Marielle -

I am not familiar with your application, but are you sure you don't just need to research "curve fitting"? That may or may not technically be "nonlinear."

Also, are you OK with what you have done for heteroscedasticity? A straightforward approach might be better. For that, you might get an idea from the following:

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The following is with regard to the nature of heteroscedasticity, and consideration of its magnitude, for various linear regressions, with emphasis on finite population sampling:  

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression

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As I said though, I am not familiar with your application. The above might be applicable even for nonlinear regression, and I have applied it to linear regression with curvature.

Best wishes.

Cheers - Jim

You are right in suggesting that normality of data is not assumed in Hayes’ PROCESS software. Moreover, bootstrapping can produce readinably reliable estimates even on non-normal data.

In fact, the assumption of normailty of data is no longer applicable in PROCESS or SEM models. We know that socisl science data is usually non-normal.

Log transformation is the easiest way to overcome the non-linearity relationship, also you may also manipulate the data, such as centering the data, or use the square root. also you need to see if you have an outliers.

Thank you very much, I solved the problem.

Hi Marielle Sträter , I was wondering how did you resolve the problem of non-linearity. were you able to use the Process Macro with the non-linearity?