Linerization of non-linear models

In summary, a student from Lithuania is seeking help with converting non-linear equations into linear form for the purpose of fitting linear regression and comparing with iterative methods. They are specifically looking for assistance in estimating unknown parameters using a SAS programming package.
  • #1
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Hello,
I'm a student from Lithuania. I have found in one forum topic your discussion about non-linear equation convertion into a linear form.. I have some problem with that...Could you help me, please? :)
For, example, I have two non-linear models:
1. y = a [1/(1+b/(c+x))]*exp(-d*x)
2. y = a*exp[b*(1-exp(-c*x))/c - d*x]
And I want to convert it into linear equation, for fitting linear regression theory, of course, I could fit a Newton or other method, but there are some problems with initial values. So, I would like to see the results of fitting to these models a linear regression and compare with iterative methods.

So, could you help me?

I think, that these two models linear form will be:
1. ln(y) = ln(a) - ln(1+b/(c+x)) - d*x + err
2. ln(y) = ln(a) + b(1-exp(-c*x))/c - d*x
lnln(y) = lnln(a) + ln(b/c)-ln(b/c)-c*x -ln(d) + ln(x)

the main problem is, how to estimate unknow a,b,c,d parameters...using for example, SAS programe package.

I would waiting from you any help.

With best regards, Ms. Dovile.
 
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  • #2
?? None of your suggested "two models linear form" are linear.
 

Related to Linerization of non-linear models

What is the purpose of linerization in non-linear models?

The purpose of linerization in non-linear models is to simplify complex, non-linear relationships between variables into linear relationships. This allows for easier analysis and interpretation of the model.

How is linerization achieved in non-linear models?

Linerization is achieved by transforming the non-linear variables into linear variables using mathematical techniques such as logarithms or polynomials. This transforms the data into a more linear form which can then be analyzed using traditional linear regression techniques.

What are the assumptions of linerization in non-linear models?

There are a few assumptions that must be met in order for linerization to be effective in non-linear models. These include the assumption of a linear relationship between the variables, normally distributed errors, and homoscedasticity (constant variance).

What are the benefits of using linerization in non-linear models?

Linerization allows for easier interpretation and analysis of the data, as well as the ability to use traditional linear regression techniques. This can also improve the accuracy of the model and reduce the impact of outliers.

Are there any limitations to using linerization in non-linear models?

Yes, there are some limitations to using linerization in non-linear models. It assumes a linear relationship between variables, which may not always be the case. It also requires careful consideration of the transformation used, as it can affect the interpretation of the results.

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