Information criteria: Various information criteria

Description

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

Extract or calculate Deviance Information Criterion from MCMCglmm and mer object.

Usage

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

Arguments

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 mer.

...

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.

Value

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.

encoding

utf-8

Details

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.

References

Mallows, C. L. (1973) Some comments on Cp. Technometrics 15: 661–675.

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: 14–21.

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: 583–616.