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Estimation in parameter-redundant models

The likelihood surface resulting from a parameter-redundant stochastic model is maximised along a completely flat ridge. This ridge may be orthogonal to some parameter axes, so that these parameters have unique maximum likelihood estimates. For exponential-family models, we show how to determine which parameter combinations are estimable. The approach requires the calculation of a derivative matrix and the determination of its null space, both of which are readily achieved in computer algebra packages. Illustrative examples are drawn from the areas of compartment modelling and ring-recovery analysis.