Non Linear Regression Initial Guesses

In summary, the conversation is about a person's first post in which they ask for help with nonlinear regression and finding good initial guesses for model parameters. They explain that they are using an analytical instrument that uses a noniterative algorithm to calculate initial guesses and they are seeking help with deriving these algorithms. The other person suggests reviewing the theory of least-squares fitting algorithms on a specific website, but the first person is unable to find the information they need.
  • #1
scantor145
4
0
Hi:

This is my first post and I'm not sure if this is the right forum. Please redirect if necessary.

I'm new to nonlinear regression, but from what I've read I realize that making "good" initial guesses for the model parameters is very important, otherwise a "best fit" may not result.

I'm using an analytical instrument where the user selects from a short list of mathematical models (please see attachments), a calibration is performed, and the model parameters are calculated. There is no other user input.

This implies, and it is stated in the Operator's Manual, that the initial guesses are calculated using a noniterative algorithm in conjunction with the calibration data.

I would love for someone to show me how to derive theses algorithms for the models attached.

If there is any other information that is required in my quest please let me know. I can supply actual data if necessary.
 

Attachments

  • 4PL 5PL.doc
    52 KB · Views: 245
  • Non Linear Models.doc
    194.5 KB · Views: 266
  • Non Linear Models 2.doc
    113 KB · Views: 253
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  • #3
Bob S said:
Review the theory of least-squares fitting algorithms at
http://mathworld.wolfram.com/LeastSquaresFitting.html
and other web sources.
Bob S

Thanks Bob S.

I went to that site but I can't find anything that would help me derive expressions needed to make initial guesses for different models. Am I missing somethig perhaps?
 

1. What is non linear regression and why are initial guesses important?

Non linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. In contrast to linear regression, non linear regression involves fitting a curve to the data rather than a straight line. Initial guesses are important in non linear regression because they help the algorithm to converge on the best fitting curve and improve the accuracy of the model.

2. How do initial guesses affect the accuracy of a non linear regression model?

The initial guesses in non linear regression help to determine the starting point for the algorithm to search for the best fitting curve. If the initial guesses are far from the true values, the algorithm may struggle to converge on the optimal solution, resulting in a less accurate model. Therefore, it is important to choose initial guesses that are as close as possible to the true values.

3. How can I choose the best initial guesses for a non linear regression model?

The best initial guesses for a non linear regression model can be chosen through a trial and error process. One approach is to plot the data and make an educated guess based on the shape of the curve. Another method is to use software that automatically generates initial guesses based on the data. It is also recommended to try multiple initial guesses to see which one yields the most accurate results.

4. Is there a specific method for determining the initial guesses in non linear regression?

There is no one specific method for determining initial guesses in non linear regression. The method used may vary depending on the complexity of the model and the available data. Some common approaches include using visual aids, using software, or using mathematical equations to generate initial guesses.

5. Can incorrect initial guesses lead to unreliable results in non linear regression?

Yes, incorrect initial guesses can lead to unreliable results in non linear regression. If the initial guesses are too far from the true values, the algorithm may not be able to converge on the optimal solution, resulting in a model that is far from the actual relationship between the variables. Therefore, it is important to carefully choose and test initial guesses to ensure accurate and reliable results.

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