spaMM (version 3.6.0)

AIC: Extractors for information criteria such as AIC

Description

get_any_IC computes model selection/information criteria such as AIC. See Details for more information about these criteria. The other extractors AIC and extractAIC are methods for HLfit objects of generic functions defined in other packages; AIC is equivalent to get_any_IC, and extractAIC additionally returns a number of degrees of freedom.

Usage

get_any_IC(object, ..., verbose=interactive() ,also_cAIC=TRUE)
# S3 method for HLfit
AIC(object, ..., k, verbose=interactive() ,also_cAIC=TRUE)
# S3 method for HLfit
extractAIC(fit, scale, k, ..., verbose=FALSE)

Arguments

object, fit

A object of class HLfit, as returned by the fitting functions in spaMM.

scale, k

Currently ignored, but are required in the definitions for consistency with the generic.

verbose

Whether to print the model selection criteria or not.

also_cAIC

Whether to include the conditional AIC in the result (its computation may be slow).

…

Other arguments that may be needed by some method.

Value

For AIC and get_any_IC, a numeric vector whose elements are described in the Details.

For extractAIC, a numeric vector of length 2, with first and second elements giving

edf

the degree of freedom of the fixed-effect terms of the model for the fitted model fit.

AIC

the (marginal) Akaike Information Criterion for fit.

This output aims to be equivalent (except for the explicit names) to the one from stats::extractAIC, despite the obscurities of the latter's documentation, and is indeed equivalent in value for GLMs (see Examples).

Details

get_any_IC computes, optionally prints, and returns invisibly the following quantities. The conditional AIC (Vaida and Blanchard 2005) is a relative measure of quality of prediction of new realizations of a mixed model, conditional on the realized values of the random effects. It involves the conditional likelihood, and degrees of freedom for (i) estimated residual error parameters and (ii) the overall linear predictor characterized by the Effective degrees of freedom already discussed by previous authors including Lee and Nelder (2001), which gave a general formula for it in HGLMs. Both a plug-in “asymptotic” estimate of the conditional AIC and of this effective df are returned by get_any_IC. Note that these may be biased estimates of conditional AIC and effective df, and that more refined formulas are discussed in the literature (e.g. Overholser and Xu 2014), some of which may be implemented in future versions of get_any_IC. Lee et al. (2006) and Ha et al (2007) defined a corrected AIC [i.e., AIC(D*) in their eq. 7] which is here interpreted as the conditional AIC. Also returned are the marginal AIC (Akaike's classical AIC), and a focussed AIC for dispersion parameters (dispersion AIC) discussed by Ha et al (2007; eq.10). This diversity of criteria should encourage users to think twice before applying model selection automatically, which is no better although more fashionable than misuses of simple null hypothesis testing. Also, alternative procedures for model choice can be considered (e.g. Cox and Donnelly, 2011, p. 130-131).

References

Cox, D. R. and Donnelly C. A. (2011) Principles of Applied Statistics. Cambridge Univ. Press.

Ha, I. D., Lee, Y. and MacKenzie, G. (2007) Model selection for multi-component frailty models. Statistics in Medicine 26: 4790-4807.

Overholser R., and Xu R. (2104) Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures. J. Multivariate Anal. 132: 160-170.

Vaida, F., and Blanchard, S. (2005) Conditional Akaike information for mixed-effects models. Biometrika 92, 351-370.

Examples

# NOT RUN {
data("wafers")
m1 <- HLfit(y ~ X1+X2+(1|batch), resid.model = ~ 1, data=wafers, method="ML")
get_any_IC(m1) 
extractAIC(m1)

# }
# NOT RUN {
# Checking consistency with glm example from help("stats::extractAIC"):
utils::example(glm)
dataf <- data.frame(counts=counts,outcome=outcome, treatment=treatment)
extractAIC(glm.D93) 
extractAIC(fitme(counts ~ outcome + treatment, family = poisson(), data=dataf))
lm.D93 <- glm(counts ~ outcome + treatment)
extractAIC(lm.D93)
extractAIC(fitme(counts ~ outcome + treatment, data=dataf))
# }
# NOT RUN {
# }