Consistent AIC

Consistent AIC

Usage

CAIC(object, ..., alpha)
# S3 method for default
CAIC(object, ..., alpha)
CAICtable(object, ..., alpha)

Arguments

object: A fitted model object.
...: More fitted model objects.
alpha: Weight factor between 0 and 1 (see Details). Default value is 0.5.

Details

CAIC = alpha * AIC + (1 - alpha) * BIC

Value

Atomic vector if only one input object provided, a data frame similar to what is returned by AIC and BIC

if there are more than one input objects.

CAICtable returns a data frame with delta CAIC (dCAIC = CAIC - min(CAIC)) and CAIC weights (wCAIC = exp(-0.5 dCAIC_i) / sum(exp(-0.5 dCAIC_i))) where i = 1,...,m are candidate models.

References

Bozdogan, H. 1987. Model selection and Akaike's information criterion (AIC): the general theory and its analytical extensions. Psychometrika, 52, 345-370.

Taper, M. 2004. Model identification from many candidates. In: Taper, M. and Lele, S. R. (eds), The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations. The University of Chicago Press, Chicago, IL, 567 pp.

Author

Subhash Lele and Peter Solymos

Examples

## compare some random models
y <- rnorm(10)
a <- lm(y ~ runif(10))
b <- lm(y ~ runif(10))

0.5*(AIC(a) + BIC(a))
#> [1] 33.73626
CAIC(a)
#> [1] 33.73626
AIC(a)
#> [1] 33.28238
CAIC(a, alpha=1)
#> [1] 33.28238
BIC(a)
#> [1] 34.19014
CAIC(a, alpha=0)
#> [1] 34.19014

CAIC(a, b)
#>   df     CAIC
#> a  3 33.73626
#> b  3 35.90616
CAIC(a, b, alpha=0.2)
#>   df     CAIC
#> a  3 34.00859
#> b  3 36.17849

CAICtable(a, b, alpha=1)
#>   df     CAIC    dCAIC     wCAIC
#> a  3 33.28238 0.000000 0.7474294
#> b  3 35.45228 2.169898 0.2525706

## you can use global option
## useful when inside of xv or bootstrap
## no need for extra argument
getOption("CAIC_alpha")
#> NULL
op <- options(CAIC_alpha = 0.2)
getOption("CAIC_alpha")
#> [1] 0.2
CAIC(a,b)
#>   df     CAIC
#> a  3 34.00859
#> b  3 36.17849
options(op)
getOption("CAIC_alpha")
#> NULL