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 or for model classes that are not currently supported by
AICc.
AICcCustom(logL, K, return.K = FALSE, second.ord = TRUE, nobs = NULL,
c.hat = 1)AICcCustom returns the AIC, AICc, QAIC, or QAICc, or the number
of estimated parameters, depending on the values of the arguments.
the value of the model log-likelihood.
the number of estimated parameters in the model.
logical. If FALSE, the function returns the information
criterion specified. If TRUE, the function returns K (number
of estimated parameters) for a given model.
logical. If TRUE, the function returns the second-order Akaike
information criterion (i.e., AICc).
the sample size required to compute the AICc or QAICc.
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)
syntax), with Poisson GLM's, single-season or dynamic occupancy
models (MacKenzie et al. 2002, 2003), N-mixture models (Royle
2004, Dail and Madsen 2011), or capture-mark-recapture models (e.g.,
Lebreton et al. 1992). If c.hat > 1, AICcCustom will return
the quasi-likelihood analogue of the information criterion requested.
Marc J. Mazerolle
AICcCustom 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 1989, 1991), the quasi-likelihood AIC (QAIC, Burnham and Anderson 2002), and the quasi-likelihood AICc (QAICc, Burnham and Anderson 2002).
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. (1989) Regression and time series model selection in small samples. Biometrika 76, 297--307.
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.
MacKenzie, D. I., Nichols, J. D., Hines, J. E., Knutson, M. G., Franklin, A. B. (2003) Estimating site occupancy, colonization, and local extinction when a species is detected imperfectly. Ecology 84, 2200--2207.
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.
AICc, aictabCustom, confset,
evidence, c_hat, modavgCustom
##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))
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