Create native Dirichlet multinomial family

[tom-peatman]

Following discussion in #1728, I've had a go at creating a native Dirichlet multinomial family.

I've attempted to update the documentation of brmsfamily, and added some tests too.

I'm not confident that the posterior_epred.R function is correct, and probably should not have included it.

Hopefully this is helpful - please let me know if you need anything more from me. And thanks again @paul-buerkner for all your help with this!

[paul-buerkner]

Thank you! This PR looks good overall, I think.

Why are not confident about posterior_epred? You should be able to test it by comparing its output against the known(?) mean of the dirichlet_mulinomial distribution. I currently don't have time to check this detail myself.

[tom-peatman]

Thanks @paul-buerkner for taking a look at the PR - much appreciated.

I've now checked posterior_epred output for some simple models fitted to simulated data, and the output of posterior_epred is consistent with the distribution means. My understanding is that posterior_epred for the dirichlet_multinomial distribution should be the same as for the multinomial distribution (as overdispersion shouldn't influence the expected mean), so I believe that it is correct.

I also had a quick scan of the checks above in case the failed checks were related to the dirichlet_multinomial family - I don't think they are.

[paul-buerkner]

I have now checked the PR once again in a bit more detail and found a few more minor things to adjust before the PR is ready to be merged.

[tom-peatman]

Thanks @paul-buerkner for reviewing my pull request, and for your helpful comments and suggestions. I've made some minor updates in the latest commit, which hopefully address your questions.

[paul-buerkner]

Thanks! Can you add the initial transformations and check also do the density function as discussed above? Then the PR should be ready for merging.

[tom-peatman]

I'll implement the checks in the density function as requested above.

Though I'm not sure what you mean by initial transformations?

Do you also want me to add a specific help page for the dirichlet multinomial describing the parameterisation of the distribution (similar to ?BetaBinomial)? I just realised that I didn't do this first time around

[paul-buerkner]

I meant

if (is.null(dim(eta))) {
    eta <- matrix(eta, nrow = 1)
  }

but you already added that. I think it is fine if we keep the density internal for now. Just as we have it with dmultinomial. I will check the PR once again and then merge.

[tom-peatman]

OK great - thanks again for all your help with this!

[paul-buerkner]

Will merge now. Thank you for your contribution to brms! I highly appreciate it!

[tom-peatman]

Thanks @paul-buerkner, it was a pleasure to contribute and the least I can do as a very grateful user of brms!