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Dose Response Parameter Fitting

ChemEng
1-Newbie

Dose Response Parameter Fitting

56 REPLIES 56

... few more models and fit added for general interest.
There is also the Mathcad work sheet "LIGANDS"

jmG

jMG,

I was able to fit the data with logistic curve and it is far better than the others in regards to the lowest SES. I am trying to fit the data using the log probit curve as well, but having difficulty. I was wondering have you used the log probit before. The log probt looks something like:

P = normal CDF x (1/A1 x ln(dose/A2))

The lob probit was included in the family of curves for fitting dose response data.

I am not certain what you meant by the term "probit."

On 8/24/2009 2:36:40 PM, Stevenlee wrote:
>jMG,
>
>I was able to fit the data
>with logistic curve and it is
>far better than the others in
>regards to the lowest SES. I
>am trying to fit the data
>using the log probit curve as
>well, but having difficulty. I
>was wondering have you used
>the log probit before. The log
>probt looks something like:
>
>P = normal CDF x (1/A1 x
>ln(dose/A2))
>
>The lob probit was included in
>the family of curves for
>fitting dose response data.
_______________________________

You MUST NEVER start/try/attempt fitting data via an unproven transformation of the independent or dependent domain. Transformation of either domain is called "Data reduction". probit(x,,) is the inverse cumulative normal distribution. There are as many "probit" than there are distributions (> 100). The point about data reduction is that it is generally simple and relates directly the type of physical transducer to the phenomenon or more generally the measured to the phenomenon ...SQRT, x^, ln, Y/X are common and easy to try, sometimes simply deceptive. You will have plenty of help in this collab, but the best is to post the data set as raw as possible, most preferably not as the previous one quiz type where the data set made no sense ... where passing a sigmoidal function makes no more sense than passing a straight line or an arc of circle/ellipse ... etc. The underlying function behind the data set, if the paper pretends it is a sigmoidal. it is as ridiculous saying the moon is square because it is seen circular. You then understand my point about data set and fitting and the plunge in unknown waters.

jmG




Probit stands for PROBability unIT:
http://en.wikipedia.org/wiki/Probit

It also feeds into Q-Q plots:
http://en.wikipedia.org/wiki/Q-Q_plot

Philip
___________________
Nobody can hear you scream in Euclidean space.

"probit" is unique as defined. "probit" and "probits,s,s,s,s ..." are solvers. Solvers are not fitters and "probit(s)" aren't even sigmoidal functions. What are "probit(s)" doing in fitting "Dose response" and "Dose responses,s,s,s..." as there are so many of those things hardly coupled with meaningful data.



jmG

http://books.google.com/books?id=vjVhhwQh9N8C&printsec=frontcover&dq=mirobial+risk+assessment#v=onepage&q=probit&f=false

See pages 278 and 279 from the google books link above for where probit is used for dose response curves.

On 8/25/2009 12:41:11 PM, Stevenlee wrote:
>http://books.google.com/books?
>id=vjVhhwQh9N8C&printsec=front
>cover&dq=mirobial+risk+assessm
>ent#v=onepage&q=probit&f=false
>
>See pages 278 and 279 from the
>google books link above for
>where probit is used for dose
>response curves.
>_____________________________

On 8/25/2009 12:41:11 PM, Stevenlee wrote:
>http://books.google.com/books?
>id=vjVhhwQh9N8C&printsec=front
>cover&dq=mirobial+risk+assessm
>ent#v=onepage&q=probit&f=false
>
>See pages 278 and 279 from the
>google books link above for
>where probit is used for dose
>response curves.
>______________________________

Sorry, I don't see any fitting something.
Please read page 277. Like said before, moon is square because it looks circular, you can also make the moon elliptical, even triangular and any shape in fact. You will get more knowledge about data fitting by posting the data set. If you presume/assume/imagine or even would like a specific curve pass through a data set, the data set must make sense to the fitter, because the fitter can't figure what kind of forgery you want or even does not know what you might want because y0u may not have an idea of what you could get from a vast grocery list that you don't know how long it is as available. Google for "Ligands", "Markov", visit the Mathcad sheet "Markov". Did you read the sheet I posted to Theodore ? Try to apply MLE to the "quiz data set" you had before.

jmG



I read as much of that PDF as I could, and conclude the authors tended to rely on the beta-Poisson domain as one most likely to contain the raw data coming in later. I use the straight random Poisson distribution to get the most likely value of medical observations made many times at random. That agrees very well with the minimum of the chi-square distribution and with the geometric and harmonic means of the data also.
The authors stressed heavily medical topics like development of infection from estimated exposute to pathogens.

