Multiple variables for the intercept (random slopes) of a Mixed Effect Model (lme4)

Question

I am a newbie in R, coming from STATA. I want to evaluate a mixed model (lme4) where my dependent variable is a means (mean speed) and I have as independent variables crosswalk, approach_width (these two in one level, street or approach), lumix, pop_dens, and empl_dens (these ones in another level, this level is the intersection). For the different levels, I have an ID (Int_ID and Approach_ID). The idea is to evaluate the effect on means that lumix, pop_dens, and empl_dens in the Int_ID level and crosswalk, approach_width in the Approach_ID have.

I have been trying to find the way to specify different random slopes on lmer function without any success. I know if I just want to evaluate the Int_ID and Approach_ID should be something like this:

memeads <- lmer(means ~ crosswalk + approach_width + lumix + pop_dens + empl_dens + (1 | Approach_ID) + (1 | Int_ID), data = db)

In STATA I'd do something like this:

xtmixed means crosswalk approach_width lumix pop_dens empl_dens || Int_ID : lumix pop_dens empl_dens || Approach_ID : crosswalk + approach_width

Any help would be appreciated

Answer 1

With @Oliver's help, I was able to fit my model. The solution is the following if any in a future.

To have more than one random variable in the slope, the model would be:

memeads <- lmer(means ~ crosswalk + approach_width + lumix + pop_dens + empl_dens + (1 + lumix + pop_dens + empl_dens | Approach_ID) + (1 +crosswalk + approach_width | Int_ID), data = db)

Thanks for the support

Answer 2

Out of curiousity, what is the difference between the solution:

memeads <- lmer(means ~ crosswalk + approach_width + lumix + pop_dens + empl_dens + (1 + lumix + pop_dens + empl_dens | Approach_ID) + (1 +crosswalk + approach_width | Int_ID), data = db)

and this?

memeads <- lmer(means ~ crosswalk + approach_width + lumix + pop_dens + empl_dens + (1 + lumix | Approach_ID) + (1 + pop_dens | Approach_ID) + (1 + empl_dens | Approach_ID) + (1 + crosswalk | Int_ID) + (1 + approach_width | Int_ID), data = db)