Mixture Distributions

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Mixture Distributions

Mixture distributions are used to model individual heterogeneity of capture probabilities (Pledger 2000, Norris and Pollock 1996) in the closed captures data type.  To change the number of mixture distributions, you have to change data type, available under the PIM menu choice. Mixture models have also been added for the occupancy data type, and the robust design occupancy data types.  In addition, mixture models for open populations are available for the Cormack-Jolly-Seber data type, the Pradel data type, the Link-Barker data type, and the Seber parameterization of dead recoveries data type (only the survival rate is included in the mixtures, Pledger and Schwarz 2002)..

Mixture models consist of a pi parameter that gives the probability of a mixture, with the sum of the pi values equaling 1.  In MARK, 1 less pi value is included in the model, so that the last pi value is obtained by substraction.  When you specify >2 mixtures, the multinomial logit link function (mlogit link function) on pi is useful to maintain this constraint.

The PIM for the parameter that is being modeled as a mixture has separate rows for each mixture.  So, as an example, for the Pradel mixture model, the p parameter is modeled as a mixture.  Each row of the p PIM corresponds to a mixture.  With 2 mixtures, there are 2 rows of p parameters.  The same structure is used for the closed capture models with mixtures.

Mixture models can have multiple modes, so care with their optimization should be taken.  The simulated annealing algorithm included in MARK is a good method to avoid local maxima.