markClosed {multimark}

Fit closed population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

This function fits closed population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

markClosed(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  parms = c("pbeta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  npoints = 500,
  a = 25,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  initial.values = NULL,
  printlog = FALSE,
  ...
)

Arguments

Enc.Mat

A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions. With a single mark type, encounter histories consist of only non-detections (0) and type 1 encounters (1).

covs

A data frame of temporal covariates for detection probabilities (ignored unless mms=NULL). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying mod.p and mod.phi.

mod.p

Model formula for detection probability. For example, mod.p=~1 specifies no effects (i.e., intercept only), mod.p~time specifies temporal effects, mod.p~c specifies behavioral reponse (i.e., trap "happy" or "shy"), mod.p~h specifies individual heterogeneity, and mod.p~time+c specifies additive temporal and behavioral effects.

parms

A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are logit-scale detection probability parameters ("pbeta"), population abundance ("N"), logit-scale individual heterogeneity variance term ("sigma2_zp"), and logit-scale individual effects ("zp"). The log posterior density ("logPosterior") may also be monitored. Setting parms="all" monitors all possible parameters and latent variables.

nchains

The number of parallel MCMC chains for the model.

iter

The number of MCMC iterations.

adapt

The number of iterations for proposal distribution adaptation. If adapt = 0 then no adaptation occurs.

bin

Bin length for calculating acceptance rates during adaptive phase (0 < bin <= iter).

thin

Thinning interval for monitored parameters.

burnin

Number of burn-in iterations (0 <= burnin < iter).

taccept

Target acceptance rate during adaptive phase (0 < taccept <= 1). Acceptance rate is monitored every bin iterations. Default is taccept = 0.44.

tuneadjust

Adjustment term during adaptive phase (0 < tuneadjust <= 1). If acceptance rate is less than taccept, then proposal term (proppbeta, propzp, or propsigmap) is multiplied by tuneadjust. If acceptance rate is greater than or equal to taccept, then proposal term is divided by tuneadjust. Default is tuneadjust = 0.95.

proppbeta

Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If proppbeta is a scaler, then this value is used for all j = 1, ..., k. Default is proppbeta = 0.1.

propzp

Scaler or vector (of length M) specifying the initial standard deviation of the Normal(zp[i], propzp[i]) proposal distribution. If propzp is a scaler, then this value is used for all i = 1, ..., M individuals. Default is propzp = 1.

propsigmap

Scaler specifying the initial Gamma(shape = 1/propsigmap, scale = sigma_zp * propsigmap) proposal distribution for sigma_zp = sqrt(sigma2_zp). Default is propsigmap=1.

npoints

Number of Gauss-Hermite quadrature points to use for numerical integration. Accuracy increases with number of points, but so does computation time.

a

Scale parameter for [sigma_z] ~ half-Cauchy(a) prior for the individual hetegeneity term sigma_zp = sqrt(sigma2_zp). Default is “uninformative” a = 25.

mu0

Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If mu0 is a scaler, then this value is used for all j = 1, ..., k. Default is mu0 = 0.

sigma2_mu0

Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If sigma2_mu0 is a scaler, then this value is used for all j = 1, ..., k. Default is sigma2_mu0 = 1.75.

initial.values

Optional list of nchain list(s) specifying initial values for "pbeta", "zp", "sigma2_zp", and "N". Default is initial.values = NULL, which causes initial values to be generated automatically.

printlog

Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when nchains=1. Updates are printed to log file as 1% increments of iter of each chain are completed. With >1 chains, setting printlog=TRUE is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when printlog=FALSE. Default is printlog=FALSE.

...

Additional "parameters" arguments for specifying mod.p. See make.design.data.

Details

The first time markClosed (or markCJS) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in markClosed. Note that setting parms="all" is required for any markClosed model output to be used in multimodelClosed.

Value

A list containing the following:

mcmc

Markov chain Monte Carlo object of class mcmc.list.

mod.p

Model formula for detection probability (as specified by mod.p above).

mod.delta

Formula always NULL; only for internal use in multimodelClosed.

DM

A list of design matrices for detection probability generated for model mod.p, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c).

initial.values

A list containing the parameter and latent variable values at iteration iter for each chain. Values are provided for "pbeta", "zp", "sigma2_zp", and "N".

mms

An object of class multimarksetup

Author(s)

Brett T. McClintock

See Also

multimodelClosed

Examples

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for simulated ``traditional'' data
data<-simdataClosed(delta_1=1,delta_2=0)$Enc.Mat
sim.dot<-markClosed(data)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)