Rdistance (version 2.1.3)

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")

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".

Value

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

Details

Regular Akaike's information criterion (http://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

# NOT RUN {
# Load the example dataset of sparrow detections from package
  data(sparrowDetectionData)
  
  # Fit detection function to perpendicular, off-transect distances
  dfunc <- dfuncEstim(dist~1,
                      detectionData=sparrowDetectionData, 
                      w.hi=150)
  
  # Compute fit statistics
  AIC(dfunc)  # AICc
  AIC(dfunc, criterion="AIC")  # AIC
  AIC(dfunc, criterion="BIC")  # BIC
# }