Dear Gerrit

The best way for dealing with such situation is to transform your data (for example logarithmic transformation) to chabge the relationship to linear then use a multiple linear regression.

Regards

I think, following Shanock L et Al(2010), YOU CAN USE RESPONSE SURFACE ANALYSIS through polynomial regression (accounting for both fixed and random effect) : "The approach allows researchers to examine the extent to which combinations of two predictor variables [which can also be two point in time measure i.e., reoeated measure on subjects, ( or effects of an intervention or two predictors/process)] relate to an outcome variable (i.e., employee satisfaction), particularly in the case when the discrepancy ([the] difference) between the two predictor variables is a central consideration." of our research.

You can try different relating models (or polynomials) step-wise selection , accounting for "carry over effects " and correlation that may influence the level of satisfaction of the subjects.

Best wishes, Ibiloye.

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See an example here: https://www.jstor.org/stable/40928705

Reference.

Shanock, L., Baran, B., Gentry, W., Pattison, S., & Heggestad, E. (2010). Polynomial Regression with Response Surface Analysis: A Powerful Approach for Examining Moderation and Overcoming Limitations of Difference Scores. Journal of Business and Psychology, 25(4), 543-554. Retrieved May 19, 2021, from http://www.jstor.org/stable/40928705

Sorry but I am a bit late to the party but you had better see Montgomery's Design and Analysis of Experiments the section on Response Surface Analysis. This is available at z-library google instructions. It doesn't look like this is what you need. Best wishes David Booth