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Rdistance (version 4.0.5)

AIC.dfunc: AIC.dfunc - AIC-related fit statistics for detection functions

Description

Computes AICc, AIC, or BIC for estimated distance functions.

Usage

# S3 method for dfunc
AIC(object, ..., criterion = "AICc")

Value

A scalar, the requested fit statistic for object.

Arguments

object

An Rdistance model frame or fitted distance function, normally produced by a call to dfuncEstim.

...

Included for compatibility with generic predict methods.

criterion

String specifying the criterion to compute. Either "AICc", "AIC", or "BIC".

Details

Regular Akaike's information criterion (https://en.wikipedia.org/wiki/Akaike_information_criterion) (\(AIC\)) is $$AIC = LL + 2p,$$ where \(LL\) is the maximized value of the log likelihood (the minimized value of the negative log likelihood) and \(p\) is the number of coefficients estimated in the detection function. For dfunc objects, \(AIC\) = obj$loglik + 2*length(coef(obj)).

A correction for small sample size, \(AIC_c\), is $$AIC_c = LL + 2p + \frac{2p(p+1)}{n-p-1},$$ where \(n\) is sample size or number of detected groups for distance analyses. By default, this function computes \(AIC_c\). \(AIC_c\) converges quickly to \(AIC\) as \(n\) increases.

The Bayesian Information Criterion (BIC) is $$BIC = LL + log(n)p,$$.

References

Burnham, K. P., and D. R. Anderson, 2002. Model selection and multi-model inference: A practical information-theoretic approach, Second ed. Springer-Verlag. ISBN 0-387-95364-7.

McQuarrie, A. D. R., and Tsai, C.-L., 1998. Regression and time series model selection. World Scientific. ISBN 981023242X

See Also

coef, dfuncEstim

Examples

Run this code
data(sparrowDf)
dfunc <- sparrowDf |> dfuncEstim(dist~1)
  
# Fit statistics
AIC(dfunc)  # AICc
AIC(dfunc, criterion="AIC")  # AIC
AIC(dfunc, criterion="BIC")  # BIC

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