Non-linear regression example

[wschrabi-disabl]

thanks a lot my friends,





I have studied now the term Fisher info and the normal non-lin regression analyses. I think there is a link between these terms, but I could not figure out it in the literature. Here another nice MC11 ws with PDF from the S-Plus paper.


Now the WS is MC11 compateble.

[ptc-1368288]

On 3/30/2010 11:02:59 AM, wschrabi wrote:
>thanks a lot my friends,
... Here another nice
>MC11 ws with PDF from the
>S-Plus paper.
__________________________

Sorry Walter,

The data table is empty [all red] .
For only 12 pairs, write them in a two columns vector.
Transmission problem ??? Conversion problem ???

jmG

[ptc-1368288]

On 3/31/2010 12:40:41 AM, jmG wrote:
>On 3/30/2010 11:02:59 AM, wschrabi
>wrote:
>>thanks a lot my friends,
>... Here another nice
>>MC11 ws with PDF from the
>>S-Plus paper.
>__________________________
>
>Sorry Walter,
>
>The data table is empty [all red] .
>For only 12 pairs, write them in a two
>columns vector.
>Transmission problem ??? Conversion
>problem ???
>
>jmG
>__________________________

The debate is circular around obsolete solvers and methods [home made too] and the most modern CAS solvers that paper writers seem to have limited applied know how. Did I read "logistic" in the paper ? Sorry, the model is not "Verhulst logistic". If the wrong model is applied, how can a band aid help ? That was my point as well as obsolete approach. Same reasoning applies to "Insulin".

jmG

[wschrabi-disabl]

Sorry jmG, my error. Hope this is ok.

[wschrabi-disabl]

On 3/31/2010 12:40:41 AM, jmG wrote:
>On 3/30/2010 11:02:59 AM, wschrabi
>wrote:
>>thanks a lot my friends,
>... Here another nice
>>MC11 ws with PDF from the
>>S-Plus paper.
>__________________________
>
>Sorry Walter,
>
>The data table is empty [all red] .
>For only 12 pairs, write them in a two
>columns vector.
>Transmission problem ??? Conversion
>problem ???
>
Convertsation problems: I realized that MC14 is wuit different to MC11. Even when I save the ws as MC11 format, a lot of stuff is different. So I had to check it in my old MC11-. But now it works.
>jmG
>
>
>

[TheodoreM.Bones]

I saved the ws to disk, then called it from disk - - no red lines.

[ptc-1368288]

On 3/31/2010 8:42:34 AM, bones7xx wrote:
>I saved the ws to disk, then
>called it from disk - - no red
>lines.
_______________________________

That's what I do do too: save in C:\Download.
I never open a ws from the collab, only download.

In 30 minutes couldn't find any census data 1790 ... 2000.

jmG

[wschrabi-disabl]

THe ws was a MC14 ws saved as MC11. But there the data is missing. NOw I have updated it and now it works, as I saved in MC11. (So MC14 makes troubles.)

[ptc-1368288]

On 3/31/2010 11:18:19 AM, wschrabi wrote:
>THe ws was a MC14 ws saved as
>MC11. But there the data is
>missing. NOw I have updated it
>and now it works, as I saved
>in MC11. (So MC14 makes
>troubles.)
_______________________________

Only the census data are needed.
Will have a quick attempt.

Have you read "Insulin", the Osdesolve & Lambert W ?

jmG

[wschrabi-disabl]

On 3/31/2010 12:49:27 PM, jmG wrote:
>On 3/31/2010 11:18:19 AM, wschrabi
>wrote:
>>THe ws was a MC14 ws saved as
>>MC11. But there the data is
>>missing. NOw I have updated it
>>and now it works, as I saved
>>in MC11. (So MC14 makes
>>troubles.)
>_______________________________
>
>Only the census data are needed.
>Will have a quick attempt.
>
>Have you read "Insulin", the Osdesolve &
>Lambert W ?
>
I will do that tomorrow. Which name of ws?
Here is another similar example with PDF. (in MC11 and MC14)
>jmG
>
>
>

[TheodoreM.Bones]

According to a very old stringent Behrens test, it takes a minimum of 8 samples of data to get within 50% probability of the mean. 6 isn't enough. Besides, Kendall's Advanced Theory of Statistics has a small footnote saying that a steady stdeviation value is assumed with Fisher's Information Matrix.

[ptc-1368288]

==> Have you read "Insulin", the Osdesolve & Lambert W ? [jmG]
==> I will do that tomorrow. Which name of ws? [Walter]
..........................

My last posting few days ago, reposted here.
In what way does the Fisher matrix info helps ?

jmG

[TheodoreM.Bones]

Fisher helps very little on small samples. It just shows the slope of the regression curve at a point, meaning high slope equals uncertainity
of the regression formula at that data point. Mostly, I would just disregard the whole mess. The Minerr process can't do any better so what is the use of snapping your fingers at it? Bad fits have a high Fisher Information > > 1.

