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R/SSFunctions.R
In drLumi: Multiplex Immunoassays Data Analysis
Defines functions
inSSexp
dSSexp
d2SSexp
d3SSexp
inSSl4
dSSl4
d2SSl4
d3SSl4
inSSl5
dSSl5
d2SSl5
d3SSl5
#' Self-Starting Nls exponential regression model
#'
#' This selfStart model evaluates the exponential growth
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{y0}, and \code{b} for a given set of data. Instead of the standard
#' \code{exp} function this implementation use the \code{10^} function.
#' \deqn{f(x)=y_0 \times 10^b}
#' @param x a numeric vector of values at which to evaluate the model
#' @param y0 a numeric parameter representing the value of the response when
#' x is 0
#' @param b a numeric parameter representing the growth rate
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSexp(x, b, y0)
#'
#' @format A selfStart model
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)$plate_1
#'
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSexp",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSexp <- selfStart( ~ y0 * 10^(x/b),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
xypos <- xy[which(xy[,"y"]>0),]
lmFit <- lm(log10(xypos[,"y"])~xypos[,"x"])
coefs <- coef(lmFit)
y0 <- 10^(coefs[1])
b <- 1/coefs[2]
value <- c(b,y0)
names(value) <- mCall[c("b","y0")]
value
}, c("b", "y0"))
# Inverse function for the SSexp (x ~ fx)
#
# @param fx MFI value
# @param b coefficient of b
# @param c coefficient of y0
inSSexp <- function(fx, b, c){
ans <- list()
ans$est <- b * log(fx/c)/log(10)
ans$formtext <- "~ x1 * log(fx/x2)/log(10)"
ans$formtext.cons <- "~ x1 * log(fx/cons)/log(10)"
ans
}
# First order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
dSSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)))
ans
}
# Second order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
d2SSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)) * (log(10) * (1/b)))
ans
}
# Third order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
d3SSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)) * (log(10) * (1/b))
* (log(10) * (1/b)))
ans
}
#' Self-Starting Nls 4 parameters logistic regression model
#'
#' This selfStart model evaluates the 4 parameters logistic
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{lAsym}, \code{Slope} and \code{xMid}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{1+10^{Slope(x-xMid)}}}
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote when
#' \code{x} trend to \code{Inf}
#' @param lAsym a numeric parameter representing the lower asymptote when
#' \code{x} trend to \code{-Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSl4(x, Slope, lAsym, hAsym, xMid)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl4",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSl4 <- selfStart( ~ lAsym + (hAsym-lAsym)/(1+10^(Slope*(x-xMid))),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
plowl <- NLSstLfAsymptote(xy)
phighl <- NLSstRtAsymptote(xy)
pslope <- -1
ped50 <- NLSstClosestX(xy, median(xy[,"y"]))
value <- c(pslope,plowl,phighl,ped50)
names(value)<-mCall[c("Slope","lAsym","hAsym","xMid")]
value
},c("Slope","lAsym","hAsym","xMid"))
# Inverse function for the SSl4 (x ~ fx)
#
# @param fx MFI value
# @param b slope parameter
# @param c low asymptote parameter
# @param d high asymptote parameter
# @param e mid concentration parameter
inSSl4 <- function(fx, b, c, d, e){
ans <- list()
ans$est <- (log((d - fx )/(fx - c)) * 1/(log(10)*b)) + e
ans$formtext <- "~ (log((x3 - fx )/(fx - x2)) * 1/(log(10)*x1)) + x4"
ans$formtext.cons <- "~ (log((x2 - fx )/(fx - cons))
* 1/(log(10)*x1)) + x3"
ans
}
# First order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
dSSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) *
(log(10) * Slope))/
(1 + 10^(Slope * (x - xMid)))^2)
ans
}
# Second order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
d2SSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))/(1 + 10^(Slope * (x - xMid)))^2 - (hAsym -
lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope)) * (2 *
(10^(Slope * (x - xMid)) * (log(10) * Slope) *
(1 + 10^(Slope * (x - xMid)))))/((1 + 10^(Slope *
(x - xMid)))^2)^2)
ans
}
# Third order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
d3SSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope) * (log(10) * Slope))/(1 + 10^(Slope *
