Proper model formulation for nonlinear mixed effects model I have a question about how to properly write an equation to describe my model formulation, which is based on nonlinear mixed effects models.
My data consists of tree heights (H) and diameters (D) distributed on different plots (plID), which are random effects in nonlinear models. The nonlinear equation I use to predict H based on D is Curtis' 2-parameter growth curve:
H(D)=bH+a(D/(1+D))^2
where a and b are model parameters.
Now I want to insert the random effect (plID) into this equation and I am not sure how to write the equation correctly.
Any help would be appreciated.

First, the model equation you have given does not make much sense, since it has $H$ on both sides! I found the paper Modeling the height-diameter relationship of planted Pinus kesiya in Zambia which contains a list of theoretical models for the height-diameter relationship, and they give the Curtis model as
$$
   H= \beta_0 + \beta_1 \left(\frac{d}{1+d}\right)^{\beta_2}
$$ (you seem to have $\beta_2=2$).
Then to your question, how to formulate this as a nonlinear mixed model?
You want plots as random effects, but must decide for what varies between plots? First, a random intercept model would be, with $i$ index for trees, and $j$ for plots:
$$  \DeclareMathOperator{\E}{\mathbb{E}}
 \E H_{ij}= \beta_{0j} + \beta_1 \left(\frac{d_{ij}}{1+d_{ij}}\right)^{\beta_2}.
$$ If you also want random slopes, the model could be written
$$
  \E H_{ij}= \beta_{0j} + \beta_{1j} \left(\frac{d_{ij}}{1+d_{ij}}\right)^{\beta_2}.
$$
