Bootstrapping Non-linear Models

[ChemEng]

I noticed that bootstrapping was mentioned in the forums and thought this would be a great place to ask some questions. I have received help from this forum before and got great response and feedback which I greatly appreciate. I am trying to determine the uncertainty or confidence levels from a MLE fitted dose response model (See attached file). I have calculated the dose response parameters and would like to bootstrap the raw data to find the 95% confidence level. The method I am trying to apply is described as follows:
1. Construct a hypothetical data set of experimental data with I (infected) individuals randomly selected as binomial variants form a distribution with parameters (I1 T2, T1)...(Ik Tk,Tk) at the respective doses. Where T is the total number of participants.
2. Fit the hypothetical data set to the dose response model, determining the MLE estimates (alpha and Beta).
3. Repeat the process a large number of times.
4. The bivarate distribution of values (alpha and beta) represents the uncertainty in the true dose response parameters.

I have attached a pdf of an example that also shows and explains the bootstrapping sampling method that I am trying to mimic with the data. I know that other mathematical or statistical softwares such as SAS and Matlab have canned bootstrapping functions for this. There is probably a way to do it with Mathcad through programming but I am not certain. Your help would be greatly appreciated. Thanks.

[PhilipOakley]

It is worth also saving as V11, as this allows other
users to also comment.
Philip Oakley

[ChemEng]

Mathcad 11 version.

[ptc-1368288]

On 10/19/2009 5:23:11 PM, Stevenlee wrote:
>Mathcad 11 version.
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There is a red phi' in 11 ?
Attached is same c/w the plot + comments.
A very similar project was done this summer,
not wisely named and maybe lost.

jmG

[ChemEng]

Here is the research article that shows the boostrapping method.

[ptc-1368288]

On 10/19/2009 5:26:32 PM, Stevenlee wrote:

>Here is the research article

>that shows the boostrapping method.

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Sorry, I can't read *.PDF split in two pages !

So, what is "bootstrapping", can you explain ? The Matlab explain is like this: bootstrapping is bootstrapping because bootstrapping is something like bootstrapping doing bootstrapping to unknown that must be bootstrapped ... Does it mean a circular rotation of some sort, performing some stat on each cycle ?

Excellent work in the sheet but the sheet itself is (no comment). You NEVER-EVER start a work sheet on the leftmost side w/o margin. For a work sheet to be readable, it must be presentable, i.e: structured for on line quick reshape. Text w/o margin can't be pushed up/down becaue the pointer at the extreme right enters the text box on push down and screws everything. Is it possible that you had phi' working and in the conversion it got screwed as bold equal, therefore red ?



Use data table (green), The value(s) 1 [alpha, beta] is magic in the Mathcad solver(s), it simplifies the guessing ! Minerr constrained added for the didactic of the constrained fit. I understand likelihood, and my question is: as you have about no data, does the Poisson fit means if you had more data they would fall around that particular model ?



jmG

[PhilipOakley]

On 10/20/2009 2:46:08 AM, jmG wrote:
>So, what is "bootstrapping", can you

Generally speaking 'bootstrapping' is where one starts off with some initail condition (deliberately in the right direction) and use regenerative feedback to get toward the goal. The feedback being toned down as you get near the goal.

It matches the 'english' phrase: pulling oneself up by one's own bootstraps. [lifting yourself up by pulling your own boot laces]

Philip Oakley

[ptc-1368288]

On 10/20/2009 6:16:48 AM, philipoakley wrote:

>On 10/20/2009 2:46:08 AM, jmG wrote:

>>So, what is "bootstrapping", can you

>

>Generally speaking 'bootstrapping' is

>where one starts off with some initail

>condition (deliberately in the right

>direction) and use regenerative feedback

>to get toward the goal. The feedback

>being toned down as you get near the

>goal.

>

>It matches the 'english' phrase: pulling

>oneself up by one's own bootstraps.

>[lifting yourself up by pulling your own

>boot laces]

>

>Philip Oakley

________________________________



I know what "bootstrapping" means as a control man. But as applied to statistics, you must provide an example of what it does before inventing a new square wheel. About 2002, I did a fit to a "black body something", bootstrap style. But a fit and statistics is not the same.



I guess more collab will have an idea to share, even an example.



jmG

[TomGutman]

Not a problem. You just do what you say. You need to rework your sheet to make all the calculations functions of the data (rather than using worksheet variables to represent the data) so that you can evaluate them for different data sets.

Given the parameters you can calculate the probblities, and then use the random number generators to do a sampling. Repeat ad naseum.
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� � � � Tom Gutman

[ChemEng]

Tom,

is there an example you know of. I will give this a try using the random number generator but unclear on how to call the confidence intervals. I suppose you could use the rnorm function.

[TomGutman]

If an event has probability p you can simulate it by using rnd(1) and considering the event to have happened if rnd(1)≤p. That is the simplest way, and the most flexible -- you can easily have as many random events for an observation as needed, with any sort of dependencies.
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� � � � Tom Gutman