st: nonlinearleastsquare

 From "Andreas Aschbacher" To statalist@hsphsun2.harvard.edu Subject st: nonlinearleastsquare Date Mon, 24 Nov 2003 14:15:52 +0100 (MET)

```I am using a textfile with 364 rows as the following:
/first column bar number,second column counts,these are results of an
measurements /
x               y
1	84
2	77
3	87
4	56
5	69
6	57
7	67
8	40
9	46
....
....

I know the result of our measurement if I fit the following function
f(x) = a1*exp(-((x-a3)/a2)^2)  +  a4*exp(-((x-a6)/a5)^2) , using x-column
and y-column above :
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
results from fitting with f(x) above using LevenbergMarquard ::
a1=~ 1138   a2= ~2.82 a3 = ~3.49 a4 = ~80.53  a5 = ~2.88 a6 = ~7.99
varianz of fit  about ~0.148,because it isn't perfect Poisson-Statistik
if I had perfect PoissonStatistik it would be in borders of : 0.925 to
1.075
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

but I don't get it by Stata.
I can't reach it by varying the parameters.
are there other possibilities to reach the aim.?
thank you very much for help

Andreas

Here's the most important from the result-window :

. do doubleGauß                                ' name of do-file

. capture program drop nlexample

. program nlexample
1. version 8
2. if "`1'" == "?" {
3. global S_1 "a1 a2 a3 a4 a5 a6"
4. global a1 = 1131
5. global a2 = 1
6. global a3 = 1
7. global a4 = 1
8. global a5 = 1
9. global a6 = 1
10. exit
11. }
12. replace `1' = \$a1*exp(-((x-\$a2)/\$a3)^2) + \$a4*exp(-((x-\$a5)/\$a6)^2)
13. end

. twoway line y x

. nl example y
(obs = 364)

Iteration 0:  residual SS =  5.70e+07
Iteration 1:  residual SS =  5.58e+07
Iteration 2:  residual SS =  3.35e+07
Iteration 3:  residual SS =  3.32e+07
Iteration 4:  residual SS =  3.32e+07
Iteration 5:  residual SS =  3.32e+07
Iteration 6:  residual SS =  3.32e+07
Iteration 7:  residual SS =  3.32e+07
Iteration 8:  residual SS =  3.32e+07
Iteration 9:  residual SS =  3.32e+07
.....................
Iteration 77:  residual SS =  1.48e+07
Iteration 78:  residual SS =  1.29e+07
Iteration 79:  residual SS =   2023443
Iteration 80:  residual SS =  315738.2
Iteration 81:  residual SS =  288846.4
Iteration 82:  residual SS =  288838.4

Source |       SS       df       MS                        Number of
obs =       364
-------------+------------------------------                  F(  2,   361)
=  25371.18
Model |    40599291     2  20299645.5             Prob > F      =
0.0000
Residual |  288838.388   361  800.106339          R-squared     =
0.9929
=    0.9929
Total |  40888129.4   363  112639.475            Root MSE      =
28.28615

Res. dev.     =
3463.222
(example)
----------------------------------------------------------------------------------------
y |      Coef.       Std. Err.      t          P>|t|     [95%
Conf.
Interval]
-------------+--------------------------------------------------------------------------
a1 |  -76051.86             .             .          .
.               .
a2 |  -132556.8             .             .          .
.               .
a3 |  -11881.27             .             .          .
.               .
a4 |   1131.814   5.267092   214.88   0.000     1121.456
1142.173
a5 |   70.13886   .1312605   534.35   0.000     69.88072
70.39699
a6 |   34.55454   .1859685   185.81   0.000     34.18882
34.92026
------------------------------------------------------------------------------
* Parameter a3 taken as constant term in model & ANOVA table
(SEs, P values, CIs, and correlations are asymptotic approximations)

.
end of do-file

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```