mscjs function

Fitting function for Multistate CJS models

A function for computing MLEs for a Multi-state Cormack-Jolly-Seber open population capture-recapture model for processed dataframe x with user specified formulas in parameters that create list of design matrices dml. This function can be called directly but is most easily called from crm that sets up needed arguments.

mscjs(
  x,
  ddl,
  dml,
  model_data = NULL,
  parameters,
  accumulate = TRUE,
  initial = NULL,
  method,
  hessian = FALSE,
  debug = FALSE,
  chunk_size = 1e+07,
  refit,
  itnmax = NULL,
  control = NULL,
  scale,
  re = FALSE,
  compile = FALSE,
  extra.args = "",
  clean = TRUE,
  ...
)

Arguments

• x: processed dataframe created by process.data
• 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
• model_data: a list of all the relevant data for fitting the model including imat, S.dm,p.dm,Psi.dm,S.fixed,p.fixed,Psi.fixed and time.intervals. It is used to save values and avoid accumulation again if the model was re-rerun with an additional call to cjs when using autoscale or re-starting with initial values. It is stored with returned model object.
• parameters: equivalent to model.parameters in crm
• accumulate: if TRUE will accumulate capture histories with common value and with a common design matrix for S and p to speed up execution
• initial: list of initial values for parameters if desired; if each is a named vector from previous run it will match to columns with same name
• method: method to use for optimization; see optim
• hessian: if TRUE will compute and return the hessian
• debug: if TRUE will print out information for each iteration
• chunk_size: specifies amount of memory to use in accumulating capture histories; amount used is 8*chunk_size/1e6 MB (default 80MB)
• refit: non-zero entry to refit
• itnmax: maximum number of iterations
• control: control string for optimization functions
• scale: vector of scale values for parameters
• re: if TRUE creates random effect model admbcjsre.tpl and runs admb optimizer
• compile: if TRUE forces re-compilation of tpl file
• extra.args: optional character string that is passed to admb
• clean: if TRUE, deletes the tpl and executable files for amdb
• ...: not currently used

Returns

The resulting value of the function is a list with the class of crm,cjs such that the generic functions print and coef can be used. - beta: named vector of parameter estimates - lnl: -2log likelihood - AIC: lnl + 2 number of parameters

• convergence: result from optim; if 0 optim thinks it converged - count: optim results of number of function evaluations - reals: dataframe of data and real S and p estimates for each animal-occasion excluding those that occurred before release

• vcv: var-cov matrix of betas if hessian=TRUE was set

Details

It is easiest to call mscjs through the function crm. Details are explained there.

Examples

# this example requires admb
# The same example is in the RMark package and it is included here to
# illustrate the differences in the handling of mlogit parameters between RMark 
# and marked.  The MARK software handles parameters like Psi which must sum to 1
# by excluding one of the cells that is used as a reference cell and is computed by
# subtracting the other cell values from 1 so the total sums to 1.  This is often
# handled with an mlogit parameter in which the cell values are exp(beta) and the
# reference cell is set to 1 and the values are divided by the sum across the cells
# so the resulting values are probabilities that sum to 1. In marked, instead of removing
# one of the cells, all are included and the user must select which should be the
# reference cell by setting the value fix=1 for that cell and others are NA so they are
# estimated. For transition parameters like Psi, the default design data is setup so 
# that the probability of remaining in the cell (stratum=tostratum) is the reference cell
# and fix set to 1.  Thus, this means 2 changes are needed to the script in RMark.
# The first is to remove the statement skagit.ddl$Psi$fix=NA because that over-rides
# the default fix values.  The other is to add
# skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="B"&skagit.ddl$Psi$tostratum=="B"&
#  skagit.ddl$Psi$time==5]=0
# to change the value from 1 to 0 which forces movement from B to A in the interval 5 to 6. If
# this is not done then Psi B to B=Psi B to A=0.5 because each is 1 and when they are normalized
# they are divided by the sum which is 2 (1/2).
if(!is(try(setup_admb("mscjs")),"try-error"))
{
data(skagit)
skagit.processed=process.data(skagit,model="Mscjs",groups=c("tag"),strata.labels=c("A","B"))
skagit.ddl=make.design.data(skagit.processed)
#
# p
#
# Can't be seen at 5A or 2B,6B (the latter 2 don't exist)
skagit.ddl$p$fix=ifelse((skagit.ddl$p$stratum=="A"&skagit.ddl$p$time==5) | 
(skagit.ddl$p$stratum=="B"&skagit.ddl$p$time%in%c(2,6)),0,NA)
# Estimated externally from current data to allow estimation of survival at last interval
skagit.ddl$p$fix[skagit.ddl$p$tag=="v7"&skagit.ddl$p$time==6&skagit.ddl$p$stratum=="A"]=0.687
skagit.ddl$p$fix[skagit.ddl$p$tag=="v9"&skagit.ddl$p$time==6&skagit.ddl$p$stratum=="A"]=0.975
#
# Psi
#
# only 3 possible transitions are A to B at time interval 2 to 3 and 
# for time interval 3 to 4 from A to B and from B to A
# rest are fixed values
############ change for RMark to marked; remove next line
#skagit.ddl$Psi$fix=NA
# stay in A for intervals 1-2, 4-5 and 5-6
skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="A"&
 skagit.ddl$Psi$tostratum=="B"&skagit.ddl$Psi$time%in%c(1,4,5)]=0
# stay in B for interval 4-5
skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="B"&skagit.ddl$Psi$tostratum=="A"
 &skagit.ddl$Psi$time==4]=0
# leave B to go to A for interval 5-6
skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="B"&skagit.ddl$Psi$tostratum=="A"&
skagit.ddl$Psi$time==5]=1
############ change for RMark to marked; add next line to set B to B to 0 otherwise it has
############ been set to 1 by default which would make psi B to B = psi B to A = 0.5
skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="B"&skagit.ddl$Psi$tostratum=="B"&
skagit.ddl$Psi$time==5]=0
# "stay" in B for interval 1-2 and 2-3 because none will be in B
skagit.ddl$Psi$fix[skagit.ddl$Psi$stratum=="B"&skagit.ddl$Psi$tostratum=="A"&
skagit.ddl$Psi$time%in%1:2]=0
# 
# S
#
# None in B, so fixing S to 1
skagit.ddl$S$fix=ifelse(skagit.ddl$S$stratum=="B"&skagit.ddl$S$time%in%c(1,2),1,NA)
skagit.ddl$S$fix[skagit.ddl$S$stratum=="A"&skagit.ddl$S$time==4]=1
# fit model
p.timexstratum.tag=list(formula=~time:stratum+tag,remove.intercept=TRUE)
Psi.sxtime=list(formula=~-1+stratum:time)
S.stratumxtime=list(formula=~-1+stratum:time)
#
mod1=crm(skagit.processed,skagit.ddl,
model.parameters=list(S=S.stratumxtime,p= p.timexstratum.tag,Psi=Psi.sxtime),hessian=TRUE)
if(!is(mod1,"try-error")) mod1
}

References

Ford, J. H., M. V. Bravington, and J. Robbins. 2012. Incorporating individual variability into mark-recapture models. Methods in Ecology and Evolution 3:1047-1054.

Author(s)

Jeff Laake