_all: in mixed models: What if it is followed by a continuous variable without the "R." part?

Dear Statalist,

I am trying to better understand how Stata deals with the _all: option in mixed/xtmixed commands. What I specifically am looking to understand is what exactly is happening when the _all: option is followed by a continuous variable rather than the more commonly used R.identifier_variable approach. From what Clyde writes in this forum, I understand that without the R. Stata tries to fit a model with random slope specified to the variable that comes after _all:. At what level then would the slope of that variable be varying?

Let me provide an example to clarify what I am looking for. I have a dataset with multiple brands (denoted by i) and each brand has several observations across months (denoted by t). The dependent variable of interest is sales (i.e., Sales_it) and the independent variable of interest is brand's monthly advertising expenditures (i.e., Adv_it). What model would be estimated if I run the following command?

Code:

 mixed sales adv || _all: adv

Will it try to estimate this model? Sales_it = a + b_it * Adv_it+ e_it (with b_it = b + u_it). If so, is my interpretation correct that the b parameter that is reported in the main part of Stata output would be the average effect of advertising on sales after accounting for time-specific or brand-specific deviations in the effectiveness of advertising on sales through the inclusion of u_it?

Is there any document going into the detail of how the above model is estimated?

Thank you very much in advance.

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