Normalising a variable to be between 0 and 1

[Chris Rooney]

Hi all,

I have four variables which each have values which range between -2.5 and 2.5.

I would like to alter the values of the variables so they are between 0 and 1.

How do I go about doing that?!

[Nick Cox]

If that is exactly correct, this is simple algebra,

replace x = (x + 2.5)/5

generalised with a foreach loop.

My instinct is always to leave original data exactly as they come and to create a new variable.

foreach v in frog toad newt dragon { 
      gen `v'2 = (`v' + 2.5)/5 
      label var `v'2 "`v' scaled to [0,1]" 
}

[Brendan Cox]

Or more generally,

foreach v of varlist ... {
    qui summ `v'
    gen `v'2 = (`v' - r(min)) / (r(max) - r(min))
}

Note that per Nick's comment, the above code assumes the desired scaling is based on the actual minimum and maximum values in the data -- i.e., that you want the data to be rescaled to [0,1] based on observed values, not exogenous definitions of the range. Nevertheless, I hope the more general formula & link are useful.

See https://en.wikipedia.org/wiki/Feature_scaling

[Nick Cox]

Brendan's method (*) may not be quite the same. For example, the definition of varying from -2.5 to 2.5 may mean that in principle these are the limits. If the extremes in the data are not the same, then the scaling will be different.

(*) We're not related. Or at least, I don't know that we are.

[Chris Rooney]

If that is exactly correct, this is simple algebra,

replace x = (x + 2.5)/5

generalised with a foreach loop.

My instinct is always to leave original data exactly as they come and to create a new variable.

foreach v in frog toad newt dragon {
gen `v'2 = (`v' + 2.5)/5
label var `v'2 "`v' scaled to [0,1]"
}

Thanks. How does one then interpret such values then?

[Brendan Cox]

Brendan's method (*) may not be quite the same. For example, the definition of varying from -2.5 to 2.5 may mean that in principle these are the limits. If the extremes in the data are not the same, then the scaling will be different.

(*) We're not related. Or at least, I don't know that we are.

Ah, yes, quite so. I will edit the post accordingly, but hopefully the more generalised formula & link prove useful references.

* Yes, an unfortunate coincidence for you. For me, perhaps it lends an extra (and undeserved) 'je ne sais quoi' to my posts.

[Nick Cox]

Coxes everywhere (we're good at survival):

We all have little stories. Long ago, I heard a lecture with an explanation of a statistical problem. (Yes, I could see that was a key problem.) And here is the standard device we use to solve it. (That's smart! I bet the other guys were kicking themselves when they saw that.) And this, of course, is the standard Cox model. (No, not me. But it still sounds great: the standard Cox model.)

That is, naturally, Sir David Cox (1924- ), much and rightly honoured, and again we are not related.

[Nick Cox]

Chris:

How does one then interpret such values then?

Not sure what you want here. The variables are now scaled to [0, 1], which is what you asked for.

[Chris Rooney]

Chris:



Not sure what you want here. The variables are now scaled to [0, 1], which is what you asked for.

True, but is there any reference on how to interpret them when I use these variables in a regression, for example. What does an increase of 0.1 in a variable which is now scaled [0, 1] mean? Does it mean a 10% increase in [normalised variable] will result in a x% increase in the dependent variable (if the dependent variable is in percent form) ?

[Nick Cox]

Forgetting about other predictors, and even the intercept, focus on y = ... + bx + ... where x varies between 0 and 1. The difference between the predicted value for x = 0 and that for x = 1 is precisely b. That's a change over the entire possible range. For any fraction of the range, multiply down.

That doesn't sound like your interpretation, although I don't understand it (what is x in your notation? the coefficient? the predictor?) .