title: Parameter redundancy in discrete state-space and integrated models.
abstract: Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.
authors.affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, England. d.j.cole@kent.ac.uk.
authors.forename: Diana J
authors.initials: DJ
authors.lastname: Cole
authors.affiliation: School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, England.
authors.forename: Rachel S
authors.initials: RS
authors.lastname: McCrea
mesh_terms: D000818:Animals; D004463:Ecology / Q000379:methods*; D008954:Models, Biological; D011336:Probability
keywords: Capture-recapture; Identifiability; Joint likelihood; Mark-recovery models; Population dynamics