Setting priors for multinomial regression in brms

Modeling
,
1

Hi, I’m new to bayesian modelling and brms so maybe my question is trivial. However, I’m fitting a multinomial regression using brms. The response variable response is modeled as a function of a binary factor GROUP and then a random intercept for subjects 1|ID. This is my model:

fit <- brm(response ~ GROUP + (1|ID),
                  cores = n_cores,
                  family = categorical(link = "logit"),
                  data = data_exp1,
                  chains = 6,
                  iter = 4000,
                  warmup = 2000,
                  control = list(adapt_delta = 0.999,
                                 max_treedepth = 15))

The control parameters were set according to some warnings about the model (following this https://mc-stan.org/misc/warnings).
This model works fine but the compilation time is very long (30 minutes) so I’ve read about putting slightly informative priors according to my parameters.

This is the prior summary (with default priors):

prior_summary(fit)
                 prior     class      coef group resp       dpar nlpar bound
1                              b                       mudisgust            
2                              b  GROUPIMS             mudisgust            
3                              b                          mufear            
4                              b  GROUPIMS                mufear            
5                              b                       musadness            
6                              b  GROUPIMS             musadness            
7                              b                      musurprise            
8                              b  GROUPIMS            musurprise            
9  student_t(3, 0, 10) Intercept                       mudisgust            
10 student_t(3, 0, 10) Intercept                          mufear            
11 student_t(3, 0, 10) Intercept                       musadness            
12 student_t(3, 0, 10) Intercept                      musurprise            
13 student_t(3, 0, 10)        sd                       mudisgust            
14 student_t(3, 0, 10)        sd                          mufear            
15 student_t(3, 0, 10)        sd                       musadness            
16 student_t(3, 0, 10)        sd                      musurprise            
17                            sd              ID       mudisgust            
18                            sd Intercept    ID       mudisgust            
19                            sd              ID          mufear            
20                            sd Intercept    ID          mufear            
21                            sd              ID       musadness            
22                            sd Intercept    ID       musadness            
23                            sd              ID      musurprise            
24                            sd Intercept    ID      musurprise

Given that my fixed effects are all odds ratio in log scale a reasonable prior might be a normal distribution with mean = 0 and a broad SD.

fixef(fit)
                       Estimate Est.Error       Q2.5     Q97.5
mudisgust_Intercept   1.3054715 0.4063684  0.5105506 2.1279143
mufear_Intercept      2.7147141 0.3380190  2.0931628 3.4193736
musadness_Intercept   0.6062926 0.4717226 -0.3891898 1.5063598
musurprise_Intercept  1.0915517 0.4007677  0.2983177 1.8751994
mudisgust_GROUPIMS    0.2545814 0.6390059 -0.9781262 1.5333117
mufear_GROUPIMS      -0.6974617 0.5408466 -1.7542061 0.3734919
musadness_GROUPIMS   -1.2186215 0.8067931 -2.8796989 0.3203030
musurprise_GROUPIMS  -0.4853391 0.6435296 -1.7527883 0.7877122

I’ve set my priors but a warning message appears during the fitting about the deprecated usage of a global priors on all beta parameters and this could bring to unexpected results.

mod_prior = c(prior_string("normal(0, 10)", class = "b"),
              prior_string("normal(0, 10)", class = "Intercept"))

Given that I would like to simply speed my fitting time what could I do?

2

You could set the SD of the normal distribution smaller (to 3 or 2.5 say) but I doubt this will speed up the computation much.

3

What could also help, is that you also set more narrower priors on the sd parameters.

4

Thanks @paul.buerkner! So can I ignore the warning message about setting a global prior? in this case I think that all my population-level fixed parameters are the same in terms of prior distribution.

5

The warning just means that this way of specification is deprecated and may not continue to work in future versions of brms.

6

Perfect! I’ve also found that another (maybe better) solution could be to remove the intercept response ~ 0 + GROUP and then setting a global prior on b class.