AIC.secr {secr} | R Documentation

## 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)

### Arguments

`object` | `secr` object output from the function `secr.fit`
`...` | 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

### 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

AICc = -2log(L(theta-hat)) + 2K + 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 = exp(-dAICc_i / 2) / sum{ exp(-dAICc_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`.

### 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

### Note

The issue of goodness-of-fit and possible adjustment of AIC for overdispersion has yet to be addressed (cf QAIC in MARK).

### Author(s)

Murray Efford murray.efford@otago.ac.nz

### 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

    data(secrdemo)
    AIC(secrdemo.0, secrdemo.b)

[Package secr version 1.3.0 Index]