(x - xMid)))^2 -
(hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope)) * (2 * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid)))))/((1 +
10^(Slope * (x - xMid)))^2)^2 - (((hAsym - lAsym) * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (log(10) * Slope)) * (2 *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid))))) + (hAsym - lAsym) * (10^(Slope * (x -
xMid)) * (log(10) * Slope)) * (2 * (10^(Slope * (x - xMid)) *
(log(10) * Slope) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid))) + 10^(Slope * (x - xMid)) * (log(10) * Slope) *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))))/((1 + 10^(Slope *
(x - xMid)))^2)^2 - (hAsym - lAsym) * (10^(Slope * (x - xMid)) *
(log(10) * Slope)) * (2 * (10^(Slope * (x - xMid)) * (log(10) *
Slope) * (1 + 10^(Slope * (x - xMid))))) * (2 * (2 * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope * (x - xMid)))) *
((1 + 10^(Slope * (x - xMid)))^2)))/(((1 + 10^(Slope * (x -
xMid)))^2)^2)^2))
ans
}
#' Self-Starting Nls 5 parameters logistic regression model
#'
#' This selfStart model evaluates the 5 parameters logistic
#' regression model and its gradient.
#' It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{lAsym}, \code{Slope}, \code{xMid} and \code{Asymetry}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{(1+10^{Slope(x-xMid)})^{Asymetry}}}
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote
#' when \code{x} trend to \code{Inf}
#' @param lAsym a numeric parameter representing the lower asymptote when
#' \code{x} trend to \code{-Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope is a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @param Asymetry is a numeric parameter representing the asymetry around
#' the inflection point
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSl5(x, Slope, lAsym, hAsym, xMid, Asymetry)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' # SSl5
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl5",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSl5 <- selfStart( ~ lAsym + (hAsym-lAsym)/(1+10^(Slope*(x-xMid)))^Asymetry,
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
plowl<- NLSstLfAsymptote(xy)
phighl<-NLSstRtAsymptote(xy)
pslope<- -1
pf<-1
ped50<-NLSstClosestX(xy, mean(xy[,"y"]))
value<-c(pslope,plowl,phighl,ped50,pf)
names(value)<-mCall[c("Slope","lAsym","hAsym","xMid","Asymetry")]
value
},c("Slope","lAsym","hAsym","xMid","Asymetry"))
# Inverse function for the SSl5 (x ~ fx)
#
# @param fx MFI value
# @param b slope parameter
# @param c low asymptote parameter
# @param d high asymptote parameter
# @param e mid concentration parameter
# @param f asymetry parameter
inSSl5 <- function(fx, b, c, d, e, f){
ans <- list()
ans$est <- (log( ((d-c)/(fx-c))^(1/f) - 1 ) * 1/(log(10)*b)) + e
t1 <- "~ (log( ((x3-x2)/(fx-x2))^(1/x5) - 1 ) * 1/(log(10)*x1)) + x4"
ans$formtext <- t1
t2 <- "~ (log( ((x2-cons)/(fx-cons))^(1/x4) - 1 ) * 1/(log(10)*x1)) + x3"
ans$formtext.cons <- t2
ans
}
# First order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry around
# the inflection point
dSSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) *
(log(10) * Slope))))/((1 + 10^(Slope * (x - xMid)))^Asymetry)^2)
ans
}
# Second order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope}
# of the function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote
# when \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote
# when \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry
# around the inflection point
d2SSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^((Asymetry -
1) - 1) * ((Asymetry - 1) * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) + (1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))))/((1 + 10^(Slope * (x - xMid)))^Asymetry)^2 -
(hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope)))) * (2 * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * ((1 + 10^(Slope * (x - xMid)))^Asymetry)))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2)
ans
}
# Third order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry around the
# inflection point
d3SSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * (((1 + 10^(Slope * (x - xMid)))^(((Asymetry -
