In the documentation to
brmsformula stands the following:
If levels of the grouping factor belong to different sub-populations, it may be reasonable to assume a different covariance matrix for each of the sub-populations. For instance, the variation within the treatment group and within the control group in a randomized control trial might differ. Suppose that y is the outcome, and x is the factor indicating the treatment and control group. Then, we could estimate different hyper-parameters of the varying effects (in this case a varying intercept) for treatment and control group via y ~ x + (1 | gr(subject, by = x)).
I am wondering whether
y ~ x + (1 | gr(subject, by = x)) is equivalent to
y ~ x + (1 | x/subject)?