Separate priors for hyperparameters of varying effects by categorical variable

[ferberkl]

Hi Paul,

I'm trying to allow the full variance-covariance matrix of the random effects to vary across groups using the gr(re, by = "cat_var") syntax (from issue 365)

One feature request and one (I think) bug report:

The feature request is to be able to specify priors on the varying SDs separately by the "by" variable. This doesn't seem to be possible at the moment (version 2.12.0).

Second, the possible bug:

The syntax works with just varying intercepts, i.e. (1 | gr(re, by = "cat_var")), but I'm running into issues when I have multiple varying effects.

Using the epilepsy data example:

This works:

fit1 <- brm(count ~ zAge + zBase * Trt + (1|gr(patient, by=Trt)),
             data = epilepsy, family = poisson(), chains = 1)

This does not work:

fit2 <- brm(count ~ zAge + zBase * Trt + (1 + visit |gr(patient, by=Trt)),
            data = epilepsy, family = poisson(), chains = 1)

The error I'm getting in this reprex and also when I try this with my data is:

Chain 1: Rejecting initial value:
Chain 1:   Error evaluating the log probability at the initial value.
Chain 1: Exception: poisson_log_lpmf: Log rate parameter[1] is nan, but must not be nan!  (in 'model3e997988b9f9_7b6d2a531910ca110e77173edeb2ac8e' at line 85)

many times, followed by

Chain 1: 
Chain 1: Initialization between (-2, 2) failed after 100 attempts. 
Chain 1:  Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
[1] "Error in sampler$call_sampler(args_list[[i]]) : Initialization failed."

Many thanks.

[paul-buerkner]

Thanks for opening this issue. The bug should already be fixed in the github version of brms I think.

With regard to the feature request, I agree that it would be nice to specify priors separately. Not sure yet how to best intergrate that into the existing interface. Suggestions are welcome!

[ferberkl]

Thanks, Paul. It does seem to be working in the github version on my end.

Regarding how to set priors, I think it would make sense to use the interaction syntax. This is how the parameters are printed in the github version. For example, in the model:

fit2 <- brm(count ~ zAge + zBase * Trt + (1 + visit |gr(patient, by=Trt)),
            data = epilepsy, family = poisson(), chains = 1)

to set priors on the SDs:

set_prior("normal(0, 1)", class = "sd", group = "patient", coef = "Intercept:Trt0")

or perhaps the underscore syntax similar to what is used for correlation matrices.

set_prior("normal(0, 1)", class = "sd", group = "patient_Trt0", coef = "Intercept")
set_prior("normal(0, 1)", class = "sd", group = "patient_Trt1", coef = "Intercept")

For the correlation matrices, maybe something like the following:

set_prior("lkj(1)", class = "cor_patient_Trt0")
set_prior("lkj(2)", class = "cor_patient_Trt1")

[paul-buerkner]

Thanks. I think by should be either part of group of coef or something entirely new. Making it part of class would be inconsistent. I will need to think more of this and its implications.

[hallg92]

Hi Paul,

I'm wondering if this feature has been added to brms. I checked the documentation, and it did not appear to be, but I just wanted to make sure I was not missing something.

Thank you for all your work on brms. It is a really amazing resource.

[paul-buerkner]

this has not been implemented yet because it needs a new argument in the prior specification functions and I have to think carefully about a name and how that can be generalized later on.

hallg92 @.***> schrieb am So., 24. Okt. 2021, 03:57:

Hi Paul,

I'm wondering if this feature has been added to brms. I checked the documentation, and it did not appear to be, but I just wanted to make sure I was not missing something.

Thank you for all your work on brms. It is a really amazing resource.

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