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 and max values (or these could be preset potential bounds for values) can be rescaled to range min' to max' by formula (max'-min')/(max-min)(v-max)+max' or (max'-min')/(max-min)(v-min)+min'.

Answer 2

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 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