I have a basic nonlinear model ( 📷). Dependent variable: crown diameter (cw) and independent variable: trunk diameter (dbh). I had 200 plots and within each plot I measured the variables: crown diameter (cw), trunk diameter (dbh), total height (h) and crown ratio (cr) for each tree. Below is part of my data. My target is to nonlinear mixed effects crown diameter models. Total height (h) and crown ratio (cr) variables are my random variables.

c📷

Now I have the following questions:

1- For the linear model, are the following functions written correctly (my basic question is about how to write the random effect function)?

📷

2- How are the functions written for the non-linear model (it gives an error with the nlmer function).

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3- We have 4 types of random effects including:

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Which of the above random effects should be considered for my study?

Please open the attached file.

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