KSPM (version 0.2.1)

extractAIC.kspm: Extract AIC from a Kernel Semi Parametric Model

Description

Computes the Akaike Information Criterion (AIC) for a kspm fit.

Usage

# S3 method for kspm
extractAIC(fit, scale = NULL, k = 2,
  correction = FALSE, ...)

Arguments

fit

fitted model, usually the result of kspm.

scale

option not available for kspm fit.

k

numeric specifying the 'weight' of the effective degrees of freedom (edf) part in the AIC formula. See details.

correction

boolean indicating if the corrected AIC should be computed instead of standard AIC, may be TRUE only for k=2. See details.

...

additional optional argument (currently unused).

Value

extractAIC.kspm returns a numeric value corresponding to AIC. Of note, the AIC obtained here differs from a constant to the AIC obtained with extractAIC applied to a lm object. If one wants to compare a kspm model with a lm model, it is preferrable to compute again the lm model using kspm function by specifying kernel = NULL and apply extractAIC method on this model.

Details

The criterion used is \(AIC = n log(RSS) + k (