Rdistance (version 1.2.2)

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 class 'dfunc':
AIC(object, \dots, k = 2, n=length(object$dist))

Arguments

object

An estimated detection function object. An estimated detection function object has class 'dfunc', and is usually produced by a call to F.dfunc.estim.

...

Required for compatability with the general AIC method. Any extra arguments to this function are ignored.

k

Scalar penalty to use in the computations. See Details.

n

Scalar sample size to use in computations. See Details.

Value

• A scalar. By default, the value of AICc for the estimated distance funciton 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 (more specifically, 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 $AIC_c$ because it converges to $AIC$ for large $n$ and is therefore generally prefered. By changing the parameters k and n, it is possible to compute at least three measures of model fit. These are:

• Settingk= 2 andn=Infproduces AIC.
• Settingk= log($n$) andn=Infproduces the Bayesian Information Criterion, or BIC.
• Settingk= 2 andn=$n$produces$AIC_c$(the default).

References

Burnham, K. P., and D. R. Anderson, 2002. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd 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, F.dfunc.estim

Examples

# Load the example dataset for sparrow detections from package
data(sparrow.detections)

# Compute perpendicular, off-transect distances from the observer's sight distance and angle
sparrow.detections$dist <- perp.dists(obs.dist=sparrow.detections$sightdist,
                                  obs.angle=sparrow.detections$sightangle)

# Fit detection function object
dfunc <- F.dfunc.estim(sparrow.detections, w.hi=150)

# Compute fit statistics
AIC(dfunc)  # AICc
AIC(dfunc, k=2, n=Inf)  # AIC
AIC(dfunc, k=log(length(dfunc$dist)), n=Inf)  # BIC