Mixed effect model

Question

I have a model:

$y=a+bx+\varepsilon_1$ for each observation (tree)

$b=c+dz+\varepsilon_2$ for each forest (group of trees)

$y$, $x$, $z$ are continuous variables. $a$, $b$, $c$, $d$ are coefficients. $z$ is a property of forests (not individual trees). Error $\varepsilon_1$ is normally distributed and varies by tree. Error $\varepsilon_2$ varies by forest and not much is known about its distribution.

Is this lme4 model specification correct?

lmer(y~x+x:z+(0+x|forest))

I will greatly appreciate your help!

Answer 1

Nominally, you are right, but it looks odd that you force no random intercept in the model, which smells like regression through the origin, in terms of making strong assumptions that some terms (or some sources of variability) in the model are zero. I would start with

lmer(y~x+x:z+(1+x|forest))

instead and see how that works.