How to rescale A variable by range

[Ayub UOM]

Hello statalist members,
i want to rescale my contious variables(x,y) by range(maximum-minimum) because of my other variables which are dichotomous.so i want to rescale my contious variables(x,y) so that thier values have a maximum range of 1.variable x is scaled by range of x by code and year, and variable y is by range of y in the focal company.
My data set is individual level i,e age, tenure ,race
Could you please guide me how can i do it please?
best regards.

[Nick Cox]

Here is some technique, but whether this makes sense for race or even tenure I really doubt.

. sysuse auto, clear
(1978 Automobile Data)

. su

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
        make |          0
       price |         74    6165.257    2949.496       3291      15906
         mpg |         74     21.2973    5.785503         12         41
       rep78 |         69    3.405797    .9899323          1          5
    headroom |         74    2.993243    .8459948        1.5          5
-------------+---------------------------------------------------------
       trunk |         74    13.75676    4.277404          5         23
      weight |         74    3019.459    777.1936       1760       4840
      length |         74    187.9324    22.26634        142        233
        turn |         74    39.64865    4.399354         31         51
displacement |         74    197.2973    91.83722         79        425
-------------+---------------------------------------------------------
  gear_ratio |         74    3.014865    .4562871       2.19       3.89
     foreign |         74    .2972973    .4601885          0          1

* this is the core part 
foreach v of var price-gear {
    su `v', meanonly
    gen `v'_s = (`v' - r(min)) / (r(max) - r(min))
    label var `v'_s "`: var label `v'', scaled"
}


. su *_s

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
     price_s |         74    .2278444    .2338086          0          1
       mpg_s |         74    .3205965    .1995001          0          1
     rep78_s |         69    .6014493    .2474831          0          1
  headroom_s |         74    .4266409    .2417128          0          1
     trunk_s |         74    .4864865    .2376336          0          1
-------------+---------------------------------------------------------
    weight_s |         74    .4089154    .2523356          0          1
    length_s |         74     .504752    .2446851          0          1
      turn_s |         74    .4324324    .2199677          0          1
displaceme~s |         74    .3418997    .2654255          0          1
gear_ratio_s |         74    .4852146    .2684042          0          1

. d *_s

              storage   display    value
variable name   type    format     label      variable label
--------------------------------------------------------------------------------------------------------
price_s         float   %9.0g                 Price, scaled
mpg_s           float   %9.0g                 Mileage (mpg), scaled
rep78_s         float   %9.0g                 Repair Record 1978, scaled
headroom_s      float   %9.0g                 Headroom (in.), scaled
trunk_s         float   %9.0g                 Trunk space (cu. ft.), scaled
weight_s        float   %9.0g                 Weight (lbs.), scaled
length_s        float   %9.0g                 Length (in.), scaled
turn_s          float   %9.0g                 Turn Circle (ft.) , scaled
displacement_s  float   %9.0g                 Displacement (cu. in.), scaled
gear_ratio_s    float   %9.0g                 Gear Ratio, scaled

[Ayub UOM]

Thank you so much sir, it is ok for my continous variables.

[JeongHoon Min]

I think you might be interested in -nscale-, ssc command doing exactly what you want. It uses exactly the same technique described in #2 but also supports some options to deal with missing values and is able to do rescaling & reverse coding at once. Try

ssc describe nscale

For these kinds of tasks(managing variables with simple criteria), this post might be useful: https://blog.stata.com/2018/10/09/ho...-common-tasks/

[Ayub UOM]

JeongHoon Min thank you so much for your kind reply.
normally we are standradizing (normalizing) variable by z statistic, having mean (0) and SD (1), and using egen function.But in my this case the base paper suggested and used range (maximum-minimum) for scaling in R program.Furthermore they standardized nominal variables by SD (1/square root 2) and contious variables by thier range,so that to give equal weights to all variables, for example age is contious variable, so we will divide it by range of age,and then we will use weights for allvariables.Further i dont know the technical point,as in standardization we are divideing it by standard deviation,but in my case i wantd to use range.but as above Nick cox sir suggestd i will use it for scaling or i will wait for some other suggestions.

[Anne Ahrens]

Hi Nick
Thank you for your code for min-.max scaling.

I was trying to invert the variable back to the original scale since we used imputation for some of the original values, which is why I need the inverted data. It should be simple but I can only get it to give the same.

I used the code below.

Thank you,
Anne


*Code from post #2:
sysuse auto, clear
summarize
brow
foreach v of var price-gear {
su `v', meanonly
gen `v'_s = (`v' - r(min)) / (r(max) - r(min))
label var `v'_s "`: var label `v'', scaled"
}
su *_s
d *_s

*My try to inverse variables back to original:
foreach v of var price_s-gear_ratio_s {
su `v', meanonly
gen n_`v' = `v'*(r(max) - r(min))+ r(min)
}

[Nick Cox]

#6 Anne Ahrens

Your *s variables were all created to have bounds [0, 1] and so minimum 0 and range 1. Hence the recipe

new = old * range + minimum

as you say boils down to

new = old * 1 + 0

or more simply

new = old.

A standardized variable whether it's a matter of

[min, max] -> [0, 1]

or

(value - mean) / SD

has the limitation that the original values have been discarded and that can be inverted or reversed only with original values or summary statistics. So, you need access to the original variables and if you have them you can go straight there.

Imputation may add some twist to this, especially if imputation can produce values not exactly consistent with the original summaries.

I fear that i am missing the question here.

[Anne Ahrens]

Thank you for your quick reply, Nick.

You are the wizard of Stata, but even you have to follow the rules of math.

[Nick Cox]

Thanks for the compliment!

I'd phrase it as that no one can escape the rules of math, or maths, as British people say.