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. Extraction ([) and logLik methods are included.

### Usage

    ## S3 method for class 'secr'
    AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"))
    ## S3 method for class 'secrlist'
    AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"))
    ## S3 method for class 'secr'
    logLik(object, ...)
    secrlist(...)
    ## S3 method for class 'secrlist'
    x[i]

### Arguments

`object` | `secr` object output from the function `secr.fit`, or a list of such objects with class c("secrlist", "list")
`...` | other `secr` objects
`sort` | logical for whether rows should be sorted by ascending AICc
`k` | numeric, penalty per parameter to be used; always k = 2 in this method
`dmax` | numeric, maximum AIC difference for inclusion in confidence set
`criterion` | character, criterion to use for model comparison and weights
`x` | secrlist
`i` | indices

### 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(-delta_i / 2) / sum{ exp(-delta_i / 2) }

, where delta refers to differences in AIC or AICc depending on the argument ‘criterion’.

Models for which delta > `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).

### 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)

And depending on `criterion`:

`dAICc` | difference between AICc of this model and the one with smallest AICc
`AICcwt` | AICc model weight

or

`dAIC` | difference between AIC of this model and the one with smallest AIC
`AICwt` | AIC model weight

`logLik.secr` returns an object of class ‘logLik’ that has attribute `df` (degrees of freedom = number of estimated parameters).

### Note

It is not be meaningful to compare models by AIC if they relate to different data or habitat masks.

Specifically:

- an ‘secrlist’ generated and saved to file by `mask.check` may be supplied as the object argument of `AIC.secrlist`, but the results are not informative

- models fitted by the conditional likelihood (`CL = TRUE`) and full likelihood (`CL = FALSE`) methods cannot be compared

- hybrid mixture models (using hcov argument of secr.fit) should not be compared with other models

- grouped models (using groups argument of secr.fit) should not be compared with other models

- multi-session models should not be compared with single-session models based on the same data.

A likelihood-ratio test (`LR.test`) is a more direct way to compare two models.

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

From version 2.6.0 the user may select between AIC and AICc for comparing models, whereas previously only AICc was used and AICc weights were reported as ‘AICwt’). There is evidence that AIC may be better for model averaging even when samples are small sizes - Turek and Fletcher (2012).

### 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.

Turek, D. and Fletcher, D. (2012) Model-averaged Wald confidence intervals. Computational statistics and data analysis 56, 2809–2815.

### 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)

[Package secr version 3.2.1 Index]