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Posts: 3

# How to compare single parameters of nonlinear regression among three different treatments

Hello All,

I need help to comparing single parameters of nonlinear regression among three different treatment.

I am analyzing a data set obtained from three different treatments. The model, which I am using, consists of monomolecular and logistic models. The blow parameters with the syntax work fine with my data and the p-value from PROBF function gave me a result that the model with separate trends fit my data better.

Now I would like to compare single parameters among three treatments (especially a parameter "p1") to test my hypothesis.

I would like to perform a sum of square reduction test for the full model and a reduced model.

I found several sites discussing this method comparing two treatments but cannot find examples of more than three treatments.

Could someone help to develop code for this test?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

proc nlin data=leaf method=newton;
parms p0=-0.1773
p1=0.6667
p2=0.00283
p3=0.0264
p4=542.2;
model leaf=p0+p1*(1-e**(-p2*GDD/p1))+(10-p1-p0)/(1+e**(-4*p3*((GDD-p4)/(10-p1-p0))));
output out=leaf_out2 p=yhat r=resid parms=p0 p1 p2 p3 p4;
run;

Posts: 2,655

## Re: How to compare single parameters of nonlinear regression among three different treatments

There is a great example of how to do this in the PROC NLIN documentation.  The following link should point to an example with code that compares nonlinear trends (and parameters) among groups.

http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_nlin_example...

Steve Denham

New Contributor
Posts: 3

## Re: How to compare single parameters of nonlinear regression among three different treatments

Thank you very much, Dr. Denham, for providing me a useful example.

I referred the link and understood how I need to process my model to compare among groups.

But I am still confused the SAS statements for this process.

The F statistics and P values for comparing the reduced and the full models gave me a value with <0.0001.

Therefore, I would like to test which parameters varies among three treatments.

In a case with two treatments, a null hypothesis is simple; however, how I should think and make SAS statements for more than two treatments.

I appreciate if you give me some tips or links that I can refer.

Best regards,

Posts: 2,655

## Re: How to compare single parameters of nonlinear regression among three different treatments

My first inclination would be to get confidence bounds on the parameters from the full model and check for overlap.

The other would be to fit the full model, and reduced models where parameters are set equal for two of the three groups.  You could do two of these to get orthogonal results.  What may be easier is to port all of this to NLMIXED, with no RANDOM effect.  You could then use a CONTRAST statement to see if two parameter estimates are equal.

Steve Denham

New Contributor
Posts: 3

## Re: How to compare single parameters of nonlinear regression among three different treatments

Dear Dr. Denham,

I will try to see what I can get from your approach.

Sincerely,

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