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.

- 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/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 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. (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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