Introducing a new framework for statistical modelling called regression by composition.
Regression by composition breaks down statistical models into building blocks called ‘flows’. Flows can modify probability distributions in a variety of ways. Shifting or scaling are familiar flows from standard regression approaches, but in combination with others they generate flexible parametric models for applications in medical statistics.
Motivated by examples from growth modelling and a randomised controlled trial in HIV, we will demonstrate how regression by composition allows us to fit nonstandard statistical models tailored to our understanding of these applications.
Via these examples, we will introduce some of the theory underlying regression by composition, in which linear predictors have group actions called flows (think “families of transformations”) on probability distributions. It turns out that properties of regression models like the collapsibility of implied contrasts relate directly to algebraic and geometric features of group actions.
Speakers
- Rhian Daniel - Professor of Statistics at Cardiff University
- Daniel Farewell - Professor of Statistics at Cardiff University
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