HELP: Non-linear regression problem
Paul
I am fitting experimental data y as a function of x, with parameters, c and h. The value of h is what I am interested in.
The functional description is:
y(x) = c/(x^2 + h^2) [1]
The program fits my data in a breeze, using expression [1], and finds a value of h=1.9, with a p-value of 0.02. However, now I am told to use the following function instead:
y(x) = c/(x^2 + k) [2]
..where k = h^2. This results in a value of k = 3.61 (clearly being 1.9^2), with a p-value of 0.1.
Intuitively, I feel the second approach is wrong. The model fit would be more sensitive to changes in h than to changes in k, so you would indeed expect a smaller p-value for h.
Am I right, or should I prevent the use of non-linear paramaters in the model, and substitute them with a linear paramater, in this case k = h^2, in other words, use the corresponding p-value (0.1) for the value h=1.9?
Thanks for your help.
Reef Fish
Your problem has nothing to do with nonlinear regression.
It has everything to do with the definition of p-value.
If you parametrized your unknown to be h^2, the only possible
Alternative Hypothesis is ONE-TAILED, or the test statistic
TA1 for h^2 > observed h^2.
On the other hand, if you parametrize your unknown to be k,
then k can be positive OR negative. and the corresponding
p-value could be one-tailed OR two-tailed, and your Test
Statistic for k, TS2, will have a different samplying distribution
from TS1.
I believe THAT's the sourse of your discrepancy. The two
different p-values are NOT comparable in their magnitudes.
BTW, your model is NONLINEAR does not depend on whether
you use h^2 or k.
-- Reef Fish Bob.
Paul
Reef Fish
Paul wrote:
> I know that h must be > 0. So this means I should not substitute k=z^2 and solve for k, right?
If you know that a priori, then it doesn't make any difference whether
you parametrice it as h^2 or k, and there is nothing to solve.
Not sure what your worries are given my explanation in the preceding
post.''
-- Reef Fish Bob.
Paul
> and there is nothing to solve.
Not sure I understand what you mean by that.
Reef Fish
Paul wrote:
> So, are you saying that the largest part of the discrepancy in the p-values result from the different distrubutions of h^2 and h?
There is NO discrepancy if you use only ONE of them.
Exclusive OR: Either h^2 OR k (or call it h if you wish)
and you'll get ONE p-value for whatever parameter and whatever H1 you
used.
>
> > and there is nothing to solve.
> Not sure I understand what you mean by that.
Paul, I think you should start by learning something about how to do
ANY
regression, and the meaning of p-value.
If you have any more questions, others will have to answer it for you.
I've done the same THREE times already.
-- Reef Fish Bob.
Paul
>
> Exclusive OR: Either h^2 OR k (or call it h
> if you wish)
>
> and you'll get ONE p-value for whatever parameter and
> whatever H1 you
> used.
>
> about how to do
> ANY
> regression, and the meaning of p-value.
>
> If you have any more questions, others will have to
> answer it for you.
> I've done the same THREE times already.
Fish,
No need to use capitals all over. I know I'm a newbie on this forum, and you seem to be one of those in the upper layers, at least your attitude makes me think so.
I'm not an expert in statistics but in quantum physics. That's why I ask questions here. If your time is so valuable that you cannot help others, next time, just ignore the question.
If you only try to show off your superiority in your "knowledge of p-values" and don't care to get insight in the view of others, I actually wonder what you're doing on this forum at all.
I'll figure it out myself. I have adequately addressed problems that were quite a bit more complex than this one.
Reef Fish
Paul wrote:
> > There is NO discrepancy if you use only ONE of them.
> >
> > Exclusive OR: Either h^2 OR k (or call it h
> > if you wish)
> >
> > and you'll get ONE p-value for whatever parameter and
> > whatever H1 you
> > used.
> >
> > Paul, I think you should start by learning something
> > about how to do
> > ANY
> > regression, and the meaning of p-value.
> >
> > If you have any more questions, others will have to
> > answer it for you.
> > I've done the same THREE times already.
>
> Fish,
>
> No need to use capitals all over. I know I'm a newbie on this forum,
Your first sentence would have implied your second, to ANYONE in this
forum.
The caps had nothing to do with YOUR newbieness. They are 'italics'.
> and you seem to be one of those in the upper layers, at least your attitude makes me think so.
>
> I'm not an expert in statistics but in quantum physics. That's why I ask questions here. If your time is so valuable that you cannot help others, next time, just ignore the question.
You mean even with the THREE times emphasized, you still didn't realize
that you've been help THREE times, each of which would have helped
anyone who had SOME idea of regression. I was in fact very polite to
you to suggest that you learn some basic definitions and meanings, such
as a p-value, before asking nonsensical questions about how to convert
one p-value to another. You didn't even know what the first one
meant.
>
> If you only try to show off your superiority in your "knowledge of p-values" and don't care to get insight in the view of others, I actually wonder what you're doing on this forum at all.
To show off the "knowledge" in p-value, would be the equivalent of
showing off the high-school knowledge that Y = a + bX is a straight
line.
You're are just like NAG. The belligerently ignorant poster who
asked stupid questions, got help; didn't understand any of it because
you were completely unprepared to ASK or to understand the answer.
Then you started wasting EVERYONE's time making posts like this
or like those of NAG.
Thank god you're nowhere as ignorant and obnoxious as any of the
Luis A. Afonsos.
> I'll figure it out myself. I have adequately addressed problems that were quite a bit more complex than this one.
Good luck. Just because you know quantum physics doesn't imply
you can learn ANYTHING about statistics by yourself. That's the
misconception that created all the Quacks in sociology, economics,
and medicine who are no more equipped to apply statistics than they
are to practice LAW or perform a simple brain surgery.
You are very much misguided by your inflated head.
-- Reef Fish Bob.
espyrian
Hi, Paul. I'll do my best to help although I'm a bit shaky. If I err
then hopefully other readers will step in...
Firstly, I'm thinking we should transform your model a bit and express
it in linear terms. (You're a quantum physicist, so I'm assuming c
represents the speed of light, or some other known constant? In any
event, you say you have no interest in estimating c). Linearly, your
model can be expressed as:
Y=AX+B where Y=c/y and X=x^2
The co-efficients A and B are what you're interested in estimating.
I'm not familiar with NLREG, but if you run a regression hopefully you
should get an ANOVA (analysis of variance) table testing whether A=B=0,
a parameter estimate table that includes tests for A=0 and B=0, and an
R^2 value between 0 & 1 (the amount of variation explained by the
model).
What are the p-values, co-efficient estimates and R^2 values when you
run the linear regression described above on your raw data? Can you
post the results here?
Also, does NLREG allow you to plot a normal quantile plot of the
residuals? Is it a nice straight line? And does the plot of residuals
vs. X show random scattering arount the residual=0 line?
P.S. Don't worry about Reef Fish. That's just his style. He's a
prickly pear (the fruit of which is aptly called 'tuna'!), but I
seriously doubt anyone here knows more about regression than him.
robert...@gmail.com
> Am I right, or should I prevent the use of non-linear paramaters in
> the model, and substitute them with a linear paramater, in this case
> k = h^2, in other words, use the corresponding p-value (0.1) for the
> value h=1.9?
You can ignore the p-values, they're a distraction anyway.
What you really want is the joint posterior distribution over the
model parameters -- from this you can compute stuff that you
really want to know, e.g. predictive distributions or
expected loss for different actions.
The "ignore all p-values" is an aspect of the Bayesian
interpretation of probability. If you are swayed at all by
arguments to authority, you might consider that several
leading Bayesians are/were physicists. This is probably
because physics problems usually include strong prior
information.
A good place to start is Tom Loredo's web page.
http://astrosun.tn.cornell.edu/staff/loredo/
http://www.astro.cornell.edu/staff/loredo/bayes/
http://www.astro.cornell.edu/staff/loredo/bayes/tjl.html
Have fun,
Robert Dodier
Reef Fish
robert.dod...@gmail.com wrote:
> Paul wrote:
>
> > Am I right, or should I prevent the use of non-linear paramaters in
> > the model, and substitute them with a linear paramater, in this case
> > k = h^2, in other words, use the corresponding p-value (0.1) for the
> > value h=1.9?
>
> You can ignore the p-values, they're a distraction anyway.
> What you really want is the joint posterior distribution over the
> model parameters -- from this you can compute stuff that you
> really want to know, e.g. predictive distributions or
> expected loss for different actions.
Talk about a completely inappropriate response to a newbie
non-Bayesian on something that YOU wouldn't know how
a TRUE Bayesian would act if your life depended on it!
So that's who Robert Dodier is, the self-proclaimed Physicist
Bayesian.
>
> The "ignore all p-values" is an aspect of the Bayesian
> interpretation of probability. If you are swayed at all by
> arguments to authority, you might consider that several
> leading Bayesians are/were physicists. This is probably
> because physics problems usually include strong prior
> information.
Tell us HOW you would access your prior in the problem
asked by JP?
Have you EVER assessed a bivariate prior distribution
that reflected your own prior belief. If so, just ONCE in
your life even, tell us HOW you did it, and I'll tell you
either how you were callous or how you are NOT a
Bayesian.
This is my challenge to see if you known ANYTHING
about Bayesian statistics.
This is 100% serious and absolutely substantive in
Bayesian statistics.
Here is your chance to show if you are just blowing smoke
or if you actually know something.
-- Reef Fish Bob.
Paul
The problem however is, that this equation cannot be linearized, because it's non-linear in its (original) parameters. But there are many programs that perform non-linear regression, so that's not the problem.
The basic question really is, if the values derived from the experimental data are statistically significant.
If I perform the regression on y(x) = c/(x^2 + h^2), you find h=1.9 which is statistically significant at p=0.02.
Of course a simple transformation of variables (k=h^2) cannot change anything about that. So the p-value of 0.1 for k (being 1.9^2) must have to do with the different distribution of k as compared to h. My guess is that the coordinate transform messes up things, because h^2 will never be negative, for example.
I also assume you should take into account the p-value of c. You cannot judge statistical significance of the data based on h only.
I assume a simple ANOVA will do, and after that you dump the p-values.
This is really fuzzy stuff. My statement is that if you need statistics to prove your point, you're in trouble anyway. :-) But some statisticians have an attitude that if the statistic tests fail, EVERYTHING is nonsense and if they succeed, EVERYTHING is 100% true.
Now try to explain THAT to a quantum physisicist... ;-)
espyrian
In an ANOVA table of coefficients the t- and p- values refer to a test
of a null hypothesis that the parameter is zero when the other
parameters are present in the model vs. an alternative hypothesis that
the parameter is not zero when the other parameters are present (i.e.
two sided). However, the squared constraint you've placed on your model
means that the parameter can never be negative, so the alternative must
become 'is greater than zero' (i.e. one-sided).
This is what Reef Fish was getting at in his original reply to you.
In your first model, y = c / (x^2 + h^2), h>0 with p=0.02
In your second model, y = c / (x^2 + k), k>0 or k<0 with p=0.1. To make
it one sided you halve the p-value. So k>0 with p=0.05
As I understand it, your two ANOVA runs are essentially agreeing with
each other, as you would expect. When c is present, h or k is
statistically significantly greater than zero at the alpha=0.05 level
with estimates of 1.9 and 3.61 respectively.
