# Mixed effect model

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!

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