Mark–Recapture: Basic Models
We consider two basic live-recapture models referred to as the CJS model (after Cormack–Jolly–Seber) that models the tagged data, and the JS model (after Jolly and Seber in Biometrika, 52:225–247, 1965), which also includes the untagged data. Likelihood methods as originally used are described, while Bayesian and random-effects methods have since been developed for the CJS model using logistic transformations of the parameters. Various goodness-of-fit tests, contingency table tests, and score tests are described for testing underlying assumptions and model fitting. Extensions we consider involve batch methods, utilizing various kinds of covariate information (including missing values), and Bayesian covariate methods. Other techniques include using splines for logistic transformations and the EM algorithm for the CJS (Cormack–Jolly–Seber) model. We consider the important development of a super-population approach that provides a better framework for dealing with hierarchical models and extensions to using groups.