Terse report on the fit of one or more spatially explicit capture--recapture models. Models with smaller values of AIC (Akaike's Information Criterion) are preferred.
# S3 method for openCR
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, use.rank = FALSE,
svtol = 1e-5, criterion = c('AIC','AICc'), n = NULL)# S3 method for openCRlist
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, use.rank = FALSE,
svtol = 1e-5, criterion = c('AIC','AICc'), n = NULL)
# S3 method for openCR
logLik(object, ...)
A data frame with one row per model. By default, rows are sorted by ascending AIC.
character string describing the fitted model
number of parameters estimated
rank of Hessian
maximized log likelihood
Akaike's Information Criterion
AIC with small-sample adjustment of Hurvich & Tsai (1989)
difference between AICc of this model and the one with smallest AIC
AICc model weight
logLik.openCR returns an object of class `logLik' that has
attribute df (degrees of freedom = number of estimated
parameters).
openCR object output from the function
openCR.fit, or openCRlist
other openCR objects
logical for whether rows should be sorted by ascending AICc
numeric, the penalty per parameter to be used; always k = 2 in this method
numeric, the maximum AIC difference for inclusion in confidence set
logical; if TRUE the number of parameters is based on the rank of the Hessian matrix
minimum singular value (eigenvalue) of Hessian used when counting non-redundant parameters
character, criterion to use for model comparison and weights
integer effective sample size
Models to be compared must have been fitted to the same data and use the same likelihood method (full vs conditional).
AIC with small sample adjustment is given by
$$ \mbox{AIC}_c = -2\log(L(\hat{\theta})) + 2K + \frac{2K(K+1)}{n-K-1} $$
where \(K\) is the number of ``beta" parameters estimated. By default, the effective sample size \(n\) is the number of individuals observed at least once (i.e. the
number of rows in capthist). This differs from the default in MARK which for CJS models is the sum of the sizes of release cohorts (see m.array).
Model weights are calculated as $$w_i = \frac{\exp(-\Delta_i / 2)}{ \sum{\exp(-\Delta_i / 2)}}$$
Models for which dAIC > dmax are given a weight of zero and are
excluded from the summation. Model weights may be used to form
model-averaged estimates of real or beta parameters with
modelAverage (see also Buckland et al. 1997, Burnham and
Anderson 2002).
The argument k is included for consistency with the generic
method AIC.
Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Model selection: an integral part of inference. Biometrics 53, 603--618.
Burnham, K. P. and Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Second edition. New York: Springer-Verlag.
Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika 76, 297--307.
AIC, openCR.fit,
print.openCR, LR.test
if (FALSE) {
m1 <- openCR.fit(ovenCH, type = 'JSSAf')
m2 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(p~session))
AIC(m1, m2)
}
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