AICcmodavg (version 2.0-3)

AICcCustom: Custom Computation of AIC, AICc, QAIC, and QAICc from User-supplied Input

Description

This function computes Akaike's information criterion (AIC), the second-order AIC (AICc), as well as their quasi-likelihood counterparts (QAIC, QAICc) from user-supplied input instead of extracting the values automatically from a model object. This function is particularly useful for output imported from other software.

Usage

AICcCustom(logL, K, return.K = FALSE, second.ord = TRUE, nobs = NULL,
           c.hat = 1)

Arguments

logL

the value of the model log-likelihood.

K

the number of estimated parameters in the model.

return.K

logical. If FALSE, the function returns the information criterion specified. If TRUE, the function returns K (number of estimated parameters) for a given model.

second.ord

logical. If TRUE, the function returns the second-order Akaike information criterion (i.e., AICc).

nobs

the sample size required to compute the AICc or QAICc.

c.hat

value of overdispersion parameter (i.e., variance inflation factor) such as that obtained from c_hat. Note that values of c.hat different from 1 are only appropriate for binomial GLM's with trials > 1 (i.e., success/tri

Value

• AICc returns the AIC, AICc, QAIC, or QAICc, or the number of estimated parameters, depending on the values of the arguments.

Details

AICc computes one of the following four information criteria: Akaike's information criterion (AIC, Akaike 1973), the second-order or small sample AIC (AICc, Sugiura 1978, Hurvich and Tsai 1991), the quasi-likelihood AIC (QAIC, Burnham and Anderson 2002), and the quasi-likelihood AICc (QAICc, Burnham and Anderson 2002).

References

Akaike, H. (1973) Information theory as an extension of the maximum likelihood principle. In: Second International Symposium on Information Theory, pp. 267--281. Petrov, B.N., Csaki, F., Eds, Akademiai Kiado, Budapest.

Burnham, K. P., Anderson, D. R. (2002) Model Selection and Multimodel Inference: a practical information-theoretic approach. Second edition. Springer: New York.

Dail, D., Madsen, L. (2011) Models for estimating abundance from repeated counts of an open population. Biometrics 67, 577--587. Hurvich, C. M., Tsai, C.-L. (1991) Bias of the corrected AIC criterion for underfitted regression and time series models. Biometrika 78, 499--509.

Lebreton, J.-D., Burnham, K. P., Clobert, J., Anderson, D. R. (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case-studies. Ecological Monographs 62, 67--118. MacKenzie, D. I., Nichols, J. D., Lachman, G. B., Droege, S., Royle, J. A., Langtimm, C. A. (2002) Estimating site occupancy rates when detection probabilities are less than one. Ecology 83, 2248--2255.

Royle, J. A. (2004) N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108--115.

Sugiura, N. (1978) Further analysis of the data by Akaike's information criterion and the finite corrections. Communications in Statistics: Theory and Methods A7, 13--26.

See Also

AICc, aictabCustom, confset, evidence, c_hat, modavgCustom

Examples

##cement data from Burnham and Anderson (2002, p. 101)
data(cement)
##run multiple regression - the global model in Table 3.2
glob.mod <- lm(y ~ x1 + x2 + x3 + x4, data = cement)

##extract log-likelihood
LL <- logLik(glob.mod)[1]

##extract number of parameters
K.mod <- coef(glob.mod) + 1

##compute AICc with full likelihood
AICcCustom(LL, K.mod, nobs = nrow(cement))