R/yeo-johnsonTransformation.R

In depCensoring: Statistical Methods for Survival Data with Dependent Censoring

#' @title Logarithmic transformation function.
#' 
#' @description Computes the logarithm of a number.
#' 
#' @param y Numerical value of which the logarithm is computed.
#' 
#' @return This function returns the logarithm of the provided argument y
#' if it is greater than zero. If y is smaller than zero, it will return 0.
#' 

log_transform = function(y) { 
  transform_y = (y>0)*y+(y<=0)*1
  return(log(transform_y)) 
} 

#' @title Power transformation function.
#' 
#' @description Computes a given power of a number.
#' 
#' @param y The number which one wants to raise to a certain power \code{pw}.
#' @param pw The power to which to raise \code{y}.
#' 
#' @return This function returns the result of raising \code{y} to the power
#' \code{pw} when \code{y > 0}. Otherwise, it will return 1.
#' 

power_transform = function(y,pw) { 
  transform_y = (y>0)*y+(y<=0)*1
  return(transform_y^pw) 
} 

#' @title Yeo-Johnson transformation function
#' 
#' @description Computes the Yeo-Johnson transformation of the provided argument.
#' 
#' @param y The argument to be supplied to the Yeo-Johnson transformation.
#' @param theta The parameter of the Yeo-Johnson transformation. This should be
#' a number in the range [0,2].
#' 
#' @return The transformed value of y.
#' 

YJtrans = function(y,theta) { 
  sg = y>=0 
  if (theta==0) {temp = log_transform(y+1)*sg+(1-sg)*(0.5-0.5*(y-1)^2)} 
  if (theta==2) {temp = sg*(-0.5+0.5*(y+1)^2)-log_transform(-y+1)*(1-sg)} 
  if ((theta!=0) & (theta!=2)) {temp = sg*(power_transform(y+1,theta)-1)/theta+(1-sg)*(1-power_transform(-y+1,2-theta))/(2-theta)} 
  return(temp) 
} 

#' @title Inverse Yeo-Johnson transformation function
#' 
#' @description Computes the inverse Yeo-Johnson transformation of the provided
#' argument.
#' 
#' @param y The argument to be supplied to the inverse Yeo-Johnson transformation.
#' @param theta The parameter of the inverted Yeo-Johnson transformation. This
#' should be a number in the range [0,2].
#' 
#' @return The transformed value of y.
#' 

IYJtrans = function(y,theta) { 
  sg = y>=0 
  if (theta==0) {temp =(exp(y)-1)*sg+(1-sg)*(1-power_transform(-2*y+1,0.5))} 
  if (theta==2) {temp = sg*(-1+power_transform(2*y+1,0.5))+(1-exp(-y))*(1-sg)} 
  if ((theta!=0) & (theta!=2)) {temp = sg*(power_transform(abs(theta)*y+1,1/theta)-1)+(1-sg)*(1-power_transform(1-(2-theta)*y,1/(2-theta)))} 
  return(temp) 
} 

#' @title Derivative of the Yeo-Johnson transformation function
#' 
#' @description Evaluates the derivative of the Yeo-Johnson transformation at
#' the provided argument.
#' 
#' @param y The argument to be supplied to the derivative of the Yeo-Johnson
#' transformation.
#' @param theta The parameter of the Yeo-Johnson transformation. This should be
#' a number in the range [0,2].
#' 
#' @return The transformed value of y.
#' 

DYJtrans = function(y,theta) { 
  sg = y>=0 
  temp = power_transform(y+1,theta-1)*sg+power_transform(-y+1,1-theta)*(1-sg) 
  return(temp) 
}