1.1 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d1.2 <- HTE3.fun(x[,1], x[,2], (parm[,1] + 10e-6), parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d1 <- (d1.2 - d1.1)/10e-6

    d2.1 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d2.2 <- HTE3.fun(x[,1], x[,2], parm[,1], (parm[,2] + 10e-6), parm[,3],
                     parm[,4], parm[,5])
    d2 <- (d2.2 - d2.1)/10e-6

    d3.1 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d3.2 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], (parm[,3] + 10e-6),
                     parm[,4], parm[,5])
    d3 <- (d3.2 - d3.1)/10e-6

    d4.1 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d4.2 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     (parm[,4] + 10e-6), parm[,5])
    d4 <- (d4.2 - d4.1)/10e-6

    d5.1 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], parm[,5])
    d5.2 <- HTE3.fun(x[,1], x[,2], parm[,1], parm[,2], parm[,3],
                     parm[,4], (parm[,5] + 10e-6))
    d5 <- (d5.2 - d5.1)/10e-6

    cbind(d1, d2, d3, d4, d5)[,notFixed]
}
text <- "Hydro-time model with shifted exponential for Pmax and polynomial model (convex up) for GR50"
returnList <- list(fct=fct, ssfct=ss, name = name, names=names, text=text, edfct=GR, deriv1=deriv1)
class(returnList) <- "drcMean"
invisible(returnList)
}