Highly variable prior predictive check. Even y is changing

[JLC]

I’m trying to refine a distributional model using a Student distribution for the outcome, but am seeing highly variable prior predictive checks. I have defined y from the data, but even the plot of y is moving all over the place.

Just wondering what I might be doing wrong with my specification.

fmla <- bf(y ~ 0 + Intercept + 
                                             Pred1.c +
                                             Pred2.c +
                                             Pred3.c +
                                             Pred4.c +
                                             Pred5.c +
                                             (1|Grp1) +
                                             (1|Grp2) +
                                             (1|Grp3) +
                                             (1|Grp4/Grp5),
                                     center = TRUE,
                                     sigma ~ 0 + (1|Grp2) + (1|Grp1),
                                     nu ~ 0 + (1|Grp2) + (1|Grp1))

## Set priors
priors <- c(
        set_prior("normal(10,5)",
                  class = "b",
                  coef = "Intercept" ),
        
        set_prior("normal(0,1)",
                  class = "b"),
        
        set_prior("normal(0,1)",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp3"),
        
        set_prior("normal(1,1)",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp4"),
        
        set_prior("normal(0,1)",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp5:Grp5"),
        
        set_prior("normal(0,3)",
                  class = "sd",
                  coef = "Intercept",
                  group = Grp1"),
        
        set_prior("normal(0,0.5)",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp1",
                  dpar = "sigma"),
        
        set_prior("normal(0,0.5)",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp2",
                  dpar = "sigma"),

        set_prior("normal(0,1/sqrt(4))",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp1",
                  dpar = "nu"),
        
        set_prior("normal(0,1/sqrt(4))",
                  class = "sd",
                  coef = "Intercept",
                  group = "Grp2",
                  dpar = "nu") 
)

Mod <- brm(
       fmla,
        Data,
        family = student(link_nu = "logm1"),
        prior = priors,
        inits = 0,
        iter = 5000,
        warmup = 2500,
        chains = 4,
        cores = ncores,
        sample_prior = "only",
        save_pars = save_pars(all = TRUE),
        control = list(max_treedepth = 14,
                       adapt_delta = 0.999)
)

With separate runs of yrep, the plot of y also changes a lot.

y <- Data$y
yrep <- posterior_predict(Mod ,nsamples = 100)

ppc_dens_overlay(y, 
                 yrep) + 
        coord_cartesian(xlim = c(-50, 50))

Am I calling something incorrectly?

[torkar]

Try to remove the coord_cartesian(xlim=c(-50,50)) to get a feeling for what happens. Is y count data, i.e., -n,..,-3,-2,-1,0,1,2,3,..n?

[JLC]

Thanks, @torkar

y is continuous and unbounded in a practical sense. I put the limits on the x-axis because the predictions are so broad that it’s difficult to see anything without the limits:

I’m curious about why the plot of y would change when it’s a static vector from the data.

[torkar]

Hi,

try scale_x_continuous(trans="log"). You have random draws from the posterior, so perhaps increase it to nsamples=500 to get a better feel for the variability?

[JLC]

Thank you! That certainly gives a better and more stable view: