backtransform `scale()` for plotting

Question

I have a explanatory variable that is centered using scale() that is used to predict a response variable:

d <- data.frame(
  x=runif(100),
           


        

Answer 1

I felt like this should be a proper function, here was my attempt at it:

#' Reverse a scale
#'
#' Computes x = sz+c, which is the inverse of z = (x - c)/s 
#' provided by the \code{scale} function.
#' 
#' @param z a numeric matrix(like) object
#' @param center either NULL or a numeric vector of length equal to the number of columns of z  
#' @param scale  either NULL or a a numeric vector of length equal to the number of columns of z
#'
#' @seealso \code{\link{scale}}
#'  mtcs <- scale(mtcars)
#'  
#'  all.equal(
#'    unscale(mtcs), 
#'    as.matrix(mtcars), 
#'    check.attributes=FALSE
#'  )
#'  
#' @export
unscale <- function(z, center = attr(z, "scaled:center"), scale = attr(z, "scaled:scale")) {
  if(!is.null(scale))  z <- sweep(z, 2, scale, `*`)
  if(!is.null(center)) z <- sweep(z, 2, center, `+`)
  structure(z,
    "scaled:center"   = NULL,
    "scaled:scale"    = NULL,
    "unscaled:center" = center,
    "unscaled:scale"  = scale
  )
}

Answer 2

tl;dr:

unscaled_vals <- xs + attr(xs, 'scaled:scale') + attr(xs, 'scaled:center')

• where xs is a scaled object created by scale(x)

---

Just for those trying to make a bit of sense about this:

How R scales:

The scale function performs both scaling and centering by default.

• Of the two, the function performs centering first.

Centering is achieved by default by subtracting the mean of all !is.na input values from each value:

data - mean(data, rm.na = T)

Scaling is achieved via:

sqrt( ( sum(x^2) ) / n - 1)

where x is the set of all !is.na values to scale and n = length(x).

• Importantly, though, when center =T in scale, x is not the original set of data, but the already centered data.

  So if center = T (the default), the scaling function is really calculating:

   sqrt( ( sum( (data - mean(data, rm.na = T))^2) ) / n - 1)
  

  • Note: [when center = T] this is the same as taking the standard deviation: sd(data).

How to Unscale:

Explanation:

1. first multiply by scaling factor:

   y = x * sqrt( ( sum( (x - mean(x , na.rm = T))^2) ) / (length(x) - 1))
   

2. then add back mean:

   y + mean(x , na.rm = T)
   

Obviously you need to know the mean of the original set of data for this manual approach to truly be useful, but I place it here for conceptual sake.

Luckily, as previous answers have shown, the "centering" value (i.e., the mean) is located in the attributes of a scale object, so this approach can be simplified to:

How to do in R:

unscaled_vals <- xs + attr(xs, 'scaled:scale') + attr(xs, 'scaled:center')

• where xs is a scaled object created by scale(x).

Answer 3

Old question, but why wouldn't you just do this:

plot(d$x, predict(m1, d))

As an easier way than manually using the attributes from the scaled object, DMwR has a function for this: unscale. It works like this:

d <- data.frame(
  x=runif(100)
)

d$y <- 17 + d$x * 12

s.x <- scale(d$x)

m1 <- lm(d$y~s.x)

library(DMwR)
unsc.x <- unscale(d$x, s.x)
plot(unsc.x, predict(m1, d))

Importantly, the second argument of unscale needs to have something with the attributes of 'scaled:scale' and 'scaled:center'

Answer 4

Just inspired by Fermando´s answer, but unscaling line with less code:

set.seed(1)
x = matrix(sample(1:12), ncol= 3)
xs = scale(x, center = TRUE, scale = TRUE)
center <- attr(xs,"scaled:center")
scale <- attr(xs,"scaled:scale")
x.orig <- t(t(xs) * scale + center) # code is less here

print(x)
[1,]    9    2    6
[2,]    4    5   11
[3,]    7    3   12
[4,]    1    8   10

print(x.orig)
[1,]    9    2    6
[2,]    4    5   11
[3,]    7    3   12
[4,]    1    8   10
attr(,"scaled:center")
[1] 5.25 4.50 9.75
attr(,"scaled:scale")
[1] 3.50 2.65 2.63

Answer 5

I am late to the party. But here is a useful tool to scale/unscale data in array format.