MLE is a sort of certification of sufficiency of the data, I guess. Very small samples may be corrected easily by (p-1)/p, where p is the # of observations.

Caution: if you fit the observed response ratios you have only six data points. With such a small sample degrees of freedom make a big difference. You should not directly compare the SSE (the common acronym for Sum of Squared Errors) of fits with different number of parameters. You have to adjust for the degrees of freedom first. Note that you can fit a quintic polynomial and it will be a perfect fit. But it will be a meaningless fit, with no validity beyond the range of observed points, and often not even between the observed values.

There's a good reason why the reference use MLE as a fit. That uses the origin data, with each individual case being an observation (vs. each dose level being an observation). The different dose levels are based on very different numbers of observations, the sampling errors for the incident ratios will be very different for the different dosages (in addition to the variation of the standard deviation with the mean for binomial distributions). Simple least squares is based on the assumption of equal variances. With unequal variances you have to apply weights.

Read the article with the data and understand why they chose the particular fitting function that they did, and why they chose to use a maximum likelihood estimate of the parameters, before wandering off into what are essentially random fits.
__________________
� � � � Tom Gutman

Getting a grasp of any MLEs from 5 different fitting models and their resultants with Mineer can't show any significant goodness of fits using the Behrens-Fisher (Student's t-test) to judge their closeness one by one. What's close is close enough to be a MLE.

Maximum likelihood is not a way of comparing different models. It is a way of estimating the parameters for a specific model. Given a model that allows for the calculations of either probabilties or probability densities MLE is well defined.
__________________
� � � � Tom Gutman

Tom,

I am trying to use MLE method get an exponential curve. I am using the same method you used for the beta poisson. Mathcad is unable to converge to a solution. The exponential is a single parameter.

You are neglecting several issues with curve fitting -- by any method.

Don't try to fit random functions. Make sure there is some theoretical basis for your choice of function.

Always plot you data and the proposed fit. You have to choose reasonable guess values. Your guess of r=1 has no justification, either theoretical or empirical.

Don't bother trying to estimate parameters for functions that are incapable of coming close to the data. It will usually not work, and will often produce completely meaningless results (when it produces any results at all. The basic plot clearly shows that your exponential function is quite incapable of approximating your data.

Do evaluate the relevant functions and understand their numerical behaviour. Here large values of r faile completely as they result in values of f2 that are exactly one (due to limitations in the computers number representations). So the complement is exactly zero, and you can't take the log of zero. Note that a zero probability means impossible, and it completely destroys a maximum likelihood calculation (if any of the probabilities are zero, the overall probability is also zero and there is nothing to maximize).

Using a much smaller guess value for r does allow maximize to produce a result. But it is a meaningless result, representing nothing more than a value at which the function could be calculated.
__________________
� � � � Tom Gutman

>Mathcad is unable to converge to a solution<<br> ____________________________

1. Start by the rules of the fitters.
2. Read less papers/books not oriented.
3. Meditate the example below Marlett, it makes clear that experiments or collected data need a sufficient number of valid points. Some weight function could be added but not shown.
4. For a greater audience, therefore greater collaboration: "Save as 11" or lower versions. Also, provide real data as raw as possible and for the interest of the general readers: better source the data.

I read more pages of the book, void of "working matters". If the same subject would have been written by a good Mathcader, it would resume in few pages and the corresponding working tools, that now you are trying to get by visiting this forum. This work sheet has no red. Again, there are too many "Dose response", that some very particular trick like MLE don't generally apply. Some function just can't be fitted by any method, only by hand. LM [Lvenberg-Marquardt] succeeds more than it fails but might fail miserably. If you jump ship/sheep, hard to follow for yourself and the collabs [Ref: probit]. A final fit requires some decision making that no maths can automate, how can you declare the truth out of the lies ! What I mean here is that no matter and how much maths some data are statistically more correct than other ones, therefore in the last comparison of your short data set, if the two first point are + true than the other ones (and that makes sense), then your model is for the birds ... like butter: you can't have it both ways, the butter and the $ of the butter. In other words, MLE is down the drain for the two first points considering they would be + true than the other ones progressively degrading to non sense.

jmG


The worksheet is very impressive in its wide scope, but won't converge, runs on forever. MC14 MO.