1) - 1) - 1) * (((Asymetry - 1) - 1) * (10^(Slope * (x -
xMid)) * (log(10) * Slope))) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) + (1 + 10^(Slope * (x -
xMid)))^((Asymetry - 1) - 1) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (log(10) * Slope)))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))) + ((1 + 10^(Slope * (x - xMid)))^((Asymetry -
1) - 1) * ((Asymetry - 1) * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope) * (log(10) * Slope))) + (1 + 10^(Slope *
(x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope) * (log(10) * Slope)))))/((1 + 10^(Slope *
(x - xMid)))^Asymetry)^2 - (hAsym - lAsym) * ((1 + 10^(Slope *
(x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) * (Asymetry * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) + (1 + 10^(Slope * (x -
xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope * (x - xMid)) *
(log(10) * Slope) * (log(10) * Slope)))) * (2 * ((1 + 10^(Slope *
(x - xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope * (x -
xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^Asymetry)))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2 - (((hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (log(10) *
Slope)))) * (2 * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^Asymetry))) + (hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))) * (2 *
(((1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (log(10) *
Slope)))) * ((1 + 10^(Slope * (x - xMid)))^Asymetry) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))))))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2 - (hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))) * (2 *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope))) * ((1 +
10^(Slope * (x - xMid)))^Asymetry))) * (2 * (2 * ((1 +
10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) * ((1 + 10^(Slope * (x -
xMid)))^Asymetry)) * (((1 + 10^(Slope *
(x - xMid)))^Asymetry)^2)))/((((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2)^2))
ans
}
#' Self-Starting Nls exponential constraint regression model
#'
#' This selfStart model evaluates the exponential growth
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{y0}, and \code{b} for a given set of data. Instead of the standard
#' \code{exp} function this implementation use the \code{10^} function.
#' \deqn{f(x)=y_0 \times 10^b}
#'
#'
#' @param ..constraint.value a numeric value representing the value of the
#' response when \code{x} is 0. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{y_0} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param b a numeric parameter representing the growth rate
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#' @usage SSexpcons(..constraint.value, x, b)
#'
#' @format A selfStart model
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)$plate_1
#'
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSexp",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but estimate
#' # one parameter).
#' b <- 3
#' y0 <- 1
#' concentration <- 2
#' SSexp(concentration, b, y0)
#' SSexpcons(y0, concentration, b)
#'
#' @export
SSexpcons <- selfStart( ~ ..constraint.value * 10^(x/b),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
xypos <- xy[which(xy[,"y"]>0),]
lmFit <- lm(log10(xypos[,"y"])~xypos[,"x"])
coefs <- coef(lmFit)
b <- 1/coefs[2]
value <- c(b)
names(value) <- mCall[c("b")]
value
}, c("b"))
#' Self-Starting Nls 4 parameters logistic constraint regression model
#'
#' This selfStart model evaluates the 4 parameters logistic
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{Slope} and \code{xMid}
#' for a given set of data.
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{1+10^{Slope(x-xMid)}}}
#'
#'
#'
#' @param ..constraint.value a numeric value representing
#' the lower asymptote when \code{x} trend to \code{-Inf}. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{lAsym} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote when
#' \code{x} trend to \code{Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#'
#'
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#' @usage SSl4cons(..constraint.value, x, Slope, hAsym, xMid)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl4",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but
#' # estimate 3 parameters).
