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st: RE: nonlinearleastsquare


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: nonlinearleastsquare
Date   Mon, 24 Nov 2003 13:30:05 -0000

In very broad terms, this looks like
a lot of parameters to fit a curve in two-space.
It looks as if you are modelling a two-peak curve.

There's presumably some physics behind this, but does
something more like

a4 * (a1*exp(-((x-a3)/a2)^2)  + (1 - a1)*exp(-((x-a6)/a5)^2))

make sense as a model?

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

Andreas Aschbacher

> I am using a textfile with 364 rows as the following:
> /first column bar number,second column counts,these are
> results of an
> experiment in radioactive
> 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 doubleGau▀                                ' 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
> -------------+------------------------------
>   Adj R-squared
> =    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)
>

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