batchMarkUnmarkOptim {extBatchMarking}

Combined Marked and Unmarked models.

Description

batchMarkUnmarkOptim function provides the batch marking and unmarked function to be optimized.

Usage

batchMarkUnmarkOptim(
  par = NULL,
  data,
  choiceModel = c("model1", "model2", "model3", "model4"),
  method = c("Nelder-Mead", "BFGS", "CG", "L-BFGS-B"),
  Umax = 1800,
  nBins = 20,
  popSize = c("Horvitz_Thompson", "Model-Based"),
  parallel = FALSE,
  lowerBound = -Inf,
  cores = 1,
  hessian = FALSE,
  control,
  ...
)

Arguments

par

Initial values for the parameters to be optimized over.

data

A capture-recapture data matrix or data frame

choiceModel

This chooses among different models and allow for model selection

method

The method to be used. See optim for details.

Umax

The maximum number of the unmarked individuals in the population for capture on any occasion.

nBins

The number of bin size into which the matrix will be divided.

popSize

The Horvitz_Thompson method or Model-Based to compute population size.

parallel

Logical. Should the algorithm be run in parallel? This will be implemented in a future version.

lowerBound

Lower bounds on the variables for the "L-BFGS-B" method.

cores

The number of cores for parallelization

hessian

Logical. Should a numerically differentiated Hessian matrix be returned?

control

a list of control parameters. See optim for details.

...

Further arguments to be passed by user which goes into the optim function.

Details

Note that arguments after ... must be matched exactly.

batchMarkUnmarkOptim depends on optim function to optimize the parameters of the combined model. By default optim performs minimization.

Example on Umax and nBins: Umax = 1800 has a matrix of 1801 x 1801 and nBins = 20, reduces the matrix to 90 x 90. This is done in Cowen et al., 2017 to reduce the computing time when dealing with large matrix.

Value

A list of the following optimized parameters will be returned.

phi

The survival probability and remaining in the population between occasion t and t+1.

p

The capture probability at occasion time t.

ll

The optimized log-likelihood value of marked model.

hessian

The hessian matrix.

AIC

The Akaike Information Criteria for model selection.

lambda

Initial mean abundance at occasion t = 1.

gam

Recruitment rate of individual into the unmarked population.

M

Total number of marked individual in the population.

U

Total number of unmarked individuals in the population available for capture at occasion t = 1,..., T.

N

Total population size at time t = 1, ..., T.

References

Laura L. E. Cowen, Panagiotis Besbeas, Byron J. T. Morgan, 2017.: Hidden Markov Models for Extended Batch Data, Biometrics, 73, 1321-1331. DOI: 10.1111/biom.12701.

Examples

# Load the package
library(extBatchMarking)

# Load the WeatherLoach data from Cowen et al., 2017.
data(WeatherLoach)

# Initial parameter values
theta <- c(0.1, 0.1, 7, -1.5)


mod1 <- batchMarkUnmarkOptim(
           par         = theta,
           data        = WeatherLoach,
           Umax        = 1800,
           nBins       = 20,
           choiceModel = "model4",
           popSize    = "Horvitz_Thompson",
           method      = "CG",
           parallel    = FALSE,
           control     = list(trace = 1))

 # Survival probability
 mod1$phi
 # Capture probability
 mod1$p
 # Optimized log-likelihood
 mod1$ll
 # The Hessian matrix
 mod1$hessian
 # The Aikaike Information Criteria
 mod1$AIC
 # The initial mean abundance
 mod1$lambda
 # Recruitment rate into the population
 mod1$gam
 # The estimated abundance of unmarked animals
 mod1$U
 # The estimated abundance of marked animals
 mod1$M
 # The estimated total abundance of marked and unmarked animals
 mod1$N
 

 
mod2 <- batchMarkUnmarkOptim(
           par         = theta,
           data        = WeatherLoach,
           Umax        = 1800,
           nBins       = 20,
           choiceModel = "model4",
           popSize    = "Model-Based",
           method      = "L-BFGS-B",
           parallel    = FALSE,
           control     = list(trace = 1))

 # Survival probability
 mod2$phi
 # Capture probability
 mod2$p
 # Optimized log-likelihood
 mod2$ll
 # The Hessian matrix
 mod2$hessian
 # The Akaike Information Criteria
 mod2$AIC
 # The initial mean abundance
 mod2$lambda
 # Recruitment rate into the population
 mod2$gam
 # The estimated abundance of unmarked animals
 mod2$U
 # The estimated abundance of marked animals
 mod2$M
 # The estimated total abundance of marked and unmarked animals
 mod2$N