On 8/26/2009 2:16:43 AM, study wrote:
>The worksheet is very
>impressive in its wide scope,
>but won't converge, runs on
>forever. MC14 MO.
_____________________________

Don't tell me that Theodore !

I have just complemented the very last example, most important comparison LM vs CG. Does that mean the 14 version Minerr is all screwed up ? More collabs should check for the benefit of this most serious community as well as PTC and part of the Mathcad reputation.

jmG

The program stalled at a plsce just above 'Function Description," and I dissected the roots (p,x0) commnd to see that the program line contained an hidden overlap, or wrap over, with dll=0. I moved that out elsewhere. Then the entire program ran all the way thru except where roots was called for. This might be my computer memory having a defect somewhere. I noticed that my computer mis-spells a word or two after I edit a line and post it. Just on text.

Change that to ddL(x)= 0.

I downloaded your MC11 worksheet 3 times and each time the overlap or wrap over of the ddL(x)=0 segment just above "Function Description" appeared and the program stalled on a green box point there.

On 8/26/2009 10:30:38 AM, study wrote:
>I downloaded your MC11
>worksheet 3 times and each
>time the overlap or wrap over
>of the ddL(x)=0 segment just
>above "Function Description"
>appeared and the program
>stalled on a green box point
>there.
_____________________________

In that sheet, I have removed the symbolic parts that don't work in your version. The MC 11 equivalent is shown in the left margin. Maybe Steven has the same problem and got lost even more ! Go Forest, Go Forest ... Go Theodore ...

Jean



On 8/24/2009 10:56:41 PM, study wrote:
>Getting a grasp of any MLEs
>from 5 different fitting
>models and their resultants
>with Mineer can't show any
>significant goodness of fits
>using the Behrens-Fisher
>(Student's t-test) to judge
>their closeness one by one.
>What's close is close enough
>to be a MLE.
_____________________________

"Maximum likelihood is not a way of comparing different models. It is a way of estimating the parameters for a specific model. Given a model that allows for the calculations of either probabilities or probability densities MLE is well defined ".
....................................

Several examples of MLE from Paul W.

Jean

Steven,

back to your very first visit:

http://collab.mathsoft.com/~Mathcad2000/read?127628,17e#127628

Please study carefully this attached work sheet, now working in your version. I bet there is no book, no paper no software that will fit the data set starting at page 5. It certainly toke me > 50 hrs and few tools only available in Mathcad. That the symbolic part fails in your version is not detrimental as this stuff is superflous. If you are in the learning process of curve fitting, the other problem is the Mathcad version compatibility. Some collab are smart enough to work their 14 in the old style 11, but some aren't or refuse by exclusion, that's why you should start by the data only, so that all versions can read. What I mean here is that if Mathcad would drop down from the shy today as is 14, very little curve fitting could be done immediately because the expertise(s) is/are prior to version 14.

Sorry for "probit" in curve fitting, just filed in "museum".

jmG

Aside from all of this, the previous idea of using MLE as an estimator was studied in a text on Kendell's Advanced Statistics and a sample is given here.

On 8/26/2009 2:31:53 PM, study wrote:
>Aside from all of this, the
>previous idea of using MLE as
>an estimator was studied in a
>text on Kendell's Advanced
>Statistics and a sample is
>given here.
_______________________________

For which, well collected data you get this beautiful logistic fit !

jmG

Nobody noticed this, so I expanded it to allow selection of eminent domains for data they prepare.

This forum has certainly been helpful for me and I thank those who have responded to my inquires. I am starting to get the big picture of curve fitting from the techniques you have shared. Allow me some time to sort out the differences and similarities from the many posts and worksheets here. The MLE is still fuzzy to me since my bachelors engineering program and statistics courses never touched on it. There appears to be several methods to find solution for the dose response parameters and I now have a good tool box for them but will need to practice my judgement to why am applying which data fitting method to a dose response model.
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