Identifiability of Linear Compartmental Models: The Effect of Moving Inputs, Outputs, and Leaks

TL;DR

This paper studies how moving, adding, or removing inputs, outputs, leaks, and edges affects the identifiability of parameters in linear compartmental models, providing conditions under which identifiability is preserved or lost.

Contribution

It characterizes the effects of structural modifications on model identifiability, offering algebraic and combinatorial criteria for preserving or losing identifiability in various models.

Findings

Moving or deleting leaks can preserve identifiability in certain models.

Cycle models with up to one leak remain identifiable when inputs or outputs are moved.

Adding leaks can make some cycle models unidentifiable.

Abstract

A mathematical model is identifiable if its parameters can be recovered from data. Here we investigate, for linear compartmental models, whether (local, generic) identifiability is preserved when parts of the model -- specifically, inputs, outputs, leaks, and edges -- are moved, added, or deleted. Our results are as follows. First, for certain catenary, cycle, and mammillary models, moving or deleting the leak preserves identifiability. Next, for cycle models with up to one leak, moving inputs or outputs preserves identifiability. Thus, every cycle model with up to one leak (and at least one input and at least one output) is identifiable. Next, we give conditions under which adding leaks renders a cycle model unidentifiable. Finally, for certain cycle models with no leaks, adding specific edges again preserves identifiability. Our proofs, which are algebraic and combinatorial in nature, rely on results on elementary symmetric polynomials and the theory of input-output equations for linear compartmental models.