Just out of interest, what are you modelling? The inverse x^2 suggests
forces between bodies?
> But some statisticians have an attitude that if the statistic tests
fail, EVERYTHING is nonsense and if they succeed, EVERYTHING is 100% true.
LOL. All statisticians are gamblers. We calculate the ODDS of
something being true. This is infinitely better than the attitude taken
by quantum physicists who believe everything is true and false
simultaneously ;-)
Paul
> by quantum physicists who believe everything is true
> and false simultaneously ;-)
I agree with you. And then again, I dont! :-D
Scott Seidman
@m73g2000cwd.googlegroups.com:
> You can ignore the p-values, they're a distraction anyway.
> What you really want is the joint posterior distribution over the
> model parameters -- from this you can compute stuff that you
> really want to know, e.g. predictive distributions or
> expected loss for different actions.
Another useful piece of information is the Coefficient of Variation, which
is the square root of the diagonal element of the variance/covariance
matrix that corresponds to the parameter, divided by the estimate, often
expressed as a percent. This gives you some grip on the precision of your
estimate.
For example, if h is estimated to be 20, the confidence (NOT as in
confidence range, but not necessarily unrelated) in the estimate will be
much greater if the CV% is 5%, as opposed to 1500%. IMO, if you publish an
estimate from a nonlinear regression, you're hiding something,
intentionally or nonintentionally.
--
Scott
Reverse name to reply
Paul
Thanks - I'll have a closer look tonight. This is a model where the distance of a point source is retrieved from the radiation intensity on a horizontal plane. So y = intensity (besides some geometrical factors), x = distance from the center of symmetry on the plane, h = distance between radiation source and the plane.
Paul
>
> -- Reef Fish Bob.
Man, I think you have a serious problem. (FYI: Not related to regression theory.)
BTW - don't think you would talk like that if you were standing in front of me :-).
Scott Seidman
news:Xns983C61DA71333sc...@130.133.1.4:
> IMO, if you publish an
> estimate from a nonlinear regression, you're hiding something,
> intentionally or nonintentionally.
>
Oops, I meant "if you publish an estimate from a nonlinear regression,
WITHOUT PROVIDING INFO ON THE CV, you're hiding something, intentionally or
Richard Ulrich
> I am using an evalutation copy of NLREG, which I use for a non-linear regression fit.
>
> I am fitting experimental data y as a function of x, with parameters, c and h. The value of h is what I am interested in.
>
> The functional description is:
>
> y(x) = c/(x^2 + h^2) [1]
>
> The program fits my data in a breeze, using expression [1], and finds a value of h=1.9, with a p-value of 0.02. However, now I am told to use the following function instead:
>
> y(x) = c/(x^2 + k) [2]
>
> ..where k = h^2. This results in a value of k = 3.61 (clearly being 1.9^2), with a p-value of 0.1.
>
> Intuitively, I feel the second approach is wrong. The model fit would be more sensitive to changes in h than to changes in k, so you would indeed expect a smaller p-value for h.
Well, not necessarily. Since the two answers are "equivalent",
the p-values might deserve to be equivalent, too. What happens
when the likelihood surface is not symmetrical around the ML
solution is problematic. (Reef Fish Bob, take note.)
There are two usual ways to get the p-value for fitting an additional
variable -- or testing this h and h^2 versus 0. One is to use the
asymptotic information at the maximum likelihood solution, and
the other is to look at the improvement of fit that is gained by
using the value instead of 0. Look at improvement of R^2 in
least-squares. In ML fitting, the test is X^= -2LL(change).
By looking at the improvement, your two answers for h and h^2
surely will give the same test, and that one is probably the best
available test.
By similar logic, you could plot the ML fit for various values of
h and h^2 from zero on up, and see which one produces a
symmetric confidence interval. That better-behavior of the likelihood
surface might be considered justification for using that parameter,
in the absence of arguments about making sure the value is positive.
>
> Am I right, or should I prevent the use of non-linear paramaters in the model, and substitute them with a linear paramater, in this case k = h^2, in other words, use the corresponding p-value (0.1) for the value h=1.9?
>
--
Rich Ulrich, wpi...@pitt.edu
http://www.pitt.edu/~wpilib/index.html
Reef Fish
And where does THIS piece of theory/quackery come from?
-- Reef Fish Bob.
Scott Seidman
news:1158104672.5...@i42g2000cwa.googlegroups.com:
Which part would you call quackery-- the idea that the coefficient of
variation can provide insight as to the precision of a parameter
estimate, or that reporting a parameter estimate from an iterative
algorithm for nonlinear least squares without reporting the CV does not
provide a full picture?
All I can say is that too many people blindly publish the results of a
parameter estimation without having any idea whether they can confidently
state that they even have the order of magnitude of the parameter
precise. Perhaps I overstated my opinion, as standard error yields much
the same info, yet I prefer the dimensionless aspect of the CV. A google
search of "coefficient of variation parameter estimation" yields 5+
million hits, and adding "nonlinear" cuts it down to 2+ million, with 9k
hits on google scholar, suggesting that I am not that far off the mark.
In any case, CV% or SE each convey more information than a p-value alone.
The p-value could be .000005, but some may want to know if the estimate
of 500 could really be closer to 5e6.
If you absolutely must have a reference, I'll refer you to Chapter 7,
Interpretation of the Estimates, in Bard, Nonlinear Parameter Estimation,
Academic Press, 1974. The chapter starts off "It is not enough to
compute a vector THETA* and to state that this is the estimated value of
the unknown parameters THETA. We must also investigate the reliability
and precision of our estimates. We wish to answer questions such as
'what are the chances that the estimate is off by no more than 1%?' or
'how much can we change the estimates and still fit the data well?' Bard
then goes on to describe some of the methodologies appropriate for
answering those questions.
Then, I'd point you to Section 7-5 of that Chapter "The covariance matrix
of the estimates".
Excellent book. The first chapter deals with the differences between a
parameter estimate and a curve fit. I'd recommend it for you.
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158104672.5...@i42g2000cwa.googlegroups.com:
>
> >
> > Scott Seidman wrote:
> >> Scott Seidman <namdie...@mindspring.com> wrote in
> >> news:Xns983C61DA71333sc...@130.133.1.4:
> >>
> >> > IMO, if you publish an
> >> > estimate from a nonlinear regression, you're hiding something,
> >> > intentionally or nonintentionally.
> >> >
> >> Oops, I meant "if you publish an estimate from a nonlinear
> >> regression, WITHOUT PROVIDING INFO ON THE CV, you're hiding
> >> something, intentionally or nonintentionally.
> >
> > And where does THIS piece of theory/quackery come from?
> >
> > -- Reef Fish Bob.
> >
> >
>
> Which part would you call quackery-- the idea that the coefficient of
> variation can provide insight as to the precision of a parameter
> estimate, or that reporting a parameter estimate from an iterative
> algorithm for nonlinear least squares without reporting the CV does not
> provide a full picture?
>
> All I can say is that too many people blindly publish the results of a
> parameter estimation without having any idea whether they can confidently
> state that they even have the order of magnitude of the parameter
> precise.
> Perhaps I overstated my opinion,
You not only GROSSLY overstated your UNSUBSTANTIATED opinion
on the estimation of parameters in nonlinear regression, I suspect you
don't even KNOW what "nonlinear" regression is!
How is the estimation of parameters different in nonlinear regression
from linear regression, in terms of one require the CV and the other
one
doesn't?
Point to a TEXTBOOK on nonlinear regression that promotes your
quackery.
> as standard error yields much
> the same info, yet I prefer the dimensionless aspect of the CV. A google
> search of "coefficient of variation parameter estimation" yields 5+
> million hits, and adding "nonlinear" cuts it down to 2+ million, with 9k
> hits on google scholar, suggesting that I am not that far off the mark.
> In any case, CV% or SE each convey more information than a p-value alone.
> The p-value could be .000005, but some may want to know if the estimate
> of 500 could really be closer to 5e6.
Do you do that for all your Linear Regression problems? Do you know
what
a Linear Regression is?
>
> If you absolutely must have a reference, I'll refer you to Chapter 7,
> Interpretation of the Estimates, in Bard, Nonlinear Parameter Estimation,
> Academic Press, 1974. The chapter starts off "It is not enough to
> compute a vector THETA* and to state that this is the estimated value of
> the unknown parameters THETA. We must also investigate the reliability
> and precision of our estimates. We wish to answer questions such as
> 'what are the chances that the estimate is off by no more than 1%?' or
> 'how much can we change the estimates and still fit the data well?' Bard
> then goes on to describe some of the methodologies appropriate for
> answering those questions.
>
> Then, I'd point you to Section 7-5 of that Chapter "The covariance matrix
> of the estimates".
Did the author of that book have ANY training in Statistics?
>
> Excellent book. The first chapter deals with the differences between a
> parameter estimate and a curve fit.
How profound!
I'd recommend it for you.
Thank you, Scott. I recommend you throw that book into the trash
can before you pollute this group with your NONSENSE. Read a
book in nonlinear regression in Statistics.
Read a book on Linear Regression Models in Statistics, and try to
understand WHY nobody computes the coefficient of variation as a
routine part of the computation and deem it necessary.
-- Reef Fish Bob.
Anon.
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158104672.5...@i42g2000cwa.googlegroups.com:
>
>
>>Scott Seidman wrote:
>>
>>>Scott Seidman <namdie...@mindspring.com> wrote in
>>>news:Xns983C61DA71333sc...@130.133.1.4:
>>>
>>>
>>>>IMO, if you publish an
>>>>estimate from a nonlinear regression, you're hiding something,
>>>>intentionally or nonintentionally.
>>>>
>>>
>>>Oops, I meant "if you publish an estimate from a nonlinear
>>>regression, WITHOUT PROVIDING INFO ON THE CV, you're hiding
>>>something, intentionally or nonintentionally.
>>
>>And where does THIS piece of theory/quackery come from?
>>
>>-- Reef Fish Bob.
>>
>>
>
>
> Which part would you call quackery-- the idea that the coefficient of
> variation can provide insight as to the precision of a parameter
> estimate, or that reporting a parameter estimate from an iterative
> algorithm for nonlinear least squares without reporting the CV does not
> provide a full picture?
>
> All I can say is that too many people blindly publish the results of a
> parameter estimation without having any idea whether they can confidently
> state that they even have the order of magnitude of the parameter
> precise. Perhaps I overstated my opinion, as standard error yields much
> the same info, yet I prefer the dimensionless aspect of the CV.
I had a similar reaction to Reef Fish's (but not quite so exteme). I
agree that some measure of uncertainty in a parameter should be given, I
think the problem is that it's not clear that the CV is always a good
statistic to use, so insisting on it is a bit OTT.
If the estimate and the standard error scale together, then it can make
sense to report it, but there are other cases where it simply doesn't.
For example, I was once asked to report the CV for a logistic
regression. After I'd picked myself up off the floor and stopped
laughing, I pointed out that (a) it would be negative for some
parameters, and (b) it would get larger (all else being equal) the
closer the estimated probability was to 0.5, which seemed rather
arbitrary. Something similar can happen for non-linear regression.
