Changing the scale of a variable to 0-100

Question

I have constructed a social capital index using PCA technique. This index comprises values both positive and negative. I want to transform / convert this index to 0-100 scale to make it easy to interpret. Please suggest me an easiest way to do so.

Answer 1

Any variable (univariate distribution) $v$ with observed $min_{old}$ and $max_{old}$ values (or these could be preset potential bounds for values) can be rescaled to range $min_{new}$ to $max_{new}$ by the following formula:

$\frac{max_{new}-min_{new}}{max_{old}-min_{old}}\cdot (v-max_{old})+max_{new}$

or

$\frac{max_{new}-min_{new}}{max_{old}-min_{old}}\cdot (v-min_{old})+min_{new}$.

Answer 2

For R there is also already available rescale function from scales package, which does exactly what you want and what @AndrewTulloch and @ttnphns described:

library(scales)
rescale(c(-10, -9, -5, 2, 6), to = c(0, 100)) ## Use scales:::rescale() if you have several packages loaded using the same function name
[1]   0.00   6.25  31.25  75.00 100.00

Answer 3

first, lets get some example data:

x <- runif(20, -10, 10)

Here are two functions that will work in R

rescale <- function(x) (x-min(x))/(max(x) - min(x)) * 100
rescale(x)

Or, you could use other transformations. For example, the logit transform was mentioned by @ondrej

plogis(x)*100

or, other transforms:

pnorm(x)*100
pnorm(x, 0, 100) * 100
punif(x, min(x), max(x))*100

Answer 4

Just to add to ttnphnss's answer, to implement this process in Python (for example), this function will do the trick:

from __future__ import division

def rescale(values, new_min = 0, new_max = 100):
    output = []
    old_min, old_max = min(values), max(values)

    for v in values:
        new_v = (new_max - new_min) / (old_max - old_min) * (v - old_min) + new_min
        output.append(new_v)

    return output

print rescale([1, 2, 3, 4, 5])
# [0.0, 25.0, 50.0, 75.0, 100.0]

Answer 5

I suggest not to bind the index to 0-100 interval, as it does not improve interpretation, but rather makes it more difficult. If the index constituents can be negative, then it is possible that the index becomes negative, and it reflects what's going on with constituents better than some low value in 0-100 range, in my opinion.

Answer 6

For R with standard packages loaded, you may just use scale() from 'base' package:

x=c(2,4,8,16)
x.scaled = scale(x,FALSE,max(x))  # divide each value in x by max(x)
x.scaled = as.vector(x.scaled) 

use 'as.vector()' to retrieve the scaled x as vector.