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st: RE: Generate new variable with an implicit formulation


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Generate new variable with an implicit formulation
Date   Wed, 8 Aug 2007 20:28:48 +0100

I have only very limited suggestions. 

1. It may not matter here but in general I feel queasy when I see stuff
like 

forval i = 0(0.001)1 { 

I would rather cycle over integers and manipulate further within the loop. 
When it ends up the same you lose nothing, but the other way round you can get bitten 
a bit more often. 

2. Relative tolerances are usually more versatile than absolute ones, 
although I can't say whether this applies to your case. 

3. It is largely cosmetic, but for a problem like this I prefer
-inrange()-. 

if x - n*`i'^(n-1) + (n-1)*`i'^n < 0.0001 & x - n*`i'^(n-1) + (n-1)*`i'^n > -0.0001

then becomes 

if inrange(x - n*`i'^(n-1) + (n-1)*`i'^n, -0.0001, 0.0001) 

Alternatively, 

if abs(x - n*`i'^(n-1) + (n-1)*`i'^n) < 0.0001

4. If this were my problem, I might move it into Mata. 

Nick 
n.j.cox@durham.ac.uk 

Bob Hammond
 
> I would like to define a new variable based on two current variables, 
> but the new variable cannot be expressed as an explicit 
> function of the 
> current variables. The relationship is:
> 
> x = n*y^(n-1) - (n-1)*y^n
> 
> where I have data on x and n and would like to create a new 
> variable, y. 
> x and y are restricted to the real numbers on the open interval (0,1) 
> and n is restricted to being a positive integer. Under these 
> restrictions, the function is well-behaved and provides a unique 
> solution, but not an explicit formulation. I can generate y with the 
> following loop:
> 
> forvalues i=0(0.001)1 {
> replace y=`i' if x - n*`i'^(n-1) + (n-1)*`i'^n < 0.0001 & x - 
> n*`i'^(n-1) + (n-1)*`i'^n > -0.0001
> }
> 
> but I am wondering if there is a more efficient and precise 
> way. If this 
> type of loop is best, what precision would you recommend for 
> the steps 
> of `i’ and the tolerance (the ><0.0001)? (I’m on Intercooled 
> Stata 9 for 
> Windows if that matters.) Thanks in advance,

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