[ptc-1368288]

Thanks Theodore about Fisher, interesting comment.
ORIGINLAB that goes so deep in the fit does not mention Fisher at all. They have more conventional criteria and their fits are = to Mathcad PW Minerr.
Two more comments in the work sheet.

jmG

[wschrabi-disabl]

Thanks a lot for that highly sophisticated ws. Yes Lambert is the winner, but it takes some time to understand that smart worksheet. Thanks a lot.

[ValeryOchkov]

On the MAS:
http://twt.mpei.ac.ru/ochkov/VPU_Book_New/mas/Genfit.htm
Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[wschrabi-disabl]

Thanks Prof Val, I did not know that genfit supplies also the tolerances for the values.



Best regards



walter





PS: Can you tell me how the F(x,a,n) is calculated in MathCad 14? there is no diff at all.

I found the solution: See diff_MC14.png <- this is wrong!

[ValeryOchkov]

On 4/1/2010 9:10:25 AM, wschrabi wrote:

PS: Can you
>tell me how the F(x,a,n) is
>calculated in MathCad 14?
>there is no diff at all.

Only in Mathcad 11!
It is a Maple function!

Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[wschrabi-disabl]

Is there really no way to make it in MC14?
THAT would be no enrichment of MC14!!!
what a pitty.

[ptc-1368288]

On 4/1/2010 10:12:31 AM, wschrabi wrote:
>Is there really no way to make
>it in MC14?
>THAT would be no enrichment of
>MC14!!!
>what a pitty.
_______________________________

There may be from Robert original converter,
but again based on Mathcad 11 coding.

jmG

[TomGutman]

My easy genfit setup has routines to calculate the necessary derivatives that work in both MC11 and MC14. No need for undocumented and unsupported Maple functions.

But there is really no reason to use genfit anyway. Minerr is generally easier to set up, more flexible, and (when used correctly) just as fast and accurate.
__________________
� � � � Tom Gutman

[wschrabi-disabl]

Thanks Mr Gutman, I also find Minerr better, but here the solution who it is done in MC14. You have to use the Gradient symbol, right?

[TomGutman]

No, I don't use the gradient symbol. I have all of my multivariate calculus functions in a sheet called jacobian etc. But the simple genfit setup has its own version of the gradient operator, tailored for the particular form of the function for genfit. You feed it the fitting function, it creates the function for genfit, with the fitting function and the derivatives combined in a single vector.
__________________
� � � � Tom Gutman

[TheodoreM.Bones]

JmG's Lambert solution is brillant. I tried to use a model equation of my own for a non-linear fit, tweaked it by eye to get good initial guesses, then Minerr to perfect those. The Minerr would not run a single step ahead. Czn anybody tell me why Minerr stalls?

[ptc-1368288]

On 4/1/2010 5:35:57 PM, bones7xx wrote:
>JmG's Lambert solution is
>brillant. I tried to use a
>model equation of my own for a
>non-linear fit, tweaked it by
>eye to get good initial
>guesses, then Minerr to
>perfect those. The Minerr
>would not run a single step
>ahead. Czn anybody tell me
>why Minerr stalls?
____________________________

Will look at your work sheet later.
Your insulin project in one iterate, like you report. Attached some notes on my reasoning, I mean reasoning the Engineer way. However one must not totally ignore that some "influence parameters" might not produce such beautiful results with different ethnic groups of the subjects and so and so ... lab tests, etc...

jmG

[ptc-1368288]

On 4/1/2010 5:35:57 PM, bones7xx wrote:
>JmG's Lambert solution is
>brillant. I tried to use a
>model equation of my own for a
>non-linear fit, tweaked it by
>eye to get good initial
>guesses, then Minerr to
>perfect those. The Minerr
>would not run a single step
>ahead. Can anybody tell me
>why Minerr stalls?
____________________________

We get something Minerr LM, but surely not a fit !
Your model is most puzzling and insufficient ?

Observe the leading exp(1) in the plot ????

jmG

[TheodoreM.Bones]

It seems the various Minerr options can't run on a range of J1 Bessel raised to a certain power combined with some other function. I got a good fit by trial & error that ran OK. But time comsuming.

[wschrabi-disabl]

Mr Gutman, can you repost your Jacobian sheet, I got nosely about this. thanks a lot.

[TomGutman]

No need to repost it. Posts stay on this collaboratory indefinitely. You can find the sheet at http://collab.mathsoft.com/read?102332,63 .
__________________
� � � � Tom Gutman

[wschrabi-disabl]

Thanks a lot for the link. YOur Worksheet is highly sophisticated. I will need some time to understand some part of it. THnaks