Example:

> (data <- array(1:8, c(2, 4)))            # create data
     [,1] [,2] [,3] [,4]
[1,]    1    3    5    7
[2,]    2    4    6    8
> obj <- Scale(data)                       # create object
> (data_scaled <- obj$scale(data))         # scale data
           [,1]       [,2]       [,3]       [,4]
[1,] -0.7071068 -0.7071068 -0.7071068 -0.7071068
[2,]  0.7071068  0.7071068  0.7071068  0.7071068
> (obj$unscale(data_scaled))               # unscale scaled data
     [,1] [,2] [,3] [,4]
[1,]    1    3    5    7
[2,]    2    4    6    8

## scale or unscale another dataset
## using the same mean/sd parameters
> (data2 <- array(seq(1, 24, 2), c(3, 4))) # create demo data
     [,1] [,2] [,3] [,4]
[1,]    1    7   13   19
[2,]    3    9   15   21
[3,]    5   11   17   23
> (data2_scaled <- obj$scale(data2))       # scale data
           [,1]      [,2]     [,3]     [,4]
[1,] -0.7071068  4.949747 10.60660 16.26346
[2,]  2.1213203  7.778175 13.43503 19.09188
[3,]  4.9497475 10.606602 16.26346 21.92031
> (obj$unscale(data2_scaled))              # unscale scaled data
     [,1] [,2] [,3] [,4]
[1,]    1    7   13   19
[2,]    3    9   15   21
[3,]    5   11   17   23

Function Scale():

Scale <- function(data, margin=2, center=TRUE, scale=TRUE){
    stopifnot(is.array(data), is.numeric(data),
              any(mode(margin) %in% c("integer", "numeric")),
              length(margin) < length(dim(data)),
              max(margin) <= length(dim(data)),
              min(margin) >= 1,
              !any(duplicated(margin)),
              is.logical(center), length(center)==1,
              is.logical(scale), length(scale)==1,
                  !(isFALSE(center) && isFALSE(scale)))
    margin <- as.integer(margin)

    m <- if(center) apply(data, 2, mean, na.rm=TRUE) else NULL
    s <- if(scale)  apply(data, 2, sd, na.rm=TRUE) else NULL
    ldim <- length(dim(data))
    cdim <- dim(data)[margin]
    data <- NULL # don't store the data

    Scale <- function(data){
        stopifnot(is.array(data), is.numeric(data),
                  length(dim(data)) == ldim,
                  dim(data)[margin] == cdim)
        if(center)
            data <- sweep(data, margin, m, `-`)
        if(scale)
            data <- sweep(data, margin, s, `/`)
        data
    }

    Unscale <- function(data){
        stopifnot(is.array(data), is.numeric(data),
                  length(dim(data)) == ldim,
                  dim(data)[margin] == cdim)
        if(scale)
            data <- sweep(data, margin, s, `*`)
        if(center)
            data <- sweep(data, margin, m, `+`)
        data
    }
    list(scale=Scale, unscale=Unscale, mean=m, sd=s)
}

Note: data.frames are not support yet.

Answer 6

For a data frame or matrix:

set.seed(1)
x = matrix(sample(1:12), ncol= 3)
xs = scale(x, center = TRUE, scale = TRUE)

x.orig = t(apply(xs, 1, function(r)r*attr(xs,'scaled:scale') + attr(xs, 'scaled:center')))

print(x)
     [,1] [,2] [,3]
[1,]    4    2    3
[2,]    5    7    1
[3,]    6   10   11
[4,]    9   12    8

print(x.orig)
     [,1] [,2] [,3]
[1,]    4    2    3
[2,]    5    7    1
[3,]    6   10   11
[4,]    9   12    8

Be careful when using functions like identical():

print(x - x.orig)
     [,1] [,2]         [,3]
[1,]    0    0 0.000000e+00
[2,]    0    0 8.881784e-16
[3,]    0    0 0.000000e+00
[4,]    0    0 0.000000e+00

identical(x, x.orig)
# FALSE