SORRY that I am answering so late,but it took me some time to experiment
with
both model-functions(see below):
//!!!!!!!!!!!!! I answered twice to Nick Cox by `answer` in my e-mail-Editor
but it did not occur in Stata-list // maybe it was the long time I
experienced //
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
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
> [email protected]
>
> 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)
> >
>
> *
> * 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/
>
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