I’d like to have a clear understanding of the mathematical model behind a formula and priors. Take for example the following call:
fit1 <- brm(brmsformula(time | cens(censored) ~ (1 | 0 | group), shape ~ (1 | 0 | group)),
data = mydata, family = weibull(),
prior = c(set_prior("normal(0,5)", class = "Intercept"),
set_prior("normal(0,4)", dpar="shape", class = "Intercept"),
set_prior("normal(0,0.1)", class = "sd", group="group")),
warmup = 1000, iter = 2000, chains = 4,
control = list(adapt_delta = 0.95))
What is the mathematical model here?
time_g = a + a_g
time_g \sim Weibull(\beta_g, \eta) and right-censored
a \sim N(0,5)
a_g \sim N(0,0.1)
\beta_g = b
b\sim N(0,4)
Is this correct?
Also, after fitting the model and calling summary()
, I see cor
and sd
. How do those relate to the mathematical model?