#' lAsym <- 1
#' Slope <- 2
#' hAsym <- 2
#' xMid <- 3
#' concentration <- 2
#' SSl4(concentration, Slope, lAsym, hAsym, xMid)
#' SSl4cons(lAsym, concentration, Slope, hAsym, xMid)
#'
#' @export
SSl4cons <- selfStart( ~ ..constraint.value + (hAsym-..constraint.value)/(1+10^(Slope*(x-xMid))),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
phighl <- NLSstRtAsymptote(xy)
pslope <- -1
ped50 <- NLSstClosestX(xy, median(xy[,"y"]))
value <- c(pslope,phighl,ped50)
names(value)<-mCall[c("Slope","hAsym","xMid")]
value
},c("Slope","hAsym","xMid"))
#' Self-Starting Nls 5 parameters logistic constraint regression model
#'
#'
#' This selfStart model evaluates the 5 parameters logistic
#' regression model and its gradient for the lower asymptote constraint method.
#' It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{Slope}, \code{xMid} and \code{Asymetry}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{(1+10^{Slope(x-xMid)})^{Asymetry}}}
#'
#'
#' @param ..constraint.value a numeric value representing
#' the lower asymptote when \code{x} trend to \code{-Inf}. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{lAsym} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote
#' when \code{x} trend to \code{Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope is a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @param Asymetry is a numeric parameter representing the asymetry around
#' the inflection point
#'
#'
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#'
#' @usage SSl5cons(..constraint.value,x, Slope, hAsym, xMid, Asymetry)
#' @format A selfStart model
#'
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' # SSl5
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl5",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but estimate
#' # 4 parameters).
#' lAsym <- 1
#' Slope <- 2
#' hAsym <- 2
#' xMid <- 3
#' Asymetry <- 1.5
#'
#' concentration <- 2
#' SSl5(concentration, Slope, lAsym, hAsym, xMid, Asymetry)
#' SSl5cons(lAsym, concentration, Slope, hAsym, xMid, Asymetry)
#'
#' @export
SSl5cons <- selfStart( ~ ..constraint.value + (hAsym-..constraint.value)/(1+10^(Slope*(x-xMid)))^Asymetry,
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
phighl<-NLSstRtAsymptote(xy)
pslope<- -1
pf<-1
ped50<-NLSstClosestX(xy, mean(xy[,"y"]))
value<-c(pslope,phighl,ped50,pf)
names(value)<-mCall[c("Slope","hAsym","xMid","Asymetry")]
value
},c("Slope","hAsym","xMid","Asymetry"))
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Defines functions inSSexp dSSexp d2SSexp d3SSexp inSSl4 dSSl4 d2SSl4 d3SSl4 inSSl5 dSSl5 d2SSl5 d3SSl5
#' Self-Starting Nls exponential regression model
#'
#' This selfStart model evaluates the exponential growth
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{y0}, and \code{b} for a given set of data. Instead of the standard
#' \code{exp} function this implementation use the \code{10^} function.
#' \deqn{f(x)=y_0 \times 10^b}
#' @param x a numeric vector of values at which to evaluate the model
#' @param y0 a numeric parameter representing the value of the response when
#' x is 0
#' @param b a numeric parameter representing the growth rate
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSexp(x, b, y0)
#'
#' @format A selfStart model
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)$plate_1
#'
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSexp",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSexp <- selfStart( ~ y0 * 10^(x/b),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
xypos <- xy[which(xy[,"y"]>0),]
lmFit <- lm(log10(xypos[,"y"])~xypos[,"x"])
coefs <- coef(lmFit)
y0 <- 10^(coefs[1])
b <- 1/coefs[2]
value <- c(b,y0)
names(value) <- mCall[c("b","y0")]
value
}, c("b", "y0"))
# Inverse function for the SSexp (x ~ fx)
#
# @param fx MFI value
# @param b coefficient of b
# @param c coefficient of y0
inSSexp <- function(fx, b, c){
ans <- list()
ans$est <- b * log(fx/c)/log(10)
ans$formtext <- "~ x1 * log(fx/x2)/log(10)"
ans$formtext.cons <- "~ x1 * log(fx/cons)/log(10)"
ans
}