If your parameters are interpretable, then it's usually better to use
the scale on which you interpret them. The standard error on this scale
should then make more sense (imagine something like human height: we
know what 5cm means, more so than a CV of 0.025). The CV loses any
context, so it can be difficult to know what a large or small value
should be.
That, at least, is my take on matters.
Bob
--
Bob O'Hara
Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf H„llstr”min katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
st...@mimosa.csv.warwick.ac.uk
Scott Seidman <namdie...@mindspring.com> writes:
>...
>>> Oops, I meant "if you publish an estimate from a nonlinear
>>> regression, WITHOUT PROVIDING INFO ON THE CV, you're hiding
>>> something, intentionally or nonintentionally.
The CV makes most sense if the parameter (theta say) has to be
positive, but then the likelihood surface/posterior distribution
tends to be less awkward (and numerical methods work better)
if you reparametrise to log(theta). The SE of log(theta) is
dimensionless, and probably more meaningful than CV(theta).
>>
>> And where does THIS piece of theory/quackery come from?
>>
>> -- Reef Fish Bob.
>...
>All I can say is that too many people blindly publish the results of a
>parameter estimation without having any idea whether they can confidently
>state that they even have the order of magnitude of the parameter
>precise. Perhaps I overstated my opinion, as standard error yields much
>the same info, yet I prefer the dimensionless aspect of the CV. A google
>search of "coefficient of variation parameter estimation" yields 5+
>million hits, and adding "nonlinear" cuts it down to 2+ million, with 9k
>hits on google scholar, suggesting that I am not that far off the mark.
>In any case, CV% or SE each convey more information than a p-value alone.
>The p-value could be .000005, but some may want to know if the estimate
>of 500 could really be closer to 5e6.
>
>If you absolutely must have a reference, I'll refer you to Chapter 7,
>Interpretation of the Estimates, in Bard, Nonlinear Parameter Estimation,
>Academic Press, 1974.
>...
I found Bard disappointing, particularly concerning the reliability
of, and relationship between, parameter estimates. Not only do
parameter estimates from nonlinear regressions tend to be highly
correlated, the log-likelihood also tends to be highly non-quadratic,
so you need more than just estimates, correlations & standard errors
(or their equivalent). I recommend "Nonlinear Regression Analysis"
by Bates & Watts (1988) for details of the geometry of nonlinear models,
though if you're not prepared to assume independent normally
distributed random variation in the data, then the geometry's nastier.
--
J.E.H.Shaw [Ewart Shaw] st...@uk.ac.warwick TEL: +44 2476 523069
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
http://www.warwick.ac.uk/statsdept http://www.ewartshaw.co.uk
3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3 6 2
Scott Seidman
>
> How is the estimation of parameters different in nonlinear regression
> from linear regression, in terms of one require the CV and the other
> one
> doesn't?
While it is always proper to report on the quality of estimates, be the
regression linear or nonlinear, I believe added information in nonlinear
regression is somewhat more important, as sensitivity (change in error to
change in parameter value) to a parameter is relatively straightforward in
linear regression, but can be a nightmare, and extremely nonintuitive, in
nonlinear regression. Problems with huge CV can, among other things, serve
to highlight sensitivity problems and problems in experimental design. CV
is an relatively convenient tool that can help you understand your model.
Of course, if you want to continue to make believe that I never said that
the SE of the estimate provides much the same information, you're free to
do so.
Scott Seidman
news:4507B481...@SOD.OFF.Spammers.helsinki.fi:
> If your parameters are interpretable, then it's usually better to use
> the scale on which you interpret them. The standard error on this scale
> should then make more sense (imagine something like human height: we
> know what 5cm means, more so than a CV of 0.025). The CV loses any
> context, so it can be difficult to know what a large or small value
> should be.
Given the CV and the parameter value, you have all the info you need, and
you do as well if you have the SE and parameter value. I think we'd all
agree that its less than useful to have one without the other.
Without some prior knowledge of what a valid height is, however, the SE
makes very little sense, but if I told you that the CV% was 15%, you could
understand that without any prior knowledge, as with a useless CV% like
1000%. I think if parameters varied by orders of magnitude, a table with
CV% in it would be easier to understand than the same table with SE in it.
Obviously, in some cases the normalized SE will be more useful, and in
others the straight SE will be more useful.
For your height example above, wouldn't everyone agree that a CV of 0.025
indicates a fairly precise estimate, while a CV of 5 wouldn't? Even if the
estimate weren't provided?
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158120341....@h48g2000cwc.googlegroups.com:
>
> >
> > How is the estimation of parameters different in nonlinear regression
> > from linear regression, in terms of one require the CV and the other
> > one
> > doesn't?
>
>
> While it is always proper to report on the quality of estimates, be the
> regression linear or nonlinear, I believe added information in nonlinear
> regression is somewhat more important, as sensitivity (change in error to
> change in parameter value) to a parameter is relatively straightforward in
> linear regression, but can be a nightmare, and extremely nonintuitive, in
> nonlinear regression.
Just wanted to make 100% that you are talking through your HAT <not
to be confused with a beta-hat>. You have exactly ONE value of the
estimate for each parameter, and just how are you going to get a
coefficient of variation of 1 number?
> Problems with huge CV can, among other things, serve
> to highlight sensitivity problems and problems in experimental design. CV
> is an relatively convenient tool that can help you understand your model.
That's YOUR quackery.
>
> Of course, if you want to continue to make believe that I never said that
> the SE of the estimate provides much the same information, you're free to
> do so.
The SE has already incorporated ALL the information (under LS) of the
statistical reliability or variation of the estimate. What I said is
that you
don't even known that there is NO coefficient of variation for that
parameter
estimate, whether the parameter is in a linear OR nonlinear regression.
That showed the DEPTH of your ignorance and Quackery.
YOu're welcome to take ANY regression estimated parameter and show
us how you get a coefficient of variation of THE PARAMETER estimate.
-- Reef Fish Fish.
Reef Fish
Scott Seidman wrote:
> "Anon." <bob....@SOD.OFF.Spammers.helsinki.fi> wrote in
> news:4507B481...@SOD.OFF.Spammers.helsinki.fi:
>
> > If your parameters are interpretable, then it's usually better to use
> > the scale on which you interpret them. The standard error on this scale
> > should then make more sense (imagine something like human height: we
> > know what 5cm means, more so than a CV of 0.025). The CV loses any
> > context, so it can be difficult to know what a large or small value
> > should be.
>
> Given the CV and the parameter value, you have all the info you need, and
> you do as well if you have the SE and parameter value. I think we'd all
> agree that its less than useful to have one without the other.
CV of WHAT?
Give youself all the CVs (of the Y and all the X's). Show us HOW
those
will tell you ANYTHING about (and beyond) what the SE of the estimated
parameter will tell you.
Be explicit.
You can't. PERIOD. YOu are just Quacking louder and louder.
Take the hint from the First Law of Holes, "When you find yourself in
one,
STOP digging".
-- Reef Fish Bob.
Scott Seidman
> You have exactly ONE value of the
> estimate for each parameter, and just how are you going to get a
> coefficient of variation of 1 number?
>
Bob--
I'm more than willing to have a polite conversation if you are, but
apparently, you are not.
So, if you are willing to actually admit you don't know something, and
might even be willing to place yourself in the gutter long enough to
actually learn something from know-nothing me, the CV is calculated as
the square root of the diagonal element of the variance-covariance matrix
for the estimation calculated at Theta=Theta* (that is, the estimate of
the vector Theta) that corresponds to the parameter of interest, divided
by the estimate
The variance-covariance matrix is calculated from the Jacobian. Each
column of the Jacobian is the sensitivity of the function being minimized
with respect to a given parameter.
Thus, if I have n observations of output Y (or, more accurately, of error
E=Y-Y*), the first column of the Jacobian will have n elements, each one
being partialE/partialTheta1, where Theta1 is the first parameter.
So, you get your estimate Theta=Theta*, you calculate the Jacobian at
Theta*, and then you calculate the variance-covariance matrix from the
Jacobian, covar=(J^T J)^{-1}, which will be k x k, where k is the number
of elements in theta (i.e., the number of parameters).
The CV for parameter i will the the square root of the ith diagonal
element of the variance-covariance matrix divided by Theta_i*
The calc of the Jacobian can become what some consider a big deal. If
the system you're doing the identification on, for example, has no closed
form solution, and is a function of time (as many such problems are), and
you only have partial(E)/partial(t), you need to solve for d^2E/dtdtheta,
and numerically solve for dE/dtheta, and those expressions can get
nightmarish. Fortunately, many iterative solvers require the Jacobian,
so you have already done the work.
If you'd like to see if this works, why don't you give it a go? Take
y=Ae^(-t/tau)+b, where t is time and tau, A, and b are your parameters,
and add some random noise to it, and do the estimations. Simulate this,
going three time constants out in t, use your favorite iterative solver,
calculate the Jacobian at the estimate (there's an easy closed form, so
long as you remember calculus), then the variance-covariance matrix, and
then the CV. Try this for various magnitudes of noise, and then try
doing it when you only have data going a half time constant out (or maybe
a half time constant out). After you've done this, perhaps you'll see
that the CV makes it immediately apparent that the estimate of b suffers
for large noise when you have data going a half time constant out. Then,
try doing this when you only allow yourself data at time beginning at 2.5
time constants, and let yourself go out in time as far as you please.
The CV's will immediately show you that you have a very precise estimate
of b, but cruddy estimates of A and tau.
By the way, don't forget that you're minimizing E=y-yhat so the Jacobian
is actually dE/dtheta=-dyhat/dtheta. If you get this wrong, any
iterative solver that uses the Jacobian will take off the wrong way, and
might never converge. It probably doesn't make a difference for
calculation of the variance-covariance matrix, though.
I confess, my experience in nonlinear parameter estimation is largely
limited to dynamic systems such as these, and in such problems I've found
CV to be one of a few enormously important tools that help to interpret
estimates.
Anon.
> "Anon." <bob....@SOD.OFF.Spammers.helsinki.fi> wrote in
> news:4507B481...@SOD.OFF.Spammers.helsinki.fi:
>
>> If your parameters are interpretable, then it's usually better to use
>> the scale on which you interpret them. The standard error on this scale
>> should then make more sense (imagine something like human height: we
>> know what 5cm means, more so than a CV of 0.025). The CV loses any
>> context, so it can be difficult to know what a large or small value
>> should be.
>
> Given the CV and the parameter value, you have all the info you need, and
> you do as well if you have the SE and parameter value. I think we'd all
> agree that its less than useful to have one without the other.
>
> Without some prior knowledge of what a valid height is, however, the SE
> makes very little sense, but if I told you that the CV% was 15%, you could
> understand that without any prior knowledge, as with a useless CV% like
> 1000%.
I don't think that's necessarily useless. If you know that it is, then
you are already admitting some prior knowledge about the parameter
you're interested in: you're assuming that it should be (relatively)
large and positive. If you know nothing about the parameter, then I
don't see where you can get such an inference.
Bob
--
Bob O'Hara
Department of Mathematics and Statistics
P.O. Box 68 (Gustaf Hällströmin katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: www.jnr-eeb.org
Scott Seidman
news:NxXNg.11431$pZ3....@reader1.news.jippii.net:
>> Without some prior knowledge of what a valid height is, however, the
>> SE makes very little sense, but if I told you that the CV% was 15%,
>> you could understand that without any prior knowledge, as with a
>> useless CV% like 1000%.
