Calculate Mallows' *Cp* and Bozdogan's ICOMP and CAIFC information criteria.

Extract or calculate Deviance Information Criterion from `MCMCglmm`

and
`merMod`

object.

```
Cp(object, ..., dispersion = NULL)
ICOMP(object, ..., REML = NULL)
CAICF(object, ..., REML = NULL)
DIC(object, ...)
```

object

a fitted model object (in case of ICOMP and CAICF, `logLik`

and `vcov`

methods must exist for the object). For `DIC`

, an
object of class `"MCMCglmm"`

or `"merMod"`

.

…

optionally more fitted model objects.

dispersion

the dispersion parameter. If `NULL`

, it is inferred
from object.

REML

optional logical value, passed to the `logLik`

method
indicating whether the restricted log-likelihood or log-likelihood should be
used. The default is to use the method used for model estimation.

If just one object is provided, the functions return a numeric value with
the corresponding IC; otherwise a `data.frame`

with rows corresponding
to the objects is returned.

Mallows' *Cp* statistic is the residual deviance plus twice the estimate of
\(\sigma^{2}\) times the residual degrees of freedom. It is closely
related to AIC (and a multiple of it if the dispersion is known).

ICOMP (I for informational and COMP for complexity) penalizes the covariance complexity of the model, rather than the number of parameters directly.

CAICF (C is for ‘consistent’ and F denotes the use of the Fisher information matrix) includes with penalty the natural logarithm of the determinant of the estimated Fisher information matrix.

Mallows, C. L. (1973) Some comments on *Cp*. *Technometrics* 15:
661<U+2013>675.

Bozdogan, H. and Haughton, D.M.A. (1998) Information complexity criteria for
regression models. *Comp. Stat. & Data Analysis* 28: 51-76.

Anderson, D. R. and Burnham, K. P. (1999) Understanding information criteria for selection among
capture-recapture or ring recovery models. *Bird Study* 46: 14<U+2013>21.

Spiegelhalter, D.J., Best, N.G., Carlin, B.R., van der Linde, A. (2002) Bayesian measures of model
complexity and fit. *Journal of the Royal Statistical Society Series B-Statistical Methodology*
64: 583<U+2013>616.

`AIC`

and `BIC`

in stats, `AICc`

.
`QIC`

for GEE model selection.
`extractDIC`

in package arm, on which the (non-visible)
method `extractDIC.merMod`

used by `DIC`

is based.