# First order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
dSSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)))
ans
}
# Second order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
d2SSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)) * (log(10) * (1/b)))
ans
}
# Third order derivative of the SSexp function
#
# @param x concentration value
# @param b coefficient of b
# @param y0 coefficient of y0
d3SSexp <- function(x, b, y0){
ans <- y0 * (10^(x/b) * (log(10) * (1/b)) * (log(10) * (1/b))
* (log(10) * (1/b)))
ans
}
#' Self-Starting Nls 4 parameters logistic regression model
#'
#' This selfStart model evaluates the 4 parameters logistic
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{lAsym}, \code{Slope} and \code{xMid}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{1+10^{Slope(x-xMid)}}}
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote when
#' \code{x} trend to \code{Inf}
#' @param lAsym a numeric parameter representing the lower asymptote when
#' \code{x} trend to \code{-Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSl4(x, Slope, lAsym, hAsym, xMid)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl4",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSl4 <- selfStart( ~ lAsym + (hAsym-lAsym)/(1+10^(Slope*(x-xMid))),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
plowl <- NLSstLfAsymptote(xy)
phighl <- NLSstRtAsymptote(xy)
pslope <- -1
ped50 <- NLSstClosestX(xy, median(xy[,"y"]))
value <- c(pslope,plowl,phighl,ped50)
names(value)<-mCall[c("Slope","lAsym","hAsym","xMid")]
value
},c("Slope","lAsym","hAsym","xMid"))
# Inverse function for the SSl4 (x ~ fx)
#
# @param fx MFI value
# @param b slope parameter
# @param c low asymptote parameter
# @param d high asymptote parameter
# @param e mid concentration parameter
inSSl4 <- function(fx, b, c, d, e){
ans <- list()
ans$est <- (log((d - fx )/(fx - c)) * 1/(log(10)*b)) + e
ans$formtext <- "~ (log((x3 - fx )/(fx - x2)) * 1/(log(10)*x1)) + x4"
ans$formtext.cons <- "~ (log((x2 - fx )/(fx - cons))
* 1/(log(10)*x1)) + x3"
ans
}
# First order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
dSSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) *
(log(10) * Slope))/
(1 + 10^(Slope * (x - xMid)))^2)
ans
}
# Second order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
d2SSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))/(1 + 10^(Slope * (x - xMid)))^2 - (hAsym -
lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope)) * (2 *
(10^(Slope * (x - xMid)) * (log(10) * Slope) *
(1 + 10^(Slope * (x - xMid)))))/((1 + 10^(Slope *
(x - xMid)))^2)^2)
ans
}
# Third order derivative of the SSl4 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
d3SSl4 <- function(x, Slope, lAsym, hAsym, xMid){
ans <- -((hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope) * (log(10) * Slope))/(1 + 10^(Slope *
(x - xMid)))^2 -
(hAsym - lAsym) * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope)) * (2 * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid)))))/((1 +
10^(Slope * (x - xMid)))^2)^2 - (((hAsym - lAsym) * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (log(10) * Slope)) * (2 *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid))))) + (hAsym - lAsym) * (10^(Slope * (x -
xMid)) * (log(10) * Slope)) * (2 * (10^(Slope * (x - xMid)) *
(log(10) * Slope) * (log(10) * Slope) * (1 + 10^(Slope *
(x - xMid))) + 10^(Slope * (x - xMid)) * (log(10) * Slope) *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))))/((1 + 10^(Slope *
(x - xMid)))^2)^2 - (hAsym - lAsym) * (10^(Slope * (x - xMid)) *
(log(10) * Slope)) * (2 * (10^(Slope * (x - xMid)) * (log(10) *
Slope) * (1 + 10^(Slope * (x - xMid))))) * (2 * (2 * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (1 + 10^(Slope * (x - xMid)))) *
((1 + 10^(Slope * (x - xMid)))^2)))/(((1 + 10^(Slope * (x -
xMid)))^2)^2)^2))
ans
}
#' Self-Starting Nls 5 parameters logistic regression model
#'
#' This selfStart model evaluates the 5 parameters logistic
#' regression model and its gradient.