>
> I don't think that's necessarily useless. If you know that it is,
> then you are already admitting some prior knowledge about the
> parameter you're interested in: you're assuming that it should be
> (relatively) large and positive. If you know nothing about the
> parameter, then I don't see where you can get such an inference.
>
> Bob
>
>
"Useless" is a poor term, granted, as you're always learning something.
Even if you expect a large positive estimate for a parameter, a CV of 1000%
pretty much means you can't even rely upon the order of magnitude of your
estimate, though, and I prefer that my estimates could at least get the
order of magnitude right. A situation like this points to problems with
the data, the experimental design, or your model. This could mean a number
of things, one of which is a large insensitivity to the parameter--maybe a
scaling problem, or the parameter simply doesn't belong in the model. It
might mean that you've overparametrized. It might mean that your data
matrix has a poor condition number, or that your model has too many
parameters, or a host of other things. In any case, a CV% of 1000% should
be a big red flag suggesting that careful interpretation is called for,
regardless of whether the estimate happens to be 0.5, 500, or 5,000,000.
One last point here is that parameter estimation has different connotation
than nonlinear regression. It's often much more than a "curve fit", and
you usually, if not always, know something about the parameters.
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158159058.9...@i42g2000cwa.googlegroups.com:
>
> > You have exactly ONE value of the
> > estimate for each parameter, and just how are you going to get a
> > coefficient of variation of 1 number?
> >
>
> Bob--
>
> I'm more than willing to have a polite conversation if you are, but
> apparently, you are not.
What's so impolite about the straightforward comment you cited?
>
> So, if you are willing to actually admit you don't know something, and
> might even be willing to place yourself in the gutter long enough to
> actually learn something from know-nothing me, the CV is calculated as
> the square root of the diagonal element of the variance-covariance matrix
> for the estimation calculated at Theta=Theta* (that is, the estimate of
> the vector Theta) that corresponds to the parameter of interest, divided
> by the estimate
I had lectured on SWEEP and how those are calculated, and that's the
way the calculations are done in SAS, eg. But the estimates of BETA
are during different steps of the SWEEP process, and the variance
covariance matrix is only in the result of X'X after the FIRST sweep of
the constant.
So, let's assume you know how to do this, even though your description
in the paragraph did not reflect that at alll!
The REST of your explanation, was nothing but your "mathematistry".
Above all, even after your Jacobian contortions (which NO statistician
and NO regression textbooks on Linear or Nonlinear models ever
suggested its usage or usefulness), you never explained in what way
that will tell you anymore than what the SE had NOT already captures.
>
> The variance-covariance matrix is calculated from the Jacobian. Each
> column of the Jacobian is the sensitivity of the function being minimized
> with respect to a given parameter.
The variance covariance is calculated from the appropriately normalized
matrix of Z'Z, where Z is (1, X, Y). The matrix is SWEEP on the
first pivotal element and you have the centered quantities of all the
NUMERATORS of the variance covariance matrix.
You did not even tell what your Jacobian matrix. The theory behind
Beaton's SWEEP operator (SWP) was explained by me last year in
some ofr the discussion about regression computation and related
regression issues.
Skip to END of Scott's mathematistry.
You have NOT indicated what GAIN you have in your Jacobian computation
over the standard regression methods and outputs. In particular, the
CVs will no more tell you anything about the degree and effect of
multicollinarity and the Statistical ACCURACY versus NUMERICAL
accuracy as discussed by Beaton, Rubin, and Barone in JASA.
>
> By the way, don't forget that you're minimizing E=y-yhat so the Jacobian
> is actually dE/dtheta=-dyhat/dtheta. If you get this wrong, any
> iterative solver that uses the Jacobian will take off the wrong way, and
> might never converge. It probably doesn't make a difference for
> calculation of the variance-covariance matrix, though.
>
> I confess, my experience in nonlinear parameter estimation is largely
> limited to dynamic systems such as these, and in such problems I've found
> CV to be one of a few enormously important tools that help to interpret
> estimates.
Never mind the nonlinear regression problem. You have NOT shown that
you understood anything about LINEAR regression parameter estimation,
of the assessment of the stability or reliability of the estimated
coefficients.
-- Reef Fish Bob.
Scott Seidman
> What's so impolite about the straightforward comment you cited?
There is nothing impolite in my citation, as I removed the offensive
material, leaving the interested to turn toward search engines to recover
it. Consider it the courtesy of not repeating text that should embarass a
person that knows how to conduct polite public discourse. When I see a
person who speaks largely in challenges and invectives, I often extend the
same benefit of the doubt that one would tend to extend to the mentally
challenged. Indeed, when I see evidence of an inability to supress the
urge to utter every impolite thought that enters one's head, especially in
a person of advancing years, I tend to attribute it to stroke (I'm quite
serious about this-- this is a common syndrome of aging). In one of simply
middle age, I often chalk it up to the all-too-common demon, John
Barleycorn. Whichever your particular ill, I truly hope that your friends,
family, and colleagues choose to remember you as you were, and not as you
are.
> You have NOT indicated what GAIN you have in your Jacobian computation
> over the standard regression methods and outputs.
You're blathering, Bob. I am not talking about applying a gain to the
Jacobian to calculate the next estimate (assuming that's what you're
getting at, as JACOBIAN CALCULATIONS DON'T HAVE A GAIN). Many estimation
algorithms, of course, do this, and I leave that to the algorithms-- though
often you can provide some sort of multiplier for the first value for the
algorithm to use, which sometimes helps jump over false minima, or can
speed up convergence. I merely said that in many cases, you've already
computed the Jacobian for the estimation algorithm, so you don't need to do
it special for CV calculation.
If you can't decipher my feeble attempts at plain text representation of
the equations, the Jacobian is plainly defined at
http://mathworld.wolfram.com/Jacobian.html. Look Ma, no gain.
All the CV is is a standard error normalized by the estimate. If you
provide the SE and the estimate, you've essentially provided the CV, and
thus provided some information on precision. If you've provided the
estimate and a p-value on that estimate, you're not providing as much
information, and the info you've left out robs your reader/client/whatever
of a tool that could help provide an assessment of the quality of your
estimate. That's all I've said, or at least what I've been trying to say.
There it is in one paragraph. If you would like to criticize that, a
polite individual would address those points of disagreement, and state
what's wrong with them.
I've run the examples I cited before in Matlab, fitting
5*exp(-t/2.5)+1+noise to the single decaying exponential with an offset
X(1)=A=5
X(2)=offset=1
X(3)=time constant=2.5
[3 1 1] is my initial guess for X
decayeh is an anonymous function E=y-yhat
lsqnonlin, by default, uses an interior-reflective Newton method, but this
makes little difference. I opted not to provide the Jacobian for the
minimization, but calculated it post-hoc. I didn't express CV's as a
percent. Feel free to multiply by 100 if you want.
>> decayeh= @(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3))...
+ x(2));
decayeh
t= [0:1000]/100;
noise=.1*randn(size(t));
x1=lsqnonlin(decayeh,[3 1 1],[],[],[],t,noise)
dydA=-exp(-t/x1(1));
dydb=ones(size(t));
dydtau=(x1(1)/x1(3)/x1(3).*t.*exp(-t/x1(3)));
jac=[ dydA' dydb' dydtau'];
varcov=inv(jac'*jac)
cv_A=sqrt(varcov(1,1))/x1(1)
cv_b=sqrt(varcov(2,2))/x1(2)
cv_tau=sqrt(varcov(3,3))/x1(3)
decayeh =
@(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3)) + x(2))
Optimization terminated: relative function value
changing by less than OPTIONS.TolFun.
x1 =
5.0133 0.9948 2.5099
varcov =
0.0213 0.0040 0.0115
0.0040 0.0069 -0.0092
0.0115 -0.0092 0.0311
cv_A =
0.0291
cv_b =
0.0835
cv_tau =
0.0703
If I increase the noise to var=1
x1 =
5.0390 1.0040 2.5165
varcov =
0.0213 0.0041 0.0114
0.0041 0.0070 -0.0092
0.0114 -0.0092 0.0310
cv_A =
0.0290
cv_b =
0.0831
cv_tau =
0.0700
If I cut off the first 2 seconds of data, and var(noise)=0.1
decayeh =
@(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3)) + x(2))
Optimization terminated: relative function value
changing by less than OPTIONS.TolFun.
x1 =
5.0522 1.0089 2.4611
varcov =
1.2541 0.0160 0.9003
0.0160 0.0075 -0.0018
0.9003 -0.0018 0.6756
cv_A =
0.2217
cv_b =
0.0856
cv_tau =
0.3340
Thus, losing precision on the time constant and gain, but we're still
relatively OK for the offset
If I just include the first 4 seconds of data, var(noise)=0.1:
decayeh =
@(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3)) + x(2))
Optimization terminated: relative function value
changing by less than OPTIONS.TolFun.
x1 =
4.9850 1.0304 2.4603
varcov =
0.3034 0.3347 -0.2095
0.3347 0.3971 -0.2732
-0.2095 -0.2732 0.2146
cv_A =
0.1105
cv_b =
0.6116
cv_tau =
0.1883
So, we've lost a bit of precision on A and tau, but the offset precision is
shot to shit.
Pretty much behaves just like it should, huh?
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158174430.7...@i42g2000cwa.googlegroups.com:
>
>
> > What's so impolite about the straightforward comment you cited?
>
> There is nothing impolite in my citation, as I removed the offensive
> material, leaving the interested to turn toward search engines to recover
> it.
In that case, it made your comment at best a waste of bandwidth, and
in reality a gratuitous comment without substantiation.
Cut the rhetoric and get on with the statitsical SUBSTANCE.
>
> > You have NOT indicated what GAIN you have in your Jacobian computation
> > over the standard regression methods and outputs.
>
>
> You're blathering, Bob.
Is that what you call POLITE speech, right after your hypocritical
lecture?
> I am not talking about applying a gain to the
> Jacobian to calculate the next estimate (assuming that's what you're
> getting at, as JACOBIAN CALCULATIONS DON'T HAVE A GAIN).
I meant your END results after your jacobian computation!! The end
result
of your CVs.
> Many estimation
> algorithms, of course, do this, and I leave that to the algorithms-- though
> often you can provide some sort of multiplier for the first value for the
> algorithm to use, which sometimes helps jump over false minima, or can
> speed up convergence. I merely said that in many cases, you've already
> computed the Jacobian for the estimation algorithm, so you don't need to do
> it special for CV calculation.
They WHY were you suggesting the computation to the OP, and you argued
that in ordinary Linear Regression Models that your CVs are equally
useful?
> If you can't decipher my feeble attempts at plain text representation of
> the equations, the Jacobian is plainly defined at
> http://mathworld.wolfram.com/Jacobian.html. Look Ma, no gain.
I already knew there is no gain. That was my point about YOUR post.
I gave you ALL the computational and necesseary theoretical details
as well as the references about multicolllinarity and the paper of
Beaton, Barone, and Rubin ... ALL pointing to the fact that there is
NOTHING to your suggestion (but Quackery) in your suggestion and
further obfuscation of the use or advantage of calculating the CVs
as ADDITION information over the conventional SEs and other
analytic measures of both the NUMERICAL and STATISTICAL
stability of the Linear Models Regression situation.
