AIC.dfunc: AICc and related fit statistics for detection function objects

Description

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

Usage

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

Value

A scalar. By default, the value of AICc for the estimated distance function obj.

Arguments

object: An estimated detection function object. An estimated detection function object has class 'dfunc', and is usually produced by a call to dfuncEstim.
...: Required for compatibility with the general AIC method. Any extra arguments to this function are ignored.
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

Examples

Run this code

  data(sparrowDetectionData)
  dfunc <- dfuncEstim(dist~1,
                      detectionData=sparrowDetectionData, 
                      w.hi=units::set_units(150, "m"))
  
  # Compute fit statistics
  AIC(dfunc)  # AICc
  AIC(dfunc, criterion="AIC")  # AIC
  AIC(dfunc, criterion="BIC")  # BIC

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