#' It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{lAsym}, \code{Slope}, \code{xMid} and \code{Asymetry}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{(1+10^{Slope(x-xMid)})^{Asymetry}}}
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote
#' when \code{x} trend to \code{Inf}
#' @param lAsym a numeric parameter representing the lower asymptote when
#' \code{x} trend to \code{-Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope is a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @param Asymetry is a numeric parameter representing the asymetry around
#' the inflection point
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#' @usage SSl5(x, Slope, lAsym, hAsym, xMid, Asymetry)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' # SSl5
#' ig <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl5",
#' bkg="ignore",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(ig)
#'
#' @author John Aponte <john.aponte@@cresib.cat>
#' @export
SSl5 <- selfStart( ~ lAsym + (hAsym-lAsym)/(1+10^(Slope*(x-xMid)))^Asymetry,
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
plowl<- NLSstLfAsymptote(xy)
phighl<-NLSstRtAsymptote(xy)
pslope<- -1
pf<-1
ped50<-NLSstClosestX(xy, mean(xy[,"y"]))
value<-c(pslope,plowl,phighl,ped50,pf)
names(value)<-mCall[c("Slope","lAsym","hAsym","xMid","Asymetry")]
value
},c("Slope","lAsym","hAsym","xMid","Asymetry"))
# Inverse function for the SSl5 (x ~ fx)
#
# @param fx MFI value
# @param b slope parameter
# @param c low asymptote parameter
# @param d high asymptote parameter
# @param e mid concentration parameter
# @param f asymetry parameter
inSSl5 <- function(fx, b, c, d, e, f){
ans <- list()
ans$est <- (log( ((d-c)/(fx-c))^(1/f) - 1 ) * 1/(log(10)*b)) + e
t1 <- "~ (log( ((x3-x2)/(fx-x2))^(1/x5) - 1 ) * 1/(log(10)*x1)) + x4"
ans$formtext <- t1
t2 <- "~ (log( ((x2-cons)/(fx-cons))^(1/x4) - 1 ) * 1/(log(10)*x1)) + x3"
ans$formtext.cons <- t2
ans
}
# First order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry around
# the inflection point
dSSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) *
(log(10) * Slope))))/((1 + 10^(Slope * (x - xMid)))^Asymetry)^2)
ans
}
# Second order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope}
# of the function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote
# when \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote
# when \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry
# around the inflection point
d2SSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^((Asymetry -
1) - 1) * ((Asymetry - 1) * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) + (1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))))/((1 + 10^(Slope * (x - xMid)))^Asymetry)^2 -
(hAsym - lAsym) * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope)))) * (2 * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * ((1 + 10^(Slope * (x - xMid)))^Asymetry)))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2)
ans
}
# Third order derivative of the SSl5 function
#
# @param x a numeric vector of values at which to evaluate the model
# @param Slope is a numeric parameter representing the \code{-slope} of the
# function at the inflection point
# @param lAsym a numeric parameter representing the lower asymptote when
# \code{x} trend to \code{-Inf}
# @param hAsym a numeric parameter representing the higher asymptote when
# \code{x} trend to \code{Inf}
# @param xMid is the x value corresponding to the inflection point
# @param Asymetry is a numeric parameter representing the asymetry around the
# inflection point
d3SSl5 <- function(x, Slope, lAsym, hAsym, xMid, Asymetry){
ans <- -((hAsym - lAsym) * (((1 + 10^(Slope * (x - xMid)))^(((Asymetry -
1) - 1) - 1) * (((Asymetry - 1) - 1) * (10^(Slope * (x -
xMid)) * (log(10) * Slope))) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) + (1 + 10^(Slope * (x -
xMid)))^((Asymetry - 1) - 1) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope) * (log(10) * Slope)))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope))) + ((1 + 10^(Slope * (x - xMid)))^((Asymetry -
1) - 1) * ((Asymetry - 1) * (10^(Slope * (x - xMid)) * (log(10) *
Slope))) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) *
Slope) * (log(10) * Slope))) + (1 + 10^(Slope *
(x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope) *