In the Nonlinear Regression context, it's inverse of the Fisher
Information matrix, which is a kind of Jacobian to yield information
analoguous to the multicollinearity condition, except the
interdependence is no long of the LINEAR type.
All of this is the STANDARD material in the graduate course I've
taught many times.
Your next paragraph is just more non-technical rhetoric and
obfuscation of the Richard Ulrich type.
>
> All the CV is is a standard error normalized by the estimate. If you
> provide the SE and the estimate, you've essentially provided the CV, and
> thus provided some information on precision. If you've provided the
> estimate and a p-value on that estimate, you're not providing as much
> information, and the info you've left out robs your reader/client/whatever
> of a tool that could help provide an assessment of the quality of your
> estimate. That's all I've said, or at least what I've been trying to say.
> There it is in one paragraph. If you would like to criticize that, a
> polite individual would address those points of disagreement, and state
> what's wrong with them.
I had already pointed out the LAST time, and in the above THIS time,
what's wrong with your CV approach.
>
>
> I've run the examples I cited before in Matlab, fitting
> 5*exp(-t/2.5)+1+noise to the single decaying exponential with an offset
ALL your Excel computation is the classic "Garbage IN, Garbage OUT"..
It's the mathematical OBFUSCATION the analogue of your verbal
obfuscation.
First of all, your example does NOT even have an unknown parameter to
be
FITTED! Where is the PARAMETER? Are you just another Afonso?
If your model is a single parameter exponential decaying model, then it
is
a well-known case of a nonlinear model that CAN be linearized. See
all the LInear Models books in statistics that uses THAT example as the
simplest one to illustrate the idea of a non-intrinsic nonlinearity.
Your NUMERICAL GARBAGE is kept just to preserve that that they
are ALL garbage.
================= Begin Scott Seidman garbage
============== End of Scott Seidman garbage ========
>
>
> --
> Scott
> Reverse name to reply
If you want to demonstrate the VALUE (that is nonzero) in your CV
approach
in a NONLINEAR regression problem that is intrisically nonlinear, take
some
REAL data and fit it to the Multicompartment model of the SUM of two
expoential decay model, with FOUR unknown parameters (I assume you
know how to write that model or can find out from the literature that
is one
of the most common model that presents all kinds of instability
problems
in the ESTIMATED parameters).
If you can take a set of data in the literature that had been analyzed
the
traditional way, so much the better. THEN, try to make you case that
by redoing the same problem YOUR way, and point out what advantage
it has.
Of course you CAN'T. I am VERY familiar with that problem and the
difficult of estimation of the parameters intrisic in THAT particular
model.
That was one of my "consulting projects" at Yale Statistics Department
(when I was a grad student) helping faculty in OTHER departments with
their valid statistical problems -- under the supervision of a faculty
member -- as part of the CURRICULUM in the Applied Statistics
Program -- of spending a FULL HALF YEAR doing nothing but
consulting (under supervision). In my case, the supervisor was
L.J.Savage who knows that problem as well as anyone else in the
world. I've encountered that nonlinear problem and many other
nonlinear problems in my applied work both in teaching and research.
Scott, what you're doing here is just KEEP DIGGING a deeper
and deeper Hole after you found yourself in one.
Your excel example is the kind that is is not even beyond a junior
undergrad level in statistics, to use to bluff you way out -- that
MIGHT have worked (in fact, I suspect it would have worked in this
group -- had there not been someone who could see throught ALL
your Quackery within a nanosecond.
The ABSENCE of some "watch dog" in this group from 1994 to
2005 is the reason Richard Ulrich had perpetrated so many
Quackery and malpractice and NOT been called to make himself
accountable until I came into this group in 2005.
Scott, I've pointed out your errors BEFORE, on much simpler models
and standard material on regression. You ABSENCE of knowledge
about NONlinear regression and your Quackery of advicing some
innocent victim about your MISUSE of CV is NOT going to get away
no matter HOW your throw your ink (as an octopus) to cover your
misguide track.
First Law of Holes: "If you find yourself in a Hole, STOP DIGGING."
You're welcome to come back with an example, on the double exponential
decay model, with real DATA, to demonstrate that your CV idea is NOT
quackery.
Failing to do that, your FREE tuition will be withdrawn -- because you
have already demonstrated beyond a reasonable doubt, that your
knowledge about nonlinear regression (or even Linear Regression) is
nothing beyond your ability to stuff some numbers into Excel or some
other statistical package or program, and exhibit that YOU are one of
those who had mastered the technique of "GARBAGE IN, GARBAGE OUT".
-- Reef Fish Bob.
Anon.
> "Anon." <bob....@NOSPAMhelsinki.fi> wrote in
> news:NxXNg.11431$pZ3....@reader1.news.jippii.net:
>
>>> Without some prior knowledge of what a valid height is, however, the
>>> SE makes very little sense, but if I told you that the CV% was 15%,
>>> you could understand that without any prior knowledge, as with a
>>> useless CV% like 1000%.
>> I don't think that's necessarily useless. If you know that it is,
>> then you are already admitting some prior knowledge about the
>> parameter you're interested in: you're assuming that it should be
>> (relatively) large and positive. If you know nothing about the
>> parameter, then I don't see where you can get such an inference.
>>
>> Bob
>>
>>
>
> "Useless" is a poor term, granted, as you're always learning something.
> Even if you expect a large positive estimate for a parameter, a CV of 1000%
> pretty much means you can't even rely upon the order of magnitude of your
> estimate, though, and I prefer that my estimates could at least get the
> order of magnitude right.
The order of magnitude may or may not be the problem: I often don't care
if my estimates of variance components vary over several orders of
magnitude, as long as they're small. A difference between 0.001 and 0.1
is nothing if the variance in the data is 1000 (say). Again, it depends
on the context, and using the CV tends to remove the context.
A situation like this points to problems with
> the data, the experimental design, or your model. This could mean a number
> of things, one of which is a large insensitivity to the parameter--maybe a
> scaling problem, or the parameter simply doesn't belong in the model. It
> might mean that you've overparametrized. It might mean that your data
> matrix has a poor condition number, or that your model has too many
> parameters, or a host of other things. In any case, a CV% of 1000% should
> be a big red flag suggesting that careful interpretation is called for,
> regardless of whether the estimate happens to be 0.5, 500, or 5,000,000.
>
> One last point here is that parameter estimation has different connotation
> than nonlinear regression. It's often much more than a "curve fit", and
> you usually, if not always, know something about the parameters.
>
Indeed. For me that's a good reason to stick to standard errors:
they're on the scale of the parameters, i.e. the scale that you know
something about.
Scott Seidman
> ALL your Excel computation is the classic "Garbage IN, Garbage OUT"..
One would think that someone as obviously gifted as yourself would
recognize Matlab.
>
> It's the mathematical OBFUSCATION the analogue of your verbal
> obfuscation.
>
> First of all, your example does NOT even have an unknown parameter to
> be
> FITTED! Where is the PARAMETER? Are you just another Afonso?
>
For god's sake, I must be speaking with a drooling idiot. Perhaps your
meds are befogging your mind.
The function is
decayeh= @(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3))+x(2));
The first part is (5*exp(-t/2.5)+1+noise). Obviously, this is the
simulated data, gain 5, time constant 2.5, offset 1, and a noise. I
could have just read this in from a file, but it was easier to change the
noise term and include different regions of time if they were passed as
paremeters. The second part is (x(1)*exp(-t/x(3))+x(2)), and is
subtracted from the first part to yield an error vector. Matlab, and
most other minimization algorithms, will sum-square this and minimize the
result. You start with a guess at the three parameters, and this guess
is adjusted by the algorithm. Thus x(1), x(2), and x(3) are all being
adjusted to yield a minimize SSE.
> If your model is a single parameter exponential decaying model, then it
> is
> a well-known case of a nonlinear model that CAN be linearized.
> See all the LInear Models books in statistics that uses THAT example as
> the simplest one to illustrate the idea of a non-intrinsic
> nonlinearity.
Yes, books often use a single decaying exponential as an example that can
be linearized, but that's highly simplified, and often not as practical
as solving it in a nonlinear fashion. For one thing, what do you do
with the data points that fall below zero due to noise present? Do you
just toss them out? What if the offset is negative? How do you
linearize this with the offset term anyway? Do you have some sort of
secret multiplication rule for log(a+b) that you're hiding from the rest
of us? The residuals, in this case, and in most real cases that I would
be interested in, are normally distributed and non-varying over time
before you take the log. What happens to the errors after you take the
log? How would you patch that up?
>
> Your NUMERICAL GARBAGE is kept just to preserve that that they
> are ALL garbage.
> ================= Begin Scott Seidman garbage
>
> You're welcome to come back with an example, on the double exponential
> decay model, with real DATA, to demonstrate that your CV idea is NOT
> quackery.
As you are welcome to show me a better analysis for my simlulated data
set. Two time constants doesn't intimidate me. As a matter of fact,
the exponential decay problem (no matter how many exponents) is extremely
simple, as its a closed form solution for a step response of a system.
Things get a tad more complex when the input is not a step, but rather
arbitrary. That doesn't intimidate me either.
I have no such data set available, but if you post one, I'd be happy to
go at it, if you promise you'll show me a more valid analysis. Maybe we
could agree on a simulated data set in advance. Would you like to go for
6*exp(-t/4) - 15*exp(-t/8) - 9. Ooops, thats five parameters!! Shit!!!!
Well, I went ahead and said it, so let's go do it. Let's have a time
axis at 100Hz, let's have it go out to four times the slowest time
constant, and let's have normal random noise with variance=0.2.
decayeh= @(x ,t, noise) (6*exp(-t/4) - 15*exp(-t/8) - 9 +noise)-(x(1)*exp
(-t/x(2))+ x(3)*exp(-t/x(4)) + x(5));
decayeh
t= [0:3200]/100;
noise=.2*randn(size(t));
options=optimset;
options.MaxFunEvals=10^10;
options.MaxIter=10^10;
options.LargeScale='off';
x1=lsqnonlin(decayeh,[10 3 -10 1 -2],[],[],options,t,noise)
dydx1=-exp(-t/x1(1));
dydx2=(x1(1)/x1(2)/x1(2).*t.*exp(-t/x1(2)));
dydx3=-exp(-t/x1(4));
dydx4=(x1(3)/x1(4)/x1(4).*t.*exp(-t/x1(5)));
dydx5=ones(size(t));
jac=[ dydx1' dydx2' dydx3' dydx4' dydx5'];
varcov=inv(jac'*jac)
for k=1:5
cv{k}=sqrt(varcov(k,k))/x1(k);
end
cv
OUTPUT:
decayeh =
@(x ,t, noise) (6*exp(-t/4) - 15*exp(-t/8) - 9 +noise)-(x(1)*exp(-t/x
(2))+ x(3)*exp(-t/x(4)) + x(5))
Optimization terminated: directional derivative along
search direction less than TolFun and infinity-norm of
gradient less than 10*(TolFun+TolX).
x1 =
5.7788 3.9585 -14.8032 8.0241 -8.9983
varcov =
3.8391 -0.7676 -4.1995 -0.0011 -0.2606
-0.7676 0.1818 0.8521 0.0002 0.0489
-4.1995 0.8521 4.6068 0.0012 0.2864
-0.0011 0.0002 0.0012 0.0000 0.0001
-0.2606 0.0489 0.2864 0.0001 0.0196
cv =
[0.3391] [0.1077] [-0.1450] [8.1352e-005] [-0.0156]
The SSE for this solution is 129.96
Interpretation: Doing much better estimating the second exponential than
the first, but not doing terribly on the first, either.
