# MRA - Mark Recapture Analysis

### Description

**Description** -
This package contains analysis functions, and associated routines, to conduct
analyses of mark-recapture (capture-recapture) data using individual,
time, and individual-time varying covariates. In general, these routines
relate vectors of capture histories to vectors of covariates using
a regression approach (Amstrup et al. 2005, Ch 9). All capture, survival,
transition, etc. parameters are functions of individual and time
specific covariates, and the estimated parameters
are coefficients in logistic-linear equations.

**Relationship to MARK** -
For the most part, these routines perform a subset of the analyses available in
program MARK or via the MARK front-end package, RMark.
However, there are differences. The most significant difference between this package
and MARK is parameterization. The parameterization used here
does not utilize triangular
"parameter information matrices" (PIMs) as MARK (and RMark) does.
Because of this, the "design" matrix utilized by
this package is not parallel to the "design" matrix of program MARK. For those new
to mark-recapture analysis, this parameterization difference will be inconsequential.
The approach taken here provides equivalent modeling flexibility, yet is
easier to grasp and visualize, in our opinion.
For those already familiar with the PIMs used
by program MARK, it is helpful to view the "PIMs" of this package as
rectangular matrices of the real parameters. I.e., the "PIMs" of this package are
rectangular matrices where cell (i,j) contains the real parameter (capture or survival)
for individual i at capture occasion j.

Analyses available here that are *not* included in program MARK include:

Estimation of population size from open population CJS models via the Horvitz-Thompson estimator.

Residuals, goodness of fit tests, and associated plots for assessing model fit in open CJS models.

**History** -
These routines grew from consulting work on multiple mark-recapture projects.
The original Fortran code, upon which the package is based, was written
by Dr. Bryan Manly for a northern spotted owl similation project in 1991.
Dr. Manly is the one
who originally envisioned and programed the non-PIM (or rectangular PIM, if you
prefer) approach. However, Dr. Manly did not realize what he had done.
In 1997, Dr. Trent McDonald almost completely revised the original
Fortran routines for use on a polar bear mark-recapture project. At that time,
the routines were stand-alone Fortran executables. Subsequent revisions
required by other projects included addition of closed-form variance estimates (originally,
variances were estimated by the bootstrap), the Horvitz-Thompson size estimates,
and goodness of fit testing. In 2003, it finally dawned on Dr. McDonald how
to call a Fortran DLL from S-Plus and R, thus
eliminating the executable version and
allowing S-Plus or R to do front-end data manipulation and plotting.
S-Plus was abandoned in favor of R in 2004.
After publication of Amstrup et al. (2005),
Dr. McDonald realized that an official R package with documentation was
needed, and learned how to make a package (not an easy process for him).
Version 1.X of MRA contained routines for open population CJS models only.
Version 2.X of MRA added closed population Huggins model estimation routines. In future,
addition of a major model type will increment the primary version number, revisions
to routines for existing models will increment the secondary version number. Thus,
the number of major model types available in MRA will be the primary version number.
Throughout the process, several statisticians, including Dr. Manly,
Dr. Jeff Laake and Dr. Gary White, have
provided comments that helped shape the approach.

**Ways You Can Help** -
It is a no-brainer that others have R routines that perform various mark-recapture analyzes.
The author of MRA views this effort as collaborative and
welcomes routines, comments, and assistance in developing MRA. The overall goal
is to develop MRA into a comprehensive repository for
mark-recapture analyzes in R. Indeed, collaboration is the strength of R and open source
code.

Along these lines, the author of MRA would especially welcome routines that perform the following analyzes:

Continuous time models. Especially those that allow inclusion of covariates.

Band recovery models.

Baysian models.

Joint live-dead recovery models.

MCMC methods or routines that can be applied to exiting models.

Plotting methods for exiting models.

Model selection methods for existing models.

Simulation methods and routines.

The above is only a partial list. All routines are welcome and will be considered. Original authors will of course be acknowledged in the routine's documentation. Assistance in formating documentation files is available. I.e., either the author of MRA will write the documentation or the routine's original author will be sent a text file to edit that contains all the necessary mark-up and sectioning.

If you have a routine that would be useful, email MRA's maintainer at the address below. Supporting papers and data sets can be distributed with MRA, and are encouraged.

### Details

Package: | mra |

Type: | Package |

License: | GNU General Public License |

List of routines:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
F.cjs.covars Returns matricies that can be used to fit a CJS model
F.cjs.estim Estimation of Cormack-Jolly-Seber (CJS) open population model
F.cjs.gof Goodness-of-fit tests for CJS models
F.cr.model.matrix Function that returns two 3-D design matricies.
F.3d.model.matrix Function that expands a formula into the type of 3-D array
needed for estimation.
F.huggins.estim Estimation of Huggin's closed population model
F.sat.lik Returns the saturated likelihood for a CJS model that does
not contain individual covariates
F.fit.table Prints table of fit statistics from a list of MRA objects
F.cjs.simulate Simulates capture data from MRA CJS model
F.step.cjs Performs step-wise variables selection for CJS models
F.cr.model.avg Performs model averaging from a list of MRA objects
mra.control Controls aspects of model fitting (interations,
tolerance, tracing, etc.)
dipper.data European Dipper data set
lines.cjs Lines method for cjs objects
plot.cjs Plot method for cjs objects
predict.cjs Predicted values for active cells of a CJS model.
print.cjs Print method for cjs objects
print.hug Print method for hug (Huggin's model) objects
print.nhat Pring method for size estimates from a CJS model
residuals.cjs Residuals for CJS models
ivar Function for specifying individual varying effects
tvar Function for specifying time varying effects
``` |

### Author(s)

Trent McDonald

Maintainer: Trent McDonald <tmcdonald@west-inc.com>

### References

Amstrup, S.C., T.L. McDonald, and B.F.J. Manly. 2005. *Handbook of
Capture-Recapture Analysis*, Princeton: Princeton University Press.