closedp.bc {Rcapture} | R Documentation |
Bias Correction for Closed Population Loglinear Models
Description
This function applies a bias correction to the abundance estimations obtained by closed population models.
Usage
closedp.bc(X, dfreq=FALSE, dtype=c("hist","nbcap"), t=NULL, t0=t,
m=c("M0","Mt","Mh","Mth","Mb","Mbh"), h=NULL, h.control=list(), ...)
## S3 method for class 'closedp.bc'
print(x, ...)
Arguments
X |
The matrix of the observed capture histories (see |
dfreq |
A logical. By default |
dtype |
A characters string, either "hist" or "nbcap", to specify the type of data. "hist", the default,
means that |
t |
Requested only if |
t0 |
A numeric used for model M0 or for an Mh model other than Chao's lower bound model :
Models are fitted considering only the frequencies of units captured
1 to |
m |
A character string indicating the model to fit, either "M0"=M0 model, "Mt"=Mt model, "Mh"=Mh model, "Mth"=Mth model, "Mb"=Mb model, "Mbh"=Mbh model. |
h |
A character string ("LB", "Chao", "Poisson", "Darroch" or "Gamma") or a
numerical |
h.control |
A list of elements to control the heterogeneous part of the model, if any.
For the Chao's lower bound Mth model:
|
... |
Further arguments to be passed to |
x |
An object, produced by the |
Details
For the Mt model:
When t=2, closedp.bc
returns the Petersen estimator with Chapman's (1951) bias correction
and the bias corrected standard error estimator of Seber (1970) and Wittes (1972).
For t>2, closedp.bc
implements the bias correction of Rivest and Levesque (2001).
The estimate for N and its variance are calculated by solving an estimating equation as proposed
in Seber (1982), not by fitting a Poisson regression. This approach works for large values of t.
For other models:
The bias correction is done through frequency modifications in Poisson regression as described
in Rivest and Levesque (2001). The variances calculated with the modified frequencies are
less biased than the standard ones, but they can overestimate the mean squared errors,
especially when the data is sparse.
This function works with fairly large data set, except if an "Mth" model is requested.
In this case, only heterogeneity of the form "LB", "Chao", "Poisson" with theta=2
or "Darroch"
is accepted.
Value
n |
The number of captured units |
t |
The total number of capture occasions in the data matrix |
t0 |
For models M0 and Mh only: the value of the argument |
results |
A table containing, for the fitted model:
|
glm.warn |
Only if the corrected population size estimation was obtained with |
neg.eta |
For Chao's lower bound model Mth only: the position of the eta parameters set to zero in the loglinear parameter vector, if any. |
Note
This function uses the glm
function of the stats package, except for models Mt and Mh Chao's lower bound for which exact calculation is performed.
Author(s)
Louis-Paul Rivest Louis-Paul.Rivest@mat.ulaval.ca and Sophie Baillargeon
References
Baillargeon, S. and Rivest, L.P. (2007) Rcapture: Loglinear models for capture-recapture in R. Journal of Statistical Software, 19(5), doi:10.18637/jss.v019.i05.
Chapman, D. G. (1951) Some properties of the hypergeometric distribution with applications to zoological sample censuses. University of California Publications in Statistics, 1(7), 131-160.
Rivest, L.P. and Levesque, T. (2001) Improved loglinear model estimators of abundance in capture-recapture experiments. Canadian Journal of Statistics, 29, 555-572.
Seber, G.A.F. (1970) The effects of trap response on tag recapture estimates. Biometrics, 26, 13-22.
Seber, G.A.F. (1982) The Estimation of Animal Abundance and Related Parameters, 2nd edition. New York: Macmillan.
Wittes, J.T. (1972) On the bias and estimated variance of Chapman's two-sample capture-recapture population estimate. Biometrics, 28, 592-597.
See Also
Examples
# Third primary period of mvole data set
period3 <- mvole[, 11:15]
closedp.bc(period3, m = "Mh", h = "Darroch")
closedp.bc(period3, m = "Mh", h = "Gamma", h.control = list(theta = 3.5))
# BBS2001 data set
closedp.bc(BBS2001, dfreq = TRUE, dtype = "nbcap", t = 50, t0 = 20,
m = "Mh", h = "Gamma", h.control = list(theta = 3.5))
# Seber (1982) p.107
# When there are 2 capture occasions, only models M0 and Mt can be fitted
X <- matrix(c(1,1,167,1,0,781,0,1,254), byrow = TRUE, ncol = 3)
closedp.bc(X, dfreq = TRUE, m = "M0")
closedp.bc(X, dfreq = TRUE, m = "Mt")