My initial guess that I fed the algorithm was [10 3 -10 1 -2]. If I
were doing this in real life, I'd likely start from a dozen or so
different locations in 5-space (one dimension for each parameter), and
look for my minimum SSE, and go with that solution.
In fact, if I were doing this in real life, I'd feed the algorithm the
Jacobian calculated at the current estimate, but that would take me a tad
longer, so I just embraced my faith and jumped in. If I didn't force the
algorithm to estimate the Jac, it would probably do a tad better.
Scott Seidman
> In fact, if I were doing this in real life, I'd feed the algorithm the
> Jacobian calculated at the current estimate, but that would take me a
> tad longer, so I just embraced my faith and jumped in. If I didn't
> force the algorithm to estimate the Jac, it would probably do a tad
> better.
>
By the by, Bob-- It wouldn't take my any longer to do this analysis on any
data set you provide, so long as I didn't have to type the f'er in by hand.
If you send me a data set, though, I would expect to see your thorough
analysis posted.
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158199700.9...@h48g2000cwc.googlegroups.com:
>
> > ALL your Excel computation is the classic "Garbage IN, Garbage OUT"..
>
> One would think that someone as obviously gifted as yourself would
> recognize Matlab.
No. I don't use Matlib OR Excel. I actually just quickly scan some
NUMBERS
you produced and knew it was Garbage.
>
> >
> > It's the mathematical OBFUSCATION the analogue of your verbal
> > obfuscation.
> >
> > First of all, your example does NOT even have an unknown parameter to
> > be
> > FITTED! Where is the PARAMETER? Are you just another Afonso?
> >
>
> For god's sake, I must be speaking with a drooling idiot. Perhaps your
> meds are befogging your mind.
LOL!! The hypocrite who kept harping about POLITE speech.
>
> The function is
> decayeh= @(x ,t, noise) (5*exp(-t/2.5)+1+noise)-(x(1)*exp(-t/x(3))+x(2));
>
> The first part is (5*exp(-t/2.5)+1+noise).
This was all that you showed! That was why I made the Afonso comment.
And I asked again -- where is your unknown parameter?
> Obviously, this is the
> simulated data, gain 5, time constant 2.5, offset 1, and a noise. I
I recognized the NOISE -- from YOU.
The point is, whatever you did, you explained it so badly that all was
left
was your GARBAGE NOISE, and you never showed whatever you did
gained anything over the standard approach WITHOUT the garbage CV
stuff.
I'll see if you did anything with the TRUELY nonlinear problem of the
SUM
of two exponential decay model as I asked.
The rest of your post added nothing to what you had NOT explained.
I'll
answer your impertinent questions though.
> > If your model is a single parameter exponential decaying model, then it
> > is
> > a well-known case of a nonlinear model that CAN be linearized.
> > See all the LInear Models books in statistics that uses THAT example as
> > the simplest one to illustrate the idea of a non-intrinsic
> > nonlinearity.
>
> Yes, books often use a single decaying exponential as an example that can
> be linearized, but that's highly simplified, and often not as practical
> as solving it in a nonlinear fashion. For one thing, what do you do
> with the data points that fall below zero due to noise present? Do you
> just toss them out? What if the offset is negative? How do you
> linearize this with the offset term anyway? Do you have some sort of
> secret multiplication rule for log(a+b) that you're hiding from the rest
> of us?
If you had WRITTEN out your model and assumptions, then each of thsoe
can be explained separately. THAT's why the exponential decay model is
such a standard example to illustrate the concept that the model can be
LINEARIZED.
You are so tied to the apron string of Matlib that you cannot even
STATE
your model in a coherent way, or what assumptions you had made in your
model.
That's just PART of yuour garbage.
> > Your NUMERICAL GARBAGE is kept just to preserve that that they
> > are ALL garbage.
> > ================= Begin Scott Seidman garbage
> >
>
>
> > You're welcome to come back with an example, on the double exponential
> > decay model, with real DATA, to demonstrate that your CV idea is NOT
> > quackery.
> As you are welcome to show me a better analysis for my simlulated data
> set.
The burden of proof is on YOU to show what gain you had for your CV.
You didn't show your simulated data and even if you did, I wouldn't
waste
my time on analyzing what any of my beginning grad students could do in
their sleep.
> Two time constants doesn't intimidate me.
What two time constants?
> As a matter of fact,
> the exponential decay problem (no matter how many exponents) is extremely
> simple, as its a closed form solution for a step response of a system.
> Things get a tad more complex when the input is not a step, but rather
> arbitrary. That doesn't intimidate me either.
That showed you didn't even KNOW what the multicompartment model of
the SUM of two exponential decay IS!
> I have no such data set available, but if you post one, I'd be happy to
> go at it, if you promise you'll show me a more valid analysis. Maybe we
> could agree on a simulated data set in advance. Would you like to go for
> 6*exp(-t/4) - 15*exp(-t/8) - 9. Ooops, thats five parameters!!
There are NO UNKNOWN parameters there, Afonso!
You are so addicted to and so dependent on your GARBAGE producing
machine that you can't even STATE a model coherently.
And if you so knowledgeable about nonlinear estimation, and you CAN'T
find an example of it in the literature using standard method of
analysis
(that is, WITHOUT ANY use of mention of your CV), that itself is
sufficient
as proof that whatever you did was pure Quackery.
> Shit!!!!
> Well, I went ahead and said it, so let's go do it.
The PC-speech Hypocrite at it again! You are looking more and more
like Afonso every time you opened your mouth. You are only missing
the
posting of his F word in the subject yet.
You were not TRAINED or EDUCATED in Statistics (I had looked up your
academic back and CURRENT employment). The Dean of the school in
which you were recently employed introduced four researchers in YOUR
non-statistical discipline, and the mention of Scott Seidman took me
several readings to FIND, sort of like lost in a footnote and carry
every
respect the polite version of NOT calling you a research assistant or
research associate like Richard Ulrich used to be in a Psychiatric
Departmemnt.
Go learn some STATISTICS, from Statisticians, or at least from
Statistical
Textbooks on the subject. Your CV stuff is nothing but QUACKERY not
sound anywhere in the statistical literature.
If it WERE, I owuld have found in in the literature when I was working
on
that multicompartment model as a graduate consultant under Jimmiie
Savage,
and HE would have mentinoed it.
As promised, your FREE tuition has been withdrawn.
Go ahead and post your favorite four-letter words, just like Afonso,
and
continue to make UNKNOWN paracters and KNOWN constants
indistinguiahable
in your statement of any problem.
Unmistaken signs of QUACKERY!
-- Reef Fish Bob.
Scott Seidman
>> For god's sake, I must be speaking with a drooling idiot. Perhaps your
>> meds are befogging your mind.
>
> LOL!! The hypocrite who kept harping about POLITE speech.
There is a big "Do unto others" thing going on.
Scott Seidman
> This was all that you showed! That was why I made the Afonso comment.
> And I asked again -- where is your unknown parameter?
>
>
Let me try one more time.
Would it help if I once again showed you that the term being minimized for
the one exponential case is the sum squared of
RESIDUALS= (SIMULATED DATA)- (A*e^(-t/tau) + offset) ?
The THREE parameters are A,tau, and offset.
I simulated data as 5*e^(-t/2.5) + 1 + noise;
The situation is similar for the two exponential, five parameter model:
yhat= A*e^(-t/tau1) + B*e^(-t/tau2) + C, where t=time, and the parameters
are A,B,C,tau1 and tau2. Perhaps we are not speaking the same language when
you say "multicompartment model of the SUM of two exponential decay", but
this looks an awful lot like a two-exponential decay to an offset to me.
If I've misunderstood, I beg your indulgance and clarification.
I included the full definition of my simulated data:
y=6*exp(-t/4) - 15*exp(-t/8) - 9 +noise, where noise is from the random
normal distribution, variance=0.2 ( noise=0.2*randn(size(t)); ). Time t
goes from 0 to 32 seconds (i.e., 4x the largest time constant in the
simulation) at 100 Hz. Are we on the same page now? Error, of course, is
y-yhat. You could reconstruct this simulated data set in Excel, Basic,
Fortran, Matlab, or an abacus.
Generally, when looking at an exponential in time, the divisor of time in
the exponent (tau1 or tau2 in this case) is known as a TIME CONSTANT--I
won't ridicule your lack of understanding of my use of the term, as we come
from two different backgrounds. Hence, this sum of two exponentials is a
two time constant model. If we replace t with a distance, then the divisor
is a "length" or "space" constant.
In any case, you specifically challenged me to show the application of this
analysis for a double exponential four parameter situation. I did it for
five parameters. I'd do it for more, but often such analysis shows that
the model is too complex for the modeller's good and adds little to
understanding, and I wouldn't want to take it on without providing the
Jacobian to the algorithm, anyway. I have no real data at hand that is
amenable to this model, but I'd invite you to provide data, or provide any
given parameters to simulate this data, even if the model doesn't quite
match the simulation. I'll do it. Rest assured, by the way, that the
analysis here included a thorough graphical examination of residuals and
sensitivities that is not so easy to pass along in plain text.
So, I answered your challenge in spades, and offered you the opportunity to
show what was wrong with this analysis, and to present your own better
analysis. Instead, what I get back is "I don't understand what your
parameters are!", "What time constant?", along with a questioning of
credentials that I've never claimed to have. I re-extend my invitation for
a parallel analysis on your part that illuminates the nature of the
parameter estimates any better than a report on the values of the
estimates, the variance/covariance matrix, and the CV, along, of course,
with a graphical analysis of the function, residuals, and sensitivity to
each parameter as a function of time. What more would you like? A
calculation of p-value and conf interval from the SE? How indeed would you
improve upon this analysis for problems of this type? I'd welcome serious
input from any particpant. I can see the point of some that it might not
be appropriate to normalize the SE by the estimate--I'll moot that by
suggesting that the SE is provided as the square root of the diagonal of
the variance/covariance matrix. Anything else??
Bob, you have the models I used, as well as the parameters of the simulated
data I used. You have every bit of my code, which you can implement in any
platform you wish.
Of course, what I expect back is exactly what you give back to everybody.
Invective, vitriol, assertions that I don't know what I'm talking about,
and everything else that doesn't look like a direct analysis of the problem
at hand. Show me I'm wrong, Bob. What more would you like to see on a
first pass through this data? Be quite specific.
Perhaps you'd enjoy seeing a dynamic solution to this, where there is not a
nice closed form solution.
Maybe the single time-constant case, where:
dy(t)/dt= A* dx(t)/dt - y(t)/tau, where x(t) is perhaps something nastier
than a unit step, such as a triangle wave. If x(t) were a simple unit
step, the closed form is a single decaying exponential, with no offset.
Reef Fish
That's what *I* call "quid pro quo" about what you and others called
impolite speech. My speech may be HARSH and strictly to the point
and not beat around the bush, but I never use the kind of VULGARITY
you and Afonso used.
