Choosing default or PC priors for BYM model

[Marina Espinasse]

Dear INLA users,

I got confused with choosing between the default priors for a spatial BYM model and penalized complexity priors. I've seen in the book of Moraga et al (2020) that PC priors have advantages like choosing less complex model. So I tried them for hyperparameters of BYM spatial model instead of just default priors.

The results change dramatically - covariates that were not important when sing default priors come out as important. And I also tested several spatial-temporal interactions, the results are also different when using default of PC priors.

I am not sure, if I should really use the PC priors. Is there any way to justify the PC priors or compare the models with two types of priors? DIC suggest that PC-based models are better but they make less practical sense, than models based on the default priors. 

Would you please give an advice how to choose the priors?

Thank you so much!

Marina

[Marina Espinasse]

Hey Håvard and Finn,

I see that my post was not commented, please, let me know if my question was not appropriate to ask here, in the rinla discussion group.

Thank you!

Marina

[Helpdesk]

Hi,

I guess you mean the 'bym2' model, which is the one developed in the
Riebler et al paper

https://journals.sagepub.com/doi/abs/10.1177/0962280216660421?journalCode=smma

these default priors make sense with Poisson data, as other likelihoods
might require a different scaling.

The default priors for precision, like those in 'bym' or 'besag' I would
not trust; they are within the 'tradition' but I do not find these
choices to be well justified anymore (please see the PC-prior paper in
Statistical Science 2017).

without scale.model=T (default for bym2), you'll have another issue,
that is an arbitrary scaling from the model itself, which some find kind
of surprising but it obvious if one look into the details.

I can be a combination of these things makes the results differ, but the
only model I trust myself is the 'bym2'.

Best
H

On Mon, 2022-01-24 at 00:06 -0800, Marina Espinasse wrote:
> >

> > I got confused with choosing between the default priors for a
> > spatial BYM model and penalized complexity priors. I've seen in the
> > book of Moraga et al (2020) that PC priors have advantages like
> > choosing less complex model. So I tried them for hyperparameters of
> > BYM spatial model instead of just default priors.
> > The results change dramatically - covariates that were not important
> > when sing default priors come out as important. And I also tested
> > several spatial-temporal interactions, the results are also
> > different when using default of PC priors.
> >
> > I am not sure, if I should really use the PC priors. Is there any
> > way to justify the PC priors or compare the models with two types of
> > priors? DIC suggest that PC-based models are better but they make
> > less practical sense, than models based on the default priors. 
> >
> > Would you please give an advice how to choose the priors?
> >
> > Thank you so much!
> >
> > Marina

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Håvard Rue
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