Re: st: RE: Rescaling variables

[<suryadipta.roy@lawrence.edu>]

Nick,

The following is what I am trying to do and the following 
are my concerns:

1. I have using two separate corruption indices in my 
regressions, one going from 0 to 6 and the other going 
from 0 to 10 for a cross-section of countries over time. 
In my regressions using these two separately as 
independent variables, I found that the latter series 
possesses more of between and within standard deviation 
than the former and (hence?) giving higher velues of t/z 
(Cross country corruption data tend to be very persistent 
for a country over time but tends to vary more across 
countries in a given year).

2. Consequently, I was thinking of converting both the 
series to one(s) where they would have the same standard 
deviations, ie. one- hence the idea of converting them to 
standard normal variables, i.e. option (a).

(Kit Baum had earlier suggested the following commands to 
do this:

ssc install center

bys country: center variable, gen(newvariable) standardize
replace newvariable=0 if newvariable==.)

I understand the problem with transformations, but my idea 
was to make the two series comparable. Please let me know 
if I am wrong in doing this.

Thanks!
Suryadipta.


 
On Tue, 8 Aug 2006 23:50:26 +0100
 "Nick Cox" <n.j.cox@durham.ac.uk> wrote:

> There is some confusion here. There is 
> a difference between 
> (a) converting to a scale on which mean is 0 and sd 1 
> and 
> (b) transforming to Gaussian (a.k.a. normal)
>
> which is unaffected by the fact that people 
> often want both. 
> I can use -egen, std()- for (a) but 
> this is just a linear rescaling and has no 
> effect of the degree of non-Gaussianity in
> the data. So, for example, skewness and 
> kurtosis are invariant under linear rescalings. 
> Thus suppose I have a variable which is 
> 42 most of the time and 3.14159 the rest 
> of the time. In this example, two spikes will 
> remain two spikes under any one-to-one mapping 
> and a bell-shape will remain out of reach, indeed
> out of sight. 
> Your own distribution does not sound so refractory, 
> but be aware of the principle that transformation
> often fails. 
> Nick 
> n.j.cox@durham.ac.uk 
> suryadipta.roy@lawrence.edu
>
>
> > I had another question on rescaling variables. At this 
> > point, I am trying to convert my some of my independent 
> > variables (running from 0 to 6) to standard normal 
> > variables. I have been able to do it by subtracting the 
> > numbers from the mean and dividing by the standard 
> > deviation for each group (I have an unbalanced panel of 
> > countries), but the problem comes for countries which 
> > had 
> > no within variation for that variable, since dividing by 
> > zero is giving missing observations in such cases. The 
> > following command does not work:
> >
> > by code, sort: egen newvar=std(oldvar), since egen does 
> > not work with by.
> >
> > Can anyone point me towards the correct command for 
> > direct 
> > conversion of numbers into their standard normals 
> > thereby 
> > circumventing the problem of dividing by zeros? Thanks 
> > as 
> > usual!
> *
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Suryadipta Roy, Ph.D.
Visiting Assistant Professor,
Department of Economics,
Lawrence University,
115 South Drew Street,
Appleton, WI-54911.
Phone: 920-832-7343.
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