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Re: st: simulated value of a ratio does not compare to manually calculated value


From   Jeph Herrin <stata@spandrel.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: simulated value of a ratio does not compare to manually calculated value
Date   Fri, 26 Apr 2013 16:44:32 -0400

More specifically, if you run the original code and list the values, it is clear that mse_ratio=mse_true/mse_tt:

  +--------------------------------+
  | mse_true     mse_tt   mse_ra~o |
  |--------------------------------|
  |  .003547   .0322058   .1101363 |
  | .0006413   .0662122   .0096851 |
  | .0053084   .0249331   .2129068 |
  | .0013864   .0317399   .0436803 |
  |  .000913   .0238286   .0383137 |
  | .0022051   .0287689   .0766471 |
  | .0147754   .0337151   .4382421 |
  | .0133145   .0008774   15.17555 |
  | .0006873   .0390971   .0175787 |
  | .0054993   .0493028   .1115405 |
  | .0007968   .0217611   .0366142 |
  | .0030441   .0083029   .3666291 |
  | .0020152    .064011   .0314826 |
  | .0016439   .0557283   .0294992 |
  | .0008482   .0004691   1.808224 |
  |   .00004   .0477381   .0008388 |
  | .0030498   .0468981   .0650293 |



On 4/26/2013 4:36 PM, Austin Nichols wrote:
Ariel Linden, DrPH <ariel.linden@gmail.com>:

The mean of a ratio generically does not equal the ratio of the means.
Put
  sc mse_t*
  corr mse_t*
  g r=mse_tr/mse_tt
  su r mse_true mse_tt mse_ratio

On Fri, Apr 26, 2013 at 4:28 PM, Ariel Linden, DrPH
<ariel.linden@gmail.com> wrote:
Hi All,

Below is a simulation that I am running in which I generate a ratio
(mse_ratio) which is simply the ratio of the mse_true / mse_tt

When running the simulation, the mse_ratio does not calculate correctly,
even though each component does come through correctly...

More specifically, you can see from the output below that the mse_true =
.0038127, and the mse_tt = .0352618  , which should
elicit a ratio of .10812551

However, the mse_ratio value is  91.79034.

I cannot figure out what in my code is not working here... Any help is
appreciated... See my code below...

Thanks in advance!

Ariel


* this is the results of the simulation code from below
. sum mse_true mse_tt mse_ratio

     Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
     mse_true |        50    .0038127    .0050518   9.49e-07   .0231653
       mse_tt |        50    .0352618    .0266384   4.62e-07   .1037486
    mse_ratio |        50    91.79034    619.6749   .0000267   4382.196


*********************************
* Start code
*******************************
program drop _all

program define sim, rclass

drop _all

set obs 1000
generate x=1
replace x=0 if _n>1000/2
generate ybase=invnorm(uniform())
generate e1=invnorm(uniform())
generate pi=(1-x)/(1+exp(-1+0.1*ybase)) + x/(1+exp(+0.9-0.1*ybase))
generate u1=uniform()
gen a=0
replace a=1 if pi>=u1
gen ysqr=ybase^2
gen intxy=x*ybase
gen intxy2=x*ysqr
generate y=0.5*a-0.45+0.35*ybase+0.1*x+0.3*intxy+0.3*intxy2+0.25*ysqr+e1

* true estimates of Y
regress y a x ybase intxy ysqr intxy2
scalar tx = _b[a]
return scalar tx = tx

scalar mse_true = (_b[a]-0.50)^2
return scalar mse_true = mse_true

*ttest estimates - naïve
ttest y, by(a)
scalar ttest1 = r(mu_2)-r(mu_1)
return scalar ttest1 = ttest1

scalar mse_tt = (ttest1-0.50)^2
return scalar mse_tt = mse_tt

scalar mse_ratio = mse_true / mse_tt
return scalar mse_ratio = mse_ratio

end

set seed 1234
simulate true=r(tx) ttest1=r(ttest1) mse_true=r(mse_true) ///
mse_tt=r(mse_tt) mse_ratio=r(mse_ratio), reps(50): sim

sum mse_true mse_tt mse_ratio

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