# 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

1 2 | ```
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 |

`second.ord` |
logical. If |

`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 |

### 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).

### Value

`AICc`

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

### Note

The actual (Q)AIC(c) values are not really interesting in themselves, as they depend directly on the data, parameters estimated, and likelihood function. Furthermore, a single value does not tell much about model fit. Information criteria become relevant when compared to one another for a given data set and set of candidate models.

### Author(s)

Marc J. Mazerolle

### 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.

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.

### See Also

`AICc`

, `aictabCustom`

, `confset`

,
`evidence`

, `c_hat`

, `modavgCustom`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
##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))
``` |