markCJS {multimark}

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

Description

This function fits Cormack-Jolly-Seber (CJS) open population models for survival probability (\phi) and capture probability (p) 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

markCJS(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  mod.phi = ~1,
  parms = c("pbeta", "phibeta"),
  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,
  propphibeta = 0.1,
  propzphi = 1,
  propsigmaphi = 1,
  pbeta0 = 0,
  pSigma0 = 1,
  phibeta0 = 0,
  phiSigma0 = 1,
  l0p = 1,
  d0p = 0.01,
  l0phi = 1,
  d0phi = 0.01,
  initial.values = NULL,
  link = "probit",
  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 (p). For example, mod.p=~1 specifies no effects (i.e., intercept only), mod.p~time specifies temporal effects, mod.p~age specifies age effects, mod.p~h specifies individual heterogeneity, and mod.p~time+age specifies additive temporal and age effects.

mod.phi

Model formula for survival probability (\phi). For example, mod.phi=~1 specifies no effects (i.e., intercept only), mod.phi~time specifies temporal effects, mod.phi~age specifies age effects, mod.phi~h specifies individual heterogeneity, and mod.phi~time+age specifies additive temporal and age effects.

parms

A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are probit-scale detection probability parameters ("pbeta" for p and "phibeta" for \phi), probit-scale individual heterogeneity variance terms ("sigma2_zp" for p and "sigma2_zphi" for \phi), and probit-scale individual effects ("zp" and "zphi"). Latent variable indicators for whether each individual was alive (1) or dead (0) during each sampling occasion ("q") and the log likelihood ("loglike") 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

Ignored; no adaptive phase is needed for "probit" link.

bin

Ignored; no adaptive phase is needed for "probit" link.

thin

Thinning interval for monitored parameters.

burnin

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

taccept

Ignored; no adaptive phase is needed for "probit" link.

tuneadjust

Ignored; no adaptive phase is needed for "probit" link.

proppbeta

Ignored; no adaptive phase is needed for "probit" link.

propzp

Ignored; no adaptive phase is needed for "probit" link.

propsigmap

Ignored; no adaptive phase is needed for "probit" link.

propphibeta

Ignored; no adaptive phase is needed for "probit" link.

propzphi

Ignored; no adaptive phase is needed for "probit" link.

propsigmaphi

Ignored; no adaptive phase is needed for "probit" link.

pbeta0

Scaler or vector (of length k) specifying mean of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If pbeta0 is a scaler, then this value is used for all j = 1, ..., k. Default is pbeta0 = 0.

pSigma0

Scaler or k x k matrix specifying covariance matrix of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If pSigma0 is a scaler, then this value is used for all pSigma0[j,j] for j = 1, ..., k (with pSigma[j,l] = 0 for all j \ne l). Default is pSigma0 = 1.

phibeta0

Scaler or vector (of length k) specifying mean of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If phibeta0 is a scaler, then this value is used for all j = 1, ..., k. Default is phibeta0 = 0.

phiSigma0

Scaler or k x k matrix specifying covariance matrix of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If phiSigma0 is a scaler, then this value is used for all phiSigma0[j,j] for j = 1, ..., k (with phiSigma[j,l] = 0 for all j \ne l). Default is phiSigma0 = 1.

l0p

Specifies "shape" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is l0p = 1.

d0p

Specifies "scale" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is d0p = 0.01.

l0phi

Specifies "shape" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is l0phi = 1.

d0phi

Specifies "scale" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is d0phi = 0.01.

initial.values

OOptional list of nchain list(s) specifying initial values for "pbeta", "phibeta", "sigma2_zp", "sigma2_zphi", "zp", "zphi", and "q". Default is initial.values = NULL, which causes initial values to be generated automatically.

link

Link function for survival and capture probabilities. Only probit link is currently implemented.

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 and mod.phi. See RMark::make.design.data.

Details

The first time markCJS (or markClosed) 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 multimarkCJS. Note that setting parms="all" is required for any markCJS model output to be used in multimodelCJS.

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.phi

Model formula for survival probability (as specified by mod.phi above).

mod.delta

Formula always NULL; only for internal use in multimodelCJS.

DM

A list of design matrices for detection and survival probability respectively generated by mod.p and mod.phi, where DM$p is the design matrix for capture probability (p) and DM$phi is the design matrix for survival probability (\phi).

initial.values

A list containing the parameter and latent variable values at iteration iter for each chain. Values are provided for "pbeta", "phibeta", "sigma2_zp", "sigma2_zphi", "zp", "zphi", and "q".

mms

An object of class multimarksetup

Author(s)

Brett T. McClintock

See Also

processdata, multimodelCJS

Examples

# These examples are excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data using defaults
data <- simdataCJS(delta_1=1,delta_2=0)$Enc.Mat

#Fit default open population model
sim.dot <- markCJS(data)

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

#Fit ``age'' model with 2 age classes (e.g., juvenile and adult) for survival
#using 'parameters' and 'right' arguments from RMark::make.design.data
sim.age <- markCJS(data,mod.phi=~age,
           parameters=list(Phi=list(age.bins=c(0,1,4))),right=FALSE)
summary(getprobsCJS(sim.age))