RMark (version 3.0.0)

robust: Robust design example data

Description

A robust design example data set that accompanies MARK as an example analysis using the various models for the robust design.

Format

A data frame with 668 observations on the following 2 variables.

ch

a character vector containing the encounter history

freq

the number of critters with that capture history

Details

This is a data set that accompanies program MARK as an example for robust models. The data are entered with the summary format using the variable freq which represents the number of critters with that capture (encounter) history. The data set represents a robust design with 5 primary occasions and within each primary occasion the number of secondary occasions is 2,2,4,5,2 respectively. This is represented with the time.intervals argument of process.data which are 0,1,0,1,0,0,0,1,0,0,0,0,1,0. The 0 time intervals represent the secondary sessions in which the population is assumed to be closed. The non-zero values are the time intervals between the primary occasions. They are all 1 in this example but they can have different non-zero values. The code determines the structure of the robust design based on the time intervals. The intervals must begin and end with at least one 0 and there must be at least one 0 between any 2 non-zero elements. The number of occasions in a secondary session is one plus the number of contiguous zeros.

Examples

# \donttest{
# This example is excluded from testing to reduce package check time
data(robust)
run.robust=function()
{
#
# data from Robust.dbf with MARK
# 5 primary sessions with secondary sessions of length 2,2,4,5,2
#
time.intervals=c(0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0)
#
# Random emigration, p=c varies by time and session, S by time
#
S.time=list(formula=~time)
p.time.session=list(formula=~-1+session:time,share=TRUE)
GammaDoublePrime.random=list(formula=~time,share=TRUE)
model.1=mark(data = robust, model = "Robust", 
            time.intervals=time.intervals,
            model.parameters=list(S=S.time,
            GammaDoublePrime=GammaDoublePrime.random,p=p.time.session),threads=2,delete=TRUE)
#
# Random emigration, p varies by session, uses Mh but pi fixed to 1, 
# S by time.This model is in the example Robust with MARK but it is
# a silly example because it uses the heterogeneity model but then fixes 
# pi=1 which means there is no heterogeneity.Probably the data were 
# not generated under Mh.  See results of model.2.b
#
pi.fixed=list(formula=~1,fixed=1)
p.session=list(formula=~-1+session,share=TRUE)
model.2.a=mark(data = robust, model = "RDHet", 
            time.intervals=time.intervals,
            model.parameters=list(S=S.time,
            GammaDoublePrime=GammaDoublePrime.random,
            p=p.session,pi=pi.fixed),threads=2,delete=TRUE)
#
# Random emigration, p varies by session, uses Mh and in this 
# case pi varies and so does p across
# mixtures with an additive session effect.
#
pi.dot=list(formula=~1)
p.session.mixture=list(formula=~session+mixture,share=TRUE)
model.2.b=mark(data = robust, model = "RDHet", 
            time.intervals=time.intervals,
            model.parameters=list(S=S.time,
            GammaDoublePrime=GammaDoublePrime.random,
            p=p.session.mixture,pi=pi.dot),threads=2,delete=TRUE)
#
# Markov constant emigration rates, pi varies by session, 
# p=c varies by session, S constant
# This model is in the example Robust with MARK 
# but it is a silly example because it
# uses the heterogeneity model but then fixes pi=1 
# which means there is no heterogeneity.
# Probably the data were not generated under Mh.  
# See results of model.3.b
#
S.dot=list(formula=~1)
pi.session=list(formula=~session)
p.session=list(formula=~-1+session,share=TRUE)
GammaDoublePrime.dot=list(formula=~1)
GammaPrime.dot=list(formula=~1)
model.3.a=mark(data = robust, model = "RDHet", 
            time.intervals=time.intervals,
            model.parameters=list(S=S.dot,
            GammaPrime=GammaPrime.dot,
            GammaDoublePrime=GammaDoublePrime.dot,
            p=p.session,pi=pi.session),threads=2,delete=TRUE)
#
# Markov constant emigration rates, pi varies by session, 
# p=c varies by session+mixture, S constant. This is model.3.a 
# but allows pi into the model by varying p/c by mixture.
#
S.dot=list(formula=~1)
pi.session=list(formula=~session)
GammaDoublePrime.dot=list(formula=~1)
GammaPrime.dot=list(formula=~1)
model.3.b=mark(data = robust, model = "RDHet", 
            time.intervals=time.intervals,
            model.parameters=list(S=S.dot,
            GammaPrime=GammaPrime.dot,
            GammaDoublePrime=GammaDoublePrime.dot,
            p=p.session.mixture,pi=pi.session),threads=2,delete=TRUE)
#
# Huggins Random emigration, p=c varies by time and session, 
# S by time
# Beware that this model is not quite the same 
# as the others above that say random emigration because
# the rates have been fixed for the last 2 occasions.  
# That was done with PIMS in the MARK example and
# here it is done by binning the times so that times 3 and 4 
# are in the same bin, so the time model
# has 3 levels (1,2, and 3-4).  By doing so the parameters 
# become identifiable but this may not be
# reasonable depending on the particulars of the data.  
# Note that the same time binning must be done both for
# GammaPrime and GammaDoublePrime because the parameters are 
# the same in the random emigration model.  If you
# forget to bin one of the parameters across time it will fit 
# a model but it won't be what you expect as it will
# not share parameters.  Note the use of the argument "right".  
# This controls whether binning is inclusive on the right (right=TRUE) 
# or on the left (right=FALSE).  Using "right" nested in the list
# of design parameters is equivalent to using it as a calling 
# argument to make.design.data or add.design.data.
#
S.time=list(formula=~time)
p.time.session=list(formula=~-1+session:time,share=TRUE)
GammaDoublePrime.random=list(formula=~time,share=TRUE)
model.4=mark(data = robust, model = "RDHuggins", 
        time.intervals=time.intervals,design.parameters=
        list(GammaDoublePrime=list(time.bins=c(1,2,5))),
        right=FALSE, model.parameters=
        list(S=S.time,GammaDoublePrime=GammaDoublePrime.random,
        p=p.time.session),threads=2,delete=TRUE)

return(collect.models())
}
robust.results=run.robust()
#
#  You will receive a warning message that the model list 
#  includes models of different types which are not compatible 
#  for comparisons of AIC.  That is because
#  the runs include closed models which include N 
#  in the likelihood and Huggins models which don't include 
#  N in the likelihood.  That can be avoided by running
#  the two types of models in different sets.
#
robust.results
# }