Interpretation: betas and alphas, common vs. alternative parameterization

[mirpie]

Hello!

First off, thanks for such an amazing package.

Second, apologies that this is more of an interpretation issue rather than a bug or technical contribution.

I am not a math person by trade, but I want to implement Dirichlet regression in order to model some flow cytometry data.

In my specific case, I have mice at 4 different timepoints (1w, 2w, 24d and 8w) which I'm treating as my IV. I want to understand how these populations change over time. I've opted for the alternative parameterization to account for changes in precision between age groups. I have a table of cell population proportions based on quadrant gating (CD4/CD8 +/-) and want to model the compositional change in single positive (CD4+ or CD8+, SP) and double positive (DP) cells over time with double negative cells being the base or reference category.

I was hoping for some guidance on how the coefficients obtained in my results (below) relate to the absolute changes in proportion as shown in the graph below.

The sign of the alphas generally seem to align with the observed changes in abundance between timepoints, and as I understand it the B coefficients can be interpreted as an odds ratio when exponentiated under this parameterization (according to the vignette). However, I am struggling to formulate my conclusions in a concrete way and could use some help relating these estimates back to expected value means and the alpha parameters of the corresponding marginal DD.

Furthermore, when I extract the alpha's, mu's and phi's from the fitted values for the model, it seems that there are still values present for the base (DN) category...why is this the case? How should I interpret these values relative to those for my variables of interest?

Thanks so much!

M