Unconditional likelihood inference for behavioural effect models based on an ad-hoc partition of the set of all partial capture histories

Description

Unconditional likelihood inference for a general model framework based on the capture probabilities conditioned on each possible partial capture history. As suggested in Alunni Fegatelli and Tardella (2012) the conditional approach originally proposed in Farcomeni (2011) [saturated reparameterization] is reviewed in terms of partitions into equivalence classes of conditional probabilities. In this function the user can directly provide the model as a partition.

Usage

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LBRecap.custom.part (data,last.column.count=FALSE, partition, neval = 1000, 
    by.incr = 1, output = c("base", "complete"))
    

Arguments

data

can be one of the following:

  1. an M by t binary matrix/data.frame

  2. a matrix/data.frame with (t+1) columns according to the value of
    last.column.count

  3. a t-dimensional array or table representing the counts of the 2^t contingency table of binary outcomes M is the number of units captured at least once and t is the number of capture occasions.

last.column.count

a logical. In the default case last.column.count=FALSE each row of data represents the complete capture history for each observed unit. When codelast.column.count=TRUE in each row the first t entries represent one of the possible observed complete capture histories and the last entry (last column) is the number of observed units with that capture history

partition

list. partition represents a partition of the set of all partial capture histories.

neval

a positive integer. neval is the number of values evaluated for the population size N. The default value is neval=1000.

by.incr

a positive integer. by.incr represents the increment on the sequence of evaluated values for N. The default value is by.incr=1.

output

character. output select the kind of output from a very basic summary info on the posterior output (point and interval estimates for the unknown N) to more complete details.

Details

The unconditional likelihood is evaluated by means of glm/glmer for each value of the N parameter and it is then maximized.

Value

(if output="complete") the function LBRecap returns a list of:

  1. N.hatunconditional maximum likelihood estimate for N

  2. CIinterval estimate for N

  3. pH.hatpoint estimate of nuisance parameters (conditional probabilities)

  4. AICAkaike information criterion.

  5. L.FailureLikelihood Failure condition

  6. N.rangesequence of N values considered

  7. log.likvalues of the log-likelihood distribution for each N considered

  8. partitionslist of subsets of partial capture histories corresponding to equivalence classes

Author(s)

Danilo Alunni Fegatelli and Luca Tardella

References

Alunni Fegatelli, D. and Tardella, L. (2012) Improved inference on capture recapture models with behavioural effects. Statistical Methods & Applications Applications Volume 22, Issue 1, pp 45-66 10.1007/s10260-012-0221-4

Farcomeni A. (2011) Recapture models under equality constraints for the conditional capture probabilities. Biometrika 98(1):237–242

See Also

partition.ch, BBRecap.custom.part, LBRecap

Examples

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data(greatcopper)
partition.Mc1=partition.ch(quant.binary,t=ncol(greatcopper),breaks=c(0,0.5,1))
mod.Mc1=LBRecap.custom.part(greatcopper,partition=partition.Mc1)
str(mod.Mc1)