probitCJS function

Perform MCMC analysis of a CJS model

Takes design data list created with the function make.design.data for model "probitCJS" and draws a sample from the posterior distribution using a Gibbs sampler.

probitCJS(
  ddl,
  dml,
  parameters,
  design.parameters,
  burnin,
  iter,
  initial = NULL,
  imat = NULL
)

Arguments

• ddl: list of dataframes for design data; created by call to make.design.data
• dml: list of design matrices created by create.dm from formula and design data
• parameters: A model specification list with a list for Phi and p containing a formula and optionally a prior specification which is a named list. See 'Priors' section below.
• design.parameters: Specification of any grouping variables for design data for each parameter
• burnin: number of iteration to initially discard for MCMC burnin
• iter: number of iteration to run the Gibbs sampler for following burnin
• initial: A named list (Phi,p). If null and imat is not null, uses cjs.initial to create initial values; otherwise assigns 0
• imat: A list of vectors and matrices constructed by process.ch from the capture history data

Returns

A list with MCMC iterations and summarized output: - beta.mcmc: list with elements Phi and p which contain MCMC iterations for each beta parameter

• real.mcmc: list with elements Phi and p which contain MCMC iterations for each real parameter

• beta: list with elements Phi and p which contain summary of MCMC iterations for each beta parameter

• reals: list with elements Phi and p which contain summary of MCMC iterations for each real parameter

Prior distribution specification

The prior distributions used in probitCJS are multivariate normal with mean mu a and variance tau*(X'X)^(-1) on the probit scale for fixed effects. The matrix X is the design matrix based on the model specification (located in parameters$Phi$formula and parameters$p$formula respectively). Priors for random effect variance components are inverse gamma with shape parameter 'a' and rate parameter 'b'. Currently, the default values are mu=0 and tau=0.01 for phi and p parameters. For all randome effects deault values are a=2 and b=1.0E-4. In addition to the variance component each random effect can be specified with a known unscaled covariance matrix, Q, if random effects are correlated. For example, to obtain a random walk model for a serially correlated effect see Examples section below. To specify different hyper-parameters for the prior distributions, it must be done in the parameters list. See the Examples section for changing the prior distributions. Note that a and b can be vectors and the Qs are specified via a list in order of the random effects specified in the model statements.

Examples

# This example is excluded from testing to reduce package check time
# Analysis of the female dipper data
data(dipper)
dipper=dipper[dipper$sex=="Female",]
# following example uses unrealistically low values for burnin and 
# iteration to reduce package testing time
fit1 = crm(dipper,model="probitCJS",model.parameters=list(Phi=list(formula=~time),
 p=list(formula=~time)), burnin=100, iter=1000)
fit1
# Real parameter summary
fit1$results$reals

# Changing prior distributions:
fit2 = crm(dipper,model="probitCJS",
   model.parameters=list(
     Phi=list(formula=~time, prior=list(mu=rep(0,6), tau=1/2.85^2)),
     p=list(formula=~time, prior=list(mu=rep(0,6), tau=1/2.85^2))
   ), burnin=100, iter=1000)
fit2
# Real parameter summary
fit2$results$reals

# Creating a Q matrix for random walk effect for 6 recapture occasions
A=1.0*(as.matrix(dist(1:6))==1)
Q = diag(apply(A,1,sum))-A

# Fit a RW survival process
fit3 = crm(dipper,model="probitCJS",
   model.parameters=list(
     Phi=list(
       formula=~(1|time), 
       prior=list(mu=0, tau=1/2.85^2, re=list(a=2, b=1.0E-4, Q=list(Q)))
       ),
     p=list(formula=~time, prior=list(mu=rep(0,6), tau=1/2.85^2))
   ), burnin=100, iter=1000)
fit3
# Real parameter summary (Not calculated for random effects yet)
fit3$results$reals

Author(s)

Devin Johnson