Non Linear Regression Initial Guesses

Click For Summary
SUMMARY

This discussion centers on the importance of making accurate initial guesses for model parameters in nonlinear regression, particularly when using an analytical instrument that selects from predefined mathematical models. The user highlights that the calibration process relies on a noniterative algorithm to calculate these initial guesses, as stated in the Operator's Manual. The need for guidance on deriving these algorithms for specific models is emphasized, alongside a reference to least-squares fitting theory as a potential resource.

PREREQUISITES
  • Understanding of nonlinear regression techniques
  • Familiarity with least-squares fitting algorithms
  • Knowledge of calibration processes in analytical instruments
  • Basic mathematical modeling concepts
NEXT STEPS
  • Research methods for deriving initial guesses in nonlinear regression models
  • Study the application of noniterative algorithms in parameter estimation
  • Explore specific mathematical models used in analytical instruments
  • Review advanced least-squares fitting techniques and their applications
USEFUL FOR

Data scientists, statisticians, and researchers involved in nonlinear regression analysis, particularly those working with analytical instruments and calibration processes.

scantor145
Messages
4
Reaction score
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

Engineering news on Phys.org
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?
 

Similar threads

High School Is Averaging Individual Slopes Equivalent to Linear Regression?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad What are the commonly used estimators in regression models?
  • · Replies 23 ·
Replies
23
Views
4K
Undergrad How to propagate errors through a regression & non-linear model?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Non-sinusoidal waveform model
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to Express Non-regular Prior Distributions by Mathematical Formula
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Regression Analysis of Tidal Phases
  • · Replies 2 ·
Replies
2
Views
2K
Linear vs. Cubic Regression: Training and Test RSS Comparison
  • · Replies 10 ·
Replies
10
Views
9K
MATLAB To what extent is the fit to experimental data good?
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Help with a difficult (?) regression
  • · Replies 7 ·
Replies
7
Views
2K
Uncertanty in a non-linear regression with least squares method
  • · Replies 3 ·
Replies
3
Views
2K