Determining the parametric structure of models

In this paper we develop a comprehensive approach to determining the parametric structure of models. This involves considering whether a model is parameter redundant or not and investigating model identifiability. The approach adopted makes use of exhaustive summaries, quantities that uniquely define the model. We review and generalise previous work on evaluating the symbolic rank of an appropriate derivative matrix to detect parameter redundancy, and then develop further tools for use within this framework, based on a matrix decomposition. Complex models, where the symbolic rank is difficult to calculate, may be simplified structurally using reparameterisation and by finding a reduced-form exhaustive summary. The approach of the paper is illustrated using examples from ecology, compartment modelling and Bayes networks. This work is topical as models in the biosciences and elsewhere are becoming increasingly complex.