Support censoring (in latent projection)

[fweber144]

This adds support for censored observations (i.e., survival or time-to-event analysis) when using the latent projection. Originally, #2 already mentioned that support for time-to-event models would be a nice feature, and the request came up again recently in https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275. This PR only makes it possible to use the latent projection for time-to-event models. For a more general perspective, see #2.

The solution presented here is not optimal because it would probably be more desirable to allow for an extension of the formula in init_refmodel() (similarly to brms's resp_cens() term), see https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275/10. Via such an extension of the init_refmodel() formula, we could also handle observation weights in a better way.

In contrast to the less elegant solution suggested in https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275/10, the solution presented here requires users to add a right-hand side formula as an attribute called cens_var to the latent_ll_oscale function. The variable named in that formula is then retrieved (internally, whenever calling the latent_ll_oscale function) from the original dataset (possibly subsetted to the observations from a given test set), newdata, or element data from varsel()'s argument d_test, whichever is applicable in the specific situation where the latent_ll_oscale function is called. The content of the retrieved variable is then passed to argument cens of the latent_ll_oscale function. In other words, the variable mentioned in the cens_var formula needs to contain the censoring indicators (e.g., 0 = uncensored, 1 = censored) which can then be used (by the user) within the latent_ll_oscale function. On the Stan Forums, I will update the Weibull (and perhaps also the log-normal) example from https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275 to illustrate this.

The solution presented here is still less elegant than the brms::resp_cens()-like solution, but in my opinion, it is preferable over the less elegant solution I suggested in https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275/10. Via the cens_var attribute, we also catch the censored-observations case (when using the latent projection) in validate_vsel_object_stats() to throw a warning if a performance statistic other than "elpd", "mlpd", or "gmpd" is used.

This is only a draft PR. Still to do:

• Update NEWS.md.
• Consider updating the vignettes. E.g., mention the support for censored observations in case of the latent projection in the main vignette (at https://mc-stan.org/projpred/articles/projpred.html#modtypes) and add an example to the latent-projection vignette. For the latter, the final example(s) from https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275 could be used.
• Consider updating the package description in the DESCRIPTION file to mention survival models.
• Add unit tests (for the latent projection with censored observations).

@avehtari: A few weeks ago, we discussed how we should make this feature available and we decided to keep this feature in a separate branch. Thinking over this again, I would say we could merge this into master as soon as the to-do's from above are completed. The reason is that I consider the implementation presented here not as "hacky" as the solution we discussed back then (which was the less elegant solution I suggested in https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275/10). But I'll leave the decision up to you and @aloctavodia what you want to do with this PR. Unfortunately, I was not able to request a review from @aloctavodia for this PR.

[fweber144]

On the Stan Forums, I will update the Weibull (and perhaps also the log-normal) example from https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275 to illustrate this.

Added now at https://discourse.mc-stan.org/t/using-projpred-latent-projection-with-brms-weibull-family-models/39275/23 (for the Weibull case).

[fweber144]

I forgot to add the new argument cens to internal latent_ll_oscale functions, but this is now done in commit 6b76269. The tests are running through now (i.e., they don't result in errors).

[avehtari]

Thinking over this again, I would say we could merge this into master as soon as the to-do's from above are completed. The reason is that I consider the implementation presented here not as "hacky" as the solution we discussed back then

OK for me to merge when it's ready