One + method serves bf() and mvbf() objects alike, so a sum of
any number of formulas reads left to right. The sum of bf(y1 ~ x),
bf(y2 ~ x) and bf(y3 ~ x) is
mvbf(bf(y1 ~ x), bf(y2 ~ x), bf(y3 ~ x)).
Details
The right-hand side can be another formula, a family, lf(),
nlf() or set_rescor(). A family added to a single formula sets
its family. A family added to a multivariate formula goes to every
response that has no family yet, so in the sum of bf(o ~ x),
cumulative(), bf(y ~ x) and gaussian() the response o stays
ordinal. brms instead gives the last family to every response. An
lf() or nlf() added to a multivariate formula names its response
with resp =.
Examples
# three responses, one family for all of them
bf(y1 ~ x) + bf(y2 ~ x) + bf(y3 ~ x) + gaussian()
#> y1 ~ x
#> Family: gaussian
#> y2 ~ x
#> Family: gaussian
#> y3 ~ x
#> Family: gaussian
#> rescor: FALSE
# a family per response, and a dpar formula for the third response
bf(o ~ x) + cumulative() + bf(y1 ~ x) + gaussian() + bf(y2 ~ x) +
lf(sigma ~ x, resp = "y2")
#> o ~ x
#> Family: cumulative
#> y1 ~ x
#> Family: gaussian
#> y2 ~ x
#> sigma ~ x
#> rescor: FALSE