What YOU did, repeatedly were gratuitous VULGAR speech, like your
"shit" and Afonso's "fuck".
Besides, I don't make it a point, like YOU did, about my speech, when
there was nothing impolite about it, and then turn around and,
hypocritically
made your own anti-PC speech over and over against.
That's what make YOU a Hypocrite beside one who is vacuous in his
Statistical knowledge.
-- Reef Fish Bob.
Scott Seidman
Try not to fall off your high horse, Bob. You'll hurt yourself. You might
not personally enjoy the use of profanity, but you seem to make your usenet
living spouting invective and derogation. You might call yourself "harsh
and strictly to the point", but others look upon the behavior as impolite,
overbearing, and gratuitously harsh, for the purpose, whether you
acknowledge it or not, to keep a rather large ego inflated, and just plain
mean. To top it off, the last few contributions of yours have not been
"strictly to the point", but you've opted to hide behind claims of
misunderstanding that are likely patently false, unless I've assigned you a
level of sophistication associated with your computational background that
you do not deserve. Neither possibility in the solution set is
particularly flattering, the former smacking of cowardice (like any other
bully), and the latter simply puts you in a discussion over your head. If
I had to vote, I'd place you in the former, but maybe the latter is true.
Just count up the number of posts on the stats groups you participate in,
and tot up the percentage that involve you in an argument. Nearly by
definition, this makes you what people with some decades of usenet
experience under their belts would call "a kook".
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158259024.7...@p79g2000cwp.googlegroups.com:
>
> >
> > Scott Seidman wrote:
> >> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> >> news:1158246531.2...@h48g2000cwc.googlegroups.com:
> >>
> >> >> For god's sake, I must be speaking with a drooling idiot. Perhaps
> >> >> your meds are befogging your mind.
> >> >
> >> > LOL!! The hypocrite who kept harping about POLITE speech.
> >>
> >> There is a big "Do unto others" thing going on.
> >
> > That's what *I* call "quid pro quo" about what you and others called
> > impolite speech. My speech may be HARSH and strictly to the point
> > and not beat around the bush, but I never use the kind of VULGARITY
> > you and Afonso used.
> >
> > What YOU did, repeatedly were gratuitous VULGAR speech, like your
> > "shit" and Afonso's "fuck".
> >
> > Besides, I don't make it a point, like YOU did, about my speech, when
> > there was nothing impolite about it, and then turn around and,
> > hypocritically
> > made your own anti-PC speech over and over against.
> >
> > That's what make YOU a Hypocrite beside one who is vacuous in his
> > Statistical knowledge.
> >
> > -- Reef Fish Bob.
> >
>
> Try not to fall off your high horse, Bob. You'll hurt yourself.
Scott, the substantive subject of nonlinear regression estimation is
OVER.
You failed to produce any evidence for your QUACKERY of using CV
over the conventional STATISTICAL methods of dealing with the problem.
YOu did not even know HOW to specifify a MODEL (linear OR nonlinear)
that has PARAMETERS to be estimated -- in a topic about the estiamtion
of parameters!
That's how deficient you are in your Statistical Education, which is
virtually NONE in your resume or your recent employment statement
by the Dean who employed you.
You are completely unfamiliar with the SUM of exponential decay model,
the one with only ONE variable t, but is the sum of two different
models
of decay rates.
You failed to name ONE single paper in the STATISTICAL literature that
supports your quackery.
In short, all you have done is to have performed your intellectual
striptease in front of a statistical audience, in viloating the First
Law
of Holes: When you find yourself in a Hole, STOP digging!
You continued ad hominem digging will not add ANY credibility ot
yourself or the justification of your quackery in the problem of
nonlinear regression parameter(s)-estimation.
This will be my FINAL Review of Scott Seidman on the "nonlinear
regression problem" thread and subject.
-- Reef Fish Bob.
Richard Ulrich
<Large_Nass...@yahoo.com> wrote:
>
> Scott Seidman wrote:
> > "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> > news:1158259024.7...@p79g2000cwp.googlegroups.com:
> >
> > >
> > > Scott Seidman wrote:
> > >> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
[snip]
>
> Scott, the substantive subject of nonlinear regression estimation is
> OVER.
>
> You failed to produce any evidence for your QUACKERY of using CV
> over the conventional STATISTICAL methods of dealing with the problem.
Quackery?
From Reef Fish Bob's historical use of the term, "quackery"
should indicate that Scott has presented an approach that
is conventional and well-accepted, that Bob disagrees with.
Even if this one is not totally conventional, I don't see much
downside to trying it.
I don't see any sin in using CV if someone finds it useful, for
his own problems. Maybe there are places that it is valuable.
It doesn't seem to cost much to keep it in mind if I ever have
similar problems.
Reef Fish Bob seems to have a lot of *strong* reactions.
[snip]
Reef Fish
Richard Ulrich wrote:
> On 14 Sep 2006 17:43:29 -0700, "Reef Fish"
> <Large_Nass...@yahoo.com> wrote:
>
> >
> > Scott Seidman wrote:
> > > "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> > > news:1158259024.7...@p79g2000cwp.googlegroups.com:
> > >
> > > >
> > > > Scott Seidman wrote:
> > > >> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> [snip]
> >
> > Scott, the substantive subject of nonlinear regression estimation is
> > OVER.
> >
> > You failed to produce any evidence for your QUACKERY of using CV
> > over the conventional STATISTICAL methods of dealing with the problem.
>
> Quackery?
>
> From Reef Fish Bob's historical use of the term, "quackery"
> should indicate that Scott has presented an approach that
> is conventional and well-accepted, that Bob disagrees with.
>
understood to be. For Statistical QUACKERY, I used it in my 1982 JASA
Review of "Correlation and Causation" because the author suggested that
correlation can be used to establish causation on OBSERVATIONAL data,
WITHOUT any controlled experiement.
Richard Ulrich argued the same, for weeks. That made Richard's
practice
a Quackery, and Richard Ulrich a Quack.
But I since learned that Karl Pearson had used the term on Science and
Statistics in 1938, long before I had used it, and he used it EXACTLY
the
way I used it, about science, medicine, and statisticians.
By "conventional", Richard Ulrich simply meant "conventional Quackery",
those kinds of Quackery that is most often perpetrated by Social
Scientists
WITHOUT any statistics education or understanding, such as Richard
Ulrich, in their MISUSE of statistics, just as Richard Ulrich used it
in
correlation, in regression, and in every respect of the regression
problem.
Scott Seidman is doing the SAME.
He suggested the use of CV in estimating the regression parameters,
in both Linear Models AND nonlinear regression.
WHen challenged to give REASONS why it's used, and what it gains,
he came up completely empty handed.
He didn't even knowo HOW to specify a MODEL with unknown parameters
when the subject is the estimation of parameters!
Once, debunked, the Scott Seidman went into his ad hominem attack,
just as Richard Ulrich did EVERY TIME after his Quackery had been
exposed -- the only difference is, Richard Ulrich had not descended to
Scott Seidman's level of using profanity, in the manner Afonso does.
That was why I had drawn the PARALLEL between Scott Seidman and
Richard Ulrich, in terms of LACK of statistical education; in terms of
their LACK of ability to argue what they did was NOT quackery.
>
> Even if this one is not totally conventional, I don't see much
> downside to trying it.
That's exactly what you said when you told an OP to check the variables
Xs in a multiple regression for normality (or that its okay, in order
to find
outliers,etc.) when there is absolutely NO requirement for the
normality
of X, nor are outliers necessarily bad or influential.
THAT was just another case of PURE Quackery on Richard Ulrich's part,
and he he doesn't see much downside to trying.
The DOWNSIDE is for social scientists to MUCK around, on practices
that have no theoretical NOR empirical basis, on account of their own
LACK of education about the subject.
That's exactly the Quackery that is common to Richard Ulrich and
Luis A. Afonso, now found a new recruit in Scott Seidman, for whom
Richard Ulrich felt his obligation to defend Scott's quackery as he
always
tried, but always unsuccessfully, to defend his own Quackery!
> I don't see any sin in using CV if someone finds it useful, for
> his own problems. Maybe there are places that it is valuable.
> It doesn't seem to cost much to keep it in mind if I ever have
> similar problems.
If someone finds it useful, he should be able to explain WHY it is
useful above the conventional estimation techinques in nonlinear
regression -- which Scott Seidman doesn't even KNOW!
>
> Reef Fish Bob seems to have a lot of *strong* reactions.
You bet! Against Statistical Quackery, especially of the kind Scott
Seidman is doing, in a topic sufficiently advanced to be beyond MOST
of the readership, and slinging his mathematical WORDS as if they
would give credency to his Quackery.
I happened to be ONE person in this group who sees through Scott's
fallacious arguments as transpently as through a clear glass! He was
running on EMPTY. He was doing his intellectual striptease on the
subject of nonlinear regression.
No amount of support by sci.stat.math's BIGGEST Quack, Richard
Ulrich, will change the Statistical SUBSTANCE of the subject, nor the
fact that Scott Seidman's failure to defend his own Quackery.
-- Reef Fish Bob.
P.S. Time to taka a little look at Grand Turk (that's NOT a Quack,
but the capitol of Turks and Caicos, in the Caribbean).
Scott Seidman
>
> He didn't even knowo HOW to specify a MODEL with unknown parameters
> when the subject is the estimation of parameters!
>
>
From an earlier post, Bob's verbally flatulated:
> This will be my FINAL Review of Scott Seidman on the "nonlinear
> regression problem" thread and subject.
Well, Bob, so much for your promise that the thread was over for you.
So, amongst your other endearing character (or lack thereof) traits, we
now find a lack of self control.
Without bothering to reply to the rest of your blather, as I feel no need
to defend myself from the likes of you (I limit my self defense for those
for whom I can scrounge up a modicum of respect, and oddly, you don't
fall into that set), I will say that the above statement clearly
demonstrates your complete lack of understanding of much of this
discussion. The equations I provided CLEARLY had simulated data, and
just as clearly had a parametrized model, the output of which was
subtracted from the simulated data to yield a vector of residuals.
Just because you fail to understand the representation of the model in
matlab, as you fail to understand what constitutes polite discourse, does
not mean that it is not valid.
The model is 100% characterized in unknown parameters represented as
x(1) through x(5) in the equations below.
decayeh= ...
@(x ,t, noise) (6*exp(-t/4) - 15*exp(-t/8) - 9 +noise)-...
(x(1)*exp(-t/x(2))+ x(3)*exp(-t/x(4)) + x(5));
t= [0:3200]/100;
noise=.2*randn(size(t))
The optimization is carried out using 100% standard Levenberg-Marquardt
methods by the commands below:
options=optimset;
options.MaxFunEvals=10^10;
options.MaxIter=10^10;
options.LargeScale='off';
x1=lsqnonlin(decayeh,[10 3 -10 1 -2],[],[],options,t,noise)
where x1, t, and noise are passed as parameters to the anonymous function
handle decayeh, and x1 is adjusted so as to minimize the sum squared
error.
The above has absolutely nothing to do with any of my assertions
regarding interpretation that you seem to take personal issue with --it
is an absolutely standard way to minimize the sum-squared of:
E = (simulated data)-(model output)
= (simulated data)- A*e^(-t/tau1) + B*e^(-t/tau2) + C,
thus the model is simple the sum of two decaying exponentials (remember--
that's the model you asked for) with an offset term (that I threw in
gratis).
