Comparative

Question 1

How does your work compare to log-ratio based approaches?

Answer 1

• bypasses log-ratio transformations, instead modelling compositional data in its original form taking into account both the relative and absolute values
• overcomes many limitations of applying log-ratio approaches specifically when there are zero or missing values present or the data has a count structure

Question 2

What are the key differences between GDM and Generalised-Dirichlet or Multinomial models?

Answer 2

• GDM extends both the GD and Multinomial distribution to provide a flexible distribution to model compositional counts
• GDM provides a flexible covariance structure which can model overdispersion in the counts
• GDM extends the GD by allowing x = 0 and x = N (total)
• Multinomial part explains some of the variability in the counts, while the GD component flexibly explain all other random variability - capturing different variance patterns
• GDM can also handle zeros (Multinomial yes, GD no) and missing values (Multinomial and GD no) in the compositions

Question 3

What trade-offs did you make between model complexity and interpretability?

Answer 3

• implemented Bayesian hierarchical models that are more complex computationally but provide greater flexibility and interpretability
• models allow latent structures (clusters, hidden states, spatial effects) to be specified
• opting for a Bayesian framework, I was also able to quantify uncertainty throughout the model, which enhances both interpretability and trustworthiness of the results

Question 4

How does your model scale with higher dimensions (more components)?

Answer 4

• each framework can scale reasonably well, but the MCMC sampling becomes more computationally demanding as complexity increases
• may not be an issue depending on the problem and time constraints of the application

Question 5

How would your models perform with compositional data from other domains?

Answer 5

• Although each framework was only tested using one example of compositional data - each approach is widely applicable across all domains of compositional data which consists of similar features to those presented.

Example:
* Environmental - Classification of soil type from repeated measurement of compositional values
* Ecological - Tracking evolution of species over time
* Epidemiological - Examining disease prevalence of multiple diseases in an area

Question 6

How does your method address overdispersion?

Answer 6

Overdispersion is addressed through the Generalised Dirichlet Multinomial, which extends the Multinomial by allowing flexible variance and correlation structures among components, component-specific dispersion parameters.

This avoids underestimating uncertainty, a common issue in traditional Multinomial.