AICcmodavg (version 1.04)

AICc: Computing AIC, AICc, QAIC, and QAICc

Description

Functions to computes Akaike's information criterion (AIC), the second-order AIC (AICc), as well as their quasi-likelihood counterparts (QAIC, QAICc).

Usage

AICc(mod, return.K = FALSE, c.hat = 1, second.ord = TRUE, nobs = NULL) 
AICc.glm(mod, return.K = FALSE, c.hat = 1, second.ord = TRUE, nobs = 
NULL)
AICc.lme(mod, return.K = FALSE, second.ord = TRUE, nobs = NULL)
AICc.mult(mod, return.K = FALSE, c.hat = 1, second.ord = TRUE, nobs =
NULL) 
AICc.polr(mod, return.K = FALSE, second.ord = TRUE, nobs = NULL)

Arguments

mod

an object of class 'lm', 'glm', 'lme', 'multinom', or 'polr' containing the output of a model.

return.K

logical. If FALSE, the function returns the information criteria specified. If TRUE, the function returns K (number of estimated parameters) for a given model. Using this argument to facilitate computation of tables was an original idea from T. Ergon.

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/trial or cbind(success, failure) syn

second.ord

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

nobs

this argument allows to specify a numeric value other than total sample size to compute the AICc. This is relevant only for linear mixed models where sample size is not straightforward. In such cases, one might want to use the total number of observation

Value

• 'AICc' selects one of the functions below based on the class of the object:

  'AICc.glm' returns the AIC, AICc, QAIC, or QAICc depending on the values of the arguments.

  'AICc.lme' returns the AIC or AICc depending on the values of the arguments.

  'AICc.mult' returns the AIC, AICc, QAIC, or QAICc depending on the values of the arguments.

  'AICc.polr' returns the AIC or AICc depending on the values of the arguments.

Details

'AICc' is a function that calls either 'AICc.glm', 'AICc.lme', 'AICc.mult', or 'AICc.polr', depending on the class of the object. The current function is implemented for 'lm','glm', 'lme', 'multinom', and 'polr' classes and 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). Note that AIC and AICc values are meaningful to select among mixed models fit by maximum likelihood; AIC and AICc based on REML are valid to select among different models that only differ in their random effects (Pinheiro and Bates 2000).

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.

Anderson, D. R. (2008) Model-based Inference in the Life Sciences: a primer on evidence. Springer: New York.

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

Burnham, K. P., Anderson, D. R. (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33, 261--304.

Hurvich, C. M., Tsai, C.-L. (1991) Bias of the corrected AIC criterion for underfitted regression and time series models. Biometrika 78, 499--509.

Pinheiro, J. C., Bates, D. M. (2000) Mixed-effect models in S and S-PLUS. Springer Verlag: New York.

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

aictab, confset, importance, evidence, c_hat, modavg, modavgpred

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)

#compute AICc with full likelihood
AICc(glob.mod, return.K = FALSE)

#compute AIC with full likelihood 
AICc(glob.mod, return.K = FALSE, second.ord = FALSE)
#note that Burnham and Anderson (2002) did not use full likelihood
#in Table 3.2 and that the MLE estimate of the variance was
#rounded to 2 digits after decimal point  



#compute AICc for mixed model on Orthodont data set in Pinheiro and
#Bates (2000)
require(nlme)
m1 <- lme(distance ~ age, random = ~1 | Subject, data = Orthodont,
method= "ML")
AICc(m1, return.K = FALSE)