secr (version 2.5.0)

AIC.secr: Compare SECR Models

Description

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.

Usage

## S3 method for class 'secr':
AIC(object, ..., sort = TRUE, k = 2, dmax = 10)
## S3 method for class 'secrlist':
AIC(object, ..., sort = TRUE, k = 2, dmax = 10)
## S3 method for class 'secr':
logLik(object, ...)
secrlist(...)

Arguments

object

secr object output from the function secr.fit, or a list of such objects with class c("list","secrlist")

...

other secr objects

sort

logical for whether rows should be sorted by ascending AICc

k

numeric, the penalty per parameter to be used; always k = 2 in this method

dmax

numeric, the maximum AIC difference for inclusion in confidence set

Value

• A data frame with one row per model. By default, rows are sorted by ascending AICc.
• model
  character string describing the fitted model
• detectfn
  shape of detection function fitted (halfnormal vs hazard-rate)
• npar
  number of parameters estimated
• logLik
  maximized log likelihood
• AIC
  Akaike's Information Criterion
• AICc
  AIC with small-sample adjustment of Hurvich & Tsai (1989)
• dAICc
  difference between AICc of this model and the one with smallest AICc
• AICwt
  AICc model weight
• logLik.secr returns an object of class `logLik' that has attribute df (degrees of freedom = number of estimated parameters).

Details

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. The sample size $n$ is the number of individuals observed at least once (i.e. the number of rows in capthist). Model weights are calculated as $$w_i = \frac{\exp(-\Delta_i / 2)}{ \sum{\exp(-\Delta_i / 2)}}$$ Models for which dAICc > 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 model.average (see also Buckland et al. 1997, Burnham and Anderson 2002). The argument k is included for consistency with the generic method AIC. secrlist forms a list of fitted models (an object of class `secrlist') from the fitted models in .... Arguments may include secrlists. If secr components are named the model names will be retained (see Examples).

References

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.

See Also

model.average, AIC, secr.fit, print.secr, score.test, LR.test, deviance.secr

Examples

## Compare two models fitted previously
## secrdemo.0 is a null model
## secrdemo.b has a learned trap response

AIC(secrdemo.0, secrdemo.b)

## Form secrlist and pass to AIC.secr
temp <- secrlist(null = secrdemo.0, learnedresponse = secrdemo.b)
AIC(temp)