The only valid criticism might be that the simulated data was chosen to
be of a form that the selected model would fit well. While I fully
acknowledge this, I dismiss that as a criticism coming from you, as I
offered you the opportunity to present your choice of simulated or real
data for analysis, and instead of actually participating, you opted to
rant, rave, and denigrate (as net kooks tend to do).
If you claim, once again to not understand this representation at this
late point, it is either a disingenous attempt to simply avoid discussion
and concession that (once again) you have blown a relatively small
disagreement entirely out of proportion (as net kooks tend to do) to
increase your inflated, yet fragile, sense of self-worth, or you are
simply slow. Perhaps your best course of action would be to take your
own counsel in your promise of future nonparticipation, and say nothing.
Hak mir nisht ken tshaynik!
Reef Fish
Scott Seidman wrote:
> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> news:1158329168.1...@p79g2000cwp.googlegroups.com:
>
> >
> > He didn't even knowo HOW to specify a MODEL with unknown parameters
> > when the subject is the estimation of parameters!
That was my comment to Richard Ulrich's post on your Quackery, wasn't
it?
> >
> >
>
> From an earlier post, Bob's verbally flatulated:
That's one talent I DON'T have. Only the hypocritical Mouth Dancers
like yourself are versed in it.
> > This will be my FINAL Review of Scott Seidman on the "nonlinear
> > regression problem" thread and subject.
And it was. Your FREE tuition has been withdrawn.
-- Reef Fish Bob.
Richard Ulrich
<Large_Nass...@yahoo.com> wrote:
>
> Richard Ulrich wrote:
> > On 14 Sep 2006 17:43:29 -0700, "Reef Fish"
> > <Large_Nass...@yahoo.com> wrote:
> >
> > >
> > > Scott Seidman wrote:
> > > > "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> > > > news:1158259024.7...@p79g2000cwp.googlegroups.com:
> > > >
> > > > >
> > > > > Scott Seidman wrote:
> > > > >> "Reef Fish" <Large_Nass...@yahoo.com> wrote in
> > [snip]
> > >
> > > Scott, the substantive subject of nonlinear regression estimation is
> > > OVER.
> > >
> > > You failed to produce any evidence for your QUACKERY of using CV
> > > over the conventional STATISTICAL methods of dealing with the problem.
> >
> > Quackery?
RU > >
> > From Reef Fish Bob's historical use of the term, "quackery"
> > should indicate that Scott has presented an approach that
> > is conventional and well-accepted, that Bob disagrees with.
RF > >
> No, my use of the term "quackery" is the way the term has always been
> understood to be. For Statistical QUACKERY, I used it in my 1982 JASA
> Review of "Correlation and Causation" because the author suggested that
> correlation can be used to establish causation on OBSERVATIONAL data,
> WITHOUT any controlled experiement.
>
> Richard Ulrich argued the same, for weeks. That made Richard's
> practice
> a Quackery, and Richard Ulrich a Quack.
Okay. I guess that does take us back to Reef Fish Professor Ling's
refusal to admit the testimony of epidemiological surveys,
including "cigarettes cause lung cancer." Who is the quack?
>
> But I since learned that Karl Pearson had used the term on Science and
> Statistics in 1938, long before I had used it, and he used it EXACTLY
> the
> way I used it, about science, medicine, and statisticians.
I don't mind that Karl Pearson used it. In 1938, the state of
medical research was terrible. "Statistics" as an area of study
was in its first decade, as Stigler estimates it -- journals getting
started, and so on. I do know that it was the 1960s before the
case against smoking was put together. R. Fisher rightfully
argued that the earlier arguments were faulty. I don't know if
he changed his mind before he died in 1962, but I don't
remember hearing of credible opposition much after that.
Only "quackery."
By the way -
I do think that I remember that K. Pearson was also known
as a bully who was willing to abuse others, from his position
as editor of Biometrika. And - Successful intimidation resulted
in him, Pearson, teaching for 8 or 10 years that the 2x2 table
has 3 degrees of freedom, because everyone was afraid to
argue with him, even though they were sure he was wrong.
> By "conventional", Richard Ulrich simply meant "conventional Quackery",
> those kinds of Quackery that is most often perpetrated by Social
> Scientists
> WITHOUT any statistics education or understanding, such as Richard
> Ulrich, in their MISUSE of statistics, just as Richard Ulrich used it
> in
> correlation, in regression, and in every respect of the regression
> problem.
Here are some of the contributions of Reef Fish's buddy,
C. Frederick Mosteller, as cited in the NY Times, in its July 27
obituary. He seems to been a scientist making extensive use
of observational data, with several notable citations below.
These studies used multiple variables, and probably OLS regression.
"In the late 1950's Dr. Mosteller assisted in analyzing data from a
large clinical study looking at the anesthetic halothane, which was
suspected of causing fatal liver damage in some patients. The
analysis showed no evidence that halothane was more dangerous than
other forms of anesthesia.
"He worked with Daniel Patrick Moynihan... on studies looking at the
impact of home life on children's performance in school. They
argued that raising families out of poverty would have a greater
educational impact than pouring money directly into schools.
[ ... snip, analysis of prose, Madison writing disputed Federalist
Papers.]
"In the 1970's, Dr. Mosteller worked on studies that questioned
whether the benefits of some surgical procedures were worth their
costs. ...
[snip, more detail.]
"In the 1970's, Dr. Mosteller was chairman of the biostatistics
department at the Harvard School of Public Health, and in the 1980's
he was chairman of the health policy and management department."
School of Public Health? Biostatistics? My sort of background.
This health stuff leans heavily on observational studies.
[snip]
RU > >
> > Even if this one is not totally conventional, I don't see much
> > downside to trying it.
RF >
> That's exactly what you said when you told an OP to check the variables
> Xs in a multiple regression for normality (or that its okay, in order
> to find
> outliers,etc.) when there is absolutely NO requirement for the
> normality
> of X, nor are outliers necessarily bad or influential.
>
> THAT was just another case of PURE Quackery on Richard Ulrich's part,
> and he he doesn't see much downside to trying.
>
> The DOWNSIDE is for social scientists to MUCK around, on practices
> that have no theoretical NOR empirical basis, on account of their own
> LACK of education about the subject.
Bob finally - just a few weeks ago - echoed my repeated assertion
that "normality of residuals is not even necessary for *regression*,
but only for the testing". I'm pleased that he could pick up this
bit of theory from me.
"Testing" has easier requirements for its assumptions, compared
to "inferring meaning."
Since Bob does not consider these processes of inferring meaning
to be licit, he ignores that whole area of regression in research.
Well, "ignoring it" would be an improvement; he sneers at it, not
offering much in argument but sneers and personal ad-hominem.
[snip]
>
> I happened to be ONE person in this group who sees through Scott's
> fallacious arguments as transpently as through a clear glass! He was
> running on EMPTY. He was doing his intellectual striptease on the
> subject of nonlinear regression.
>
> No amount of support by sci.stat.math's BIGGEST Quack, Richard
> Ulrich, will change the Statistical SUBSTANCE of the subject, nor the
> fact that Scott Seidman's failure to defend his own Quackery.
[ snip]
I can admit that I did not try to follow what-all that Scott
was posting. But when Scott says that Bob is not paying
proper attention or responding to good arguments, that is
a *very* familiar complaint about Bob. It rings true to me.
That is why, for the most part, I do not address my words to
Bob, but to the wider audience.
Reef Fish
Quit changing the subject. My QUACKERY review was on CORRELATION
and CAUSATION. Those medical studies that are based solely on
undesigned observational data would automatically qualify for quackery
if causal conclusion is unwarantedly claimed.
In fact, there's plenty of quackery in epidemiology, well beyond what
YOU
committed and blamed it on epidemiology.
On the other hand, you blamed many things on epidemiology when it had
nothing to do with epidemiology -- they were your ORIGINAL quackery.
> >
> > But I since learned that Karl Pearson had used the term on Science and
> > Statistics in 1938, long before I had used it, and he used it EXACTLY
> > the
> > way I used it, about science, medicine, and statisticians.
>
> I don't mind that Karl Pearson used it. In 1938, the state of
> medical research was terrible. "Statistics" as an area of study
> was in its first decade, as Stigler estimates it -- journals getting
> started, and so on. I do know that it was the 1960s before the
> case against smoking was put together. R. Fisher rightfully
> argued that the earlier arguments were faulty. I don't know if
> he changed his mind before he died in 1962, but I don't
> remember hearing of credible opposition much after that.
Do YOU or anyone really think that statistics is any better today?
With the MISUSE of computer software packages, I am in the camp
that says the abuse of statistics is MUCH WORSE today. In the
early days, the quacks at least had to learn a formula or two and
know how to compute them.
Today, any quack can just get a computer program, stuff numbers
into it, and VOILA, instant quackery!
Richard Ulrich is pretty good at THAT kind quackery -- such as
suggesting normality check on the X's of regression when there
is absolutely no such assumption.
>
> Only "quackery."
>
> By the way -
> I do think that I remember that K. Pearson was also known
> as a bully who was willing to abuse others, from his position
> as editor of Biometrika. And - Successful intimidation resulted
> in him, Pearson, teaching for 8 or 10 years that the 2x2 table
> has 3 degrees of freedom, because everyone was afraid to
> argue with him, even though they were sure he was wrong.
What you call "bully" is anyone who finds fault in the Quacks.
You call me a "bully" when I correct only statistical errors you and
others made. I am proud to be in the company of Karl Pearson,
as Quack Ulrich's bully!
>
>
> > By "conventional", Richard Ulrich simply meant "conventional Quackery",
> > those kinds of Quackery that is most often perpetrated by Social
> > Scientists
> > WITHOUT any statistics education or understanding, such as Richard
> > Ulrich, in their MISUSE of statistics, just as Richard Ulrich used it
> > in
> > correlation, in regression, and in every respect of the regression
> > problem.
>
> Here are some of the contributions of Reef Fish's buddy,
> C. Frederick Mosteller, as cited in the NY Times, in its July 27
> obituary. He seems to been a scientist making extensive use
> of observational data, with several notable citations below.
> These studies used multiple variables, and probably OLS regression.
So? ALL statisticians make PLENTY of studies on OBSERVATIONAL
data -- the condition is NOT to draw unwarranted conclusions from them.
The fact that Richard Ulrich didn't know the differece between
analyzing
observational data and drawing causal conclusions from observational
data WITHOUT any control or design -- is just another confirmation of
his Quackery.
If you want get down to earth and go back to YOUR quackery, committed
in sci.stat.math, you can find it in the archives. Rahash those in
your
own mind and time, and spare the rest of us your PROVEN Quackery.
-- Reef Fish Bob.
Nag
ass-backward fashion:
> You're are just like NAG. The belligerently ignorant poster who
> asked stupid questions, got help; didn't understand any of it because
> you were completely unprepared to ASK or to understand the answer.
> Then you started wasting EVERYONE's time making posts like this
> or like those of NAG.
You retarded piece of *#$@: you have no idea what I asked. Just
referred to your ancient article (worse than toilet paper) and now you
keep blowing hot air.
Nag