Weibull multilevel regression with different shapes by group

Interfaces brms
1

Dear all,

I am trying to reproduce example 8.2 from Liu & Abeyratne’s “Practical applications of Bayesian Reliability”. The original example (related to hierarchical models) was done in JAGS and I want to reproduce it on BRMS.

I was able to create and run a model where the Weibull shape is common to all groups (in the example, it is nine product generations).

Now I would like to make now a model where I can also model an “average” shape and the effect of each group just like it does to intercept

This is the model that worked, where the scale is common to all groups:

priors <-
        set_prior("gamma(a, b)", class = "Intercept") + 
        set_prior("gamma(c, d)", class = "shape") + 
        set_prior("target += gamma_lpdf(a | 6, 0.4) - 1 * gamma_lccdf(0 | 6, 0.4) + 
                  gamma_lpdf(b | 2, 0.2) - 1 * gamma_lccdf(0 |2, 0.2) ", 
                  check = FALSE) + 
        set_prior("target += gamma_lpdf(c | 1, 1) - 1 * gamma_lccdf(0 | 1, 1) + 
                  gamma_lpdf(d | 1, 1) - 1 * gamma_lccdf(0 | 1, 1) ", 
                  check = FALSE)

stanvars <- stanvar(scode = "real<lower=0> a; real<lower=0> b; real<lower=0> c; real<lower=0> d;",                 block = "parameters")
        
brmsHyperModel <- brm( ttf | cens(censor) ~ 1 + (1 | gen), family = weibull, data = brmsData,              prior = priors, stanvars = stanvars, iter = 41000, warmup = 4000, chains = 4, cores = 4, seed = 4,               control = list(adapt_delta = .99))

I would like to run something like this:

brmsForm <- bf( ttf | cens(censor) ~ 1 + (1 | gen), shape ~ 1 + (1 | gen))

If I just add this second equation, I got the following error:

Error: The following priors do not correspond to any model parameter: shape ~ gamma(c, d)

I tried to, instead of adding a second equation, change the “priors”, adding a group variable to shape, like this:

priors <-
        set_prior("gamma(a, b)", class = "Intercept") + 
        set_prior("gamma(c, d)", class = "shape", group = 'gen' ) + 
        set_prior("target += gamma_lpdf(a | 6, 0.4) - 1 * gamma_lccdf(0 | 6, 0.4) + 
                  gamma_lpdf(b | 2, 0.2) - 1 * gamma_lccdf(0 |2, 0.2) ", 
                  check = FALSE) + 
        set_prior("target += gamma_lpdf(c | 1, 1) - 1 * gamma_lccdf(0 | 1, 1) + 
                  gamma_lpdf(d | 1, 1) - 1 * gamma_lccdf(0 | 1, 1) ", 
                  check = FALSE)

But then the error I got was:

Error: The following priors do not correspond to any model parameter: shape_gen ~ gamma(c, d)

Doing both also lead me to an error. I am imagining that there is some interplay between model specification and prior specification that I am missing!

Could anybody help me?

  • Windows 10
  • brms Version: 2.13.3
2

Perhaps you can see more clearly what the correct class and group for each prior is by running:

get_prior(brmsForm, family = 'weibull', data = brmsData)

?