AICc {wiqid}

Akaike's Information Criterion with small-sample correction - AICc

Description

Akaike's Information Criterion with small-sample correction - AICc

Usage

AICc(object, ..., nobs, df)

Arguments

object

a fitted model object for which there exists a logLik method to extract the corresponding log-likelihood, number of parameters, and number of observations.

...

optionally more fitted model objects.

nobs

scalar; the value to use for the effective sample size; overrides the value contained in the model object(s).

df

the value to use for the number of parameters; usually a vector of length = number of models; non-NA elements override the value contained in the corresponding model object.

Details

AICc is Akaike's information Criterion (AIC) with a small sample correction. It is

AICc = AIC + 2K(K + 1) / (n - K - 1)

where K is the number of parameters and n is the number of observations.

This is an S3 generic, with a default method which calls logLik, and should work with any class that has a logLik method.

Value

If just one object is provided, the corresponding AICc.

If multiple objects are provided, a data frame with rows corresponding to the objects and columns representing the number of parameters in the model (df) and the AICc.

The result will be Inf for over-parameterised models, ie. when df >= nobs - 1.

Note

For some data types, including occupancy data, there is debate on the appropriate effective sample size to use.

Author(s)

Essentially the same as AIC in package stats. Modified to return AICc by Mike Meredith.

References

Burnham, K P; D R Anderson 2002. Model selection and multimodel inference: a practical information-theoretic approach. Springer-Verlag.

See Also

AIC.

Examples

# Occupancy models
data(salamanders)
mt <- occSStime(salamanders, p ~ .time, plot=FALSE)
mT <- occSStime(salamanders, p ~ .Time, plot=FALSE)
AIC(mt, mT)
AICc(mt, mT)
# The default sample size = the number of sites
nobs(mt) == nrow(salamanders)
# It is sometimes taken to be the total number of surveys...
AICc(mt, mT, nobs=length(salamanders))
# ... or the minimum of ...
n <- min(sum(rowSums(salamanders) > 0), # sites where species was detected
         sum(rowSums(salamanders) == 0)) # sites where species was not detected
AICc(mt, mT, nobs=n)

# Survival models
data(dippers)
DH <- dippers[1:7]  # Extract the detection histories
null <- survCJS(DH)  # the phi(.) p(.) model
phit <- survCJS(DH, phi ~ .time)  # the phi(t) p(.) model
full <- survCJS(DH, list(phi ~ .time, p ~ .time))  # the phi(t) p(t) model
AICc(null, phit, full)
# for the full model, all 12 parameters cannot be estimated;
#   we can manually set df=11 for this model:
AICc(null, phit, full, df=c(NA, NA, 11))