Guidance on prior predictive checks in ordinal model

[natpac]

Thanks for the information avehtari. I think I better understand the

@avehtari

If you haven’t yet developed intuition about R2D2 prior, it might be better to not use it, and use something simpler for which you can more easily get understanding how to define it based on the external information.

I guess I have to revert back to more ‘classic’ priors for now and wait for more papers and guidance on how to use R2D2 priors… I am looking forward to it and thank you for the help still!

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@avehtari

This is what you said in your first post, and even if the data are not very informative on the coefficients, you can still be possible to do variable selection in the sense of which variables are sufficient for getting similar predictive performance as the full model performance and which variables can be dropped as redundant. Nothing needs to be said about whether the variables are true or false variables. Also the causal assumptions have to come from somewhere else.

@avehtari

Do you have strong prior-data conflict for the predictions? Do you care only about the predictions and which variables are needed for good predictive performance, or are you going to posterior marginals of coefficients for something?

My aim is to identify the meaningful coefficients (ecological traits) that predict (/drive) the extinction risk of species (my response variable).
(1) I get that projpred can help find a simpler model with similar predictive performance as the full model, but can it indicates which variables are dropped because they do not explain much vs which are redundant ? I am asking this as I have multiple covariates and some are numeric and others are categorical so it is hard to synthetize the redundancy between them.

@avehtari

It would be good to scale the covariates to have the same variance, as discussed in the paper. The paper has an example where different covariate scales cause prior-data conflict.

(2) About scaling covariates, I already scaled the two numeric covariates (one sd, not two) but I am stuck on the categorical covariates (and ordered; they can have up to 5 levels).
I have explored the non-linear syntax but setting the global intercept to 0 does not work with ordinal model.
I saw this post on dummy/index coding but the model takes forever to run with no good convergence + I am not sure if this techniques work when having multiple categorical covariates. Do you have suggestions ?