(log(10) * Slope) * (log(10) * Slope)))))/((1 + 10^(Slope *
(x - xMid)))^Asymetry)^2 - (hAsym - lAsym) * ((1 + 10^(Slope *
(x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry - 1) * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) * (Asymetry * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) + (1 + 10^(Slope * (x -
xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope * (x - xMid)) *
(log(10) * Slope) * (log(10) * Slope)))) * (2 * ((1 + 10^(Slope *
(x - xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope * (x -
xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^Asymetry)))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2 - (((hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (log(10) *
Slope)))) * (2 * ((1 + 10^(Slope * (x - xMid)))^(Asymetry -
1) * (Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^Asymetry))) + (hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))) * (2 *
(((1 + 10^(Slope * (x - xMid)))^((Asymetry - 1) - 1) * ((Asymetry -
1) * (10^(Slope * (x - xMid)) * (log(10) * Slope))) *
(Asymetry * (10^(Slope * (x - xMid)) * (log(10) * Slope))) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope) * (log(10) *
Slope)))) * ((1 + 10^(Slope * (x - xMid)))^Asymetry) +
(1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope))) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))))))/(((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2 - (hAsym - lAsym) *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope)))) * (2 *
((1 + 10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry *
(10^(Slope * (x - xMid)) * (log(10) * Slope))) * ((1 +
10^(Slope * (x - xMid)))^Asymetry))) * (2 * (2 * ((1 +
10^(Slope * (x - xMid)))^(Asymetry - 1) * (Asymetry * (10^(Slope *
(x - xMid)) * (log(10) * Slope))) * ((1 + 10^(Slope * (x -
xMid)))^Asymetry)) * (((1 + 10^(Slope *
(x - xMid)))^Asymetry)^2)))/((((1 +
10^(Slope * (x - xMid)))^Asymetry)^2)^2)^2))
ans
}
#' Self-Starting Nls exponential constraint regression model
#'
#' This selfStart model evaluates the exponential growth
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{y0}, and \code{b} for a given set of data. Instead of the standard
#' \code{exp} function this implementation use the \code{10^} function.
#' \deqn{f(x)=y_0 \times 10^b}
#'
#'
#' @param ..constraint.value a numeric value representing the value of the
#' response when \code{x} is 0. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{y_0} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param b a numeric parameter representing the growth rate
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#' @usage SSexpcons(..constraint.value, x, b)
#'
#' @format A selfStart model
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)$plate_1
#'
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSexp",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but estimate
#' # one parameter).
#' b <- 3
#' y0 <- 1
#' concentration <- 2
#' SSexp(concentration, b, y0)
#' SSexpcons(y0, concentration, b)
#'
#' @export
SSexpcons <- selfStart( ~ ..constraint.value * 10^(x/b),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
xypos <- xy[which(xy[,"y"]>0),]
lmFit <- lm(log10(xypos[,"y"])~xypos[,"x"])
coefs <- coef(lmFit)
b <- 1/coefs[2]
value <- c(b)
names(value) <- mCall[c("b")]
value
}, c("b"))
#' Self-Starting Nls 4 parameters logistic constraint regression model
#'
#' This selfStart model evaluates the 4 parameters logistic
#' regression model and its gradient. It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{Slope} and \code{xMid}
#' for a given set of data.
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{1+10^{Slope(x-xMid)}}}
#'
#'
#'
#' @param ..constraint.value a numeric value representing
#' the lower asymptote when \code{x} trend to \code{-Inf}. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{lAsym} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote when
#' \code{x} trend to \code{Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#'
#'
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#' @usage SSl4cons(..constraint.value, x, Slope, hAsym, xMid)
#' @format A selfStart model
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl4",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but
#' # estimate 3 parameters).
