  # Re: st: RE: nonlinearleastsquare

 From "Andreas Aschbacher" To statalist@hsphsun2.harvard.edu Subject Re: st: RE: nonlinearleastsquare Date Thu, 27 Nov 2003 14:47:27 +0100 (MET)

```> 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
> > 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)
> >
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>

You are right in assuming that I try to fit a twopeak-curve-
a4 * (a1*exp(-((x-a3)/a2)^2)  + (1 - a1)*exp(-((x-a6)/a5)^2)) -
makes physical-sense and I am successful and happy to reach convergence with
both models yours and mine the old one: f(x) = a1*exp(-((x-a3)/a2)^2)  +
a4*exp(-((x-a6)/a5)^2) :
I varied the parameters in both cases(model-functions) and tried  to
vary tolerance ;
stepsize and  iterations with help from numerical recipes/method of
Levenberg-Marquardt/
but - this is my problem - only successful in another statistical software,
I have problems to program and vary tolerance;stepsize and iterations in
Stata,writing the do-file
with initial parameter-setting  works wthout mistakes(see do-file above).
I can't find >> Royston,P 1992 sg 1.2 Nonlinear Regression Command. Stata
Technical Bulletin 7: 11- 18
Reprinted in Stata Technical Bulletin reprints vol 2,pp. 112 - 120  <<
anywhere , I want to know
the algorithm very exactly.
any help will be very appreciated                                andreas

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```