#' lAsym <- 1
#' Slope <- 2
#' hAsym <- 2
#' xMid <- 3
#' concentration <- 2
#' SSl4(concentration, Slope, lAsym, hAsym, xMid)
#' SSl4cons(lAsym, concentration, Slope, hAsym, xMid)
#'
#' @export
SSl4cons <- selfStart( ~ ..constraint.value + (hAsym-..constraint.value)/(1+10^(Slope*(x-xMid))),
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
phighl <- NLSstRtAsymptote(xy)
pslope <- -1
ped50 <- NLSstClosestX(xy, median(xy[,"y"]))
value <- c(pslope,phighl,ped50)
names(value)<-mCall[c("Slope","hAsym","xMid")]
value
},c("Slope","hAsym","xMid"))
#' Self-Starting Nls 5 parameters logistic constraint regression model
#'
#'
#' This selfStart model evaluates the 5 parameters logistic
#' regression model and its gradient for the lower asymptote constraint method.
#' It has an \code{initial}
#' attribute that will evaluate initial estimates of the parameters
#' \code{hAsym}, \code{Slope}, \code{xMid} and \code{Asymetry}
#' for a given set of data
#' Instead of the standard \code{exp} function this implementation use
#' the \code{10^} function.
#' \deqn{f(x)=lAsym +\frac{hAsym-lAsym}{(1+10^{Slope(x-xMid)})^{Asymetry}}}
#'
#'
#' @param ..constraint.value a numeric value representing
#' the lower asymptote when \code{x} trend to \code{-Inf}. In this
#' function this value is not a parameter is just a numeric value to
#' constraint \code{lAsym} parameter.
#' @param x a numeric vector of values at which to evaluate the model
#' @param hAsym a numeric parameter representing the higher asymptote
#' when \code{x} trend to \code{Inf}
#' @param xMid is the x value corresponding to the inflection point
#' @param Slope is a numeric parameter representing the \code{-slope} of the
#' function at the inflection point
#' @param Asymetry is a numeric parameter representing the asymetry around
#' the inflection point
#'
#'
#' @return The value returned is a list containing the nonlinear function,
#' the self starter function and the parameter names.
#'
#'
#' @usage SSl5cons(..constraint.value,x, Slope, hAsym, xMid, Asymetry)
#' @format A selfStart model
#'
#'
#' @examples
#' # Load data
#' data(ecdata)
#' data(mfidata)
#'
#' # Select analyte FGF for plate 1
#' dat <- mfidata[mfidata$plate=="plate_1" & mfidata$analyte=="FGF",]
#'
#' sdf <- data_selection(dat, ecdata)[[1]]
#'
#' # SSl5
#' cons <- scluminex("plate_1",sdf$standard, sdf$background,
#' lfct="SSl5",
#' bkg="constraint",
#' fmfi="mfi",
#' verbose=FALSE)
#'
#' summary(cons)
#'
#' # Comparison constraint vs no constraint (same returning value but estimate
#' # 4 parameters).
#' lAsym <- 1
#' Slope <- 2
#' hAsym <- 2
#' xMid <- 3
#' Asymetry <- 1.5
#'
#' concentration <- 2
#' SSl5(concentration, Slope, lAsym, hAsym, xMid, Asymetry)
#' SSl5cons(lAsym, concentration, Slope, hAsym, xMid, Asymetry)
#'
#' @export
SSl5cons <- selfStart( ~ ..constraint.value + (hAsym-..constraint.value)/(1+10^(Slope*(x-xMid)))^Asymetry,
function(mCall, LHS, data)
{
xy <- sortedXyData(mCall[["x"]], LHS, data)
phighl<-NLSstRtAsymptote(xy)
pslope<- -1
pf<-1
ped50<-NLSstClosestX(xy, mean(xy[,"y"]))
value<-c(pslope,phighl,ped50,pf)
names(value)<-mCall[c("Slope","hAsym","xMid","Asymetry")]
value
},c("Slope","hAsym","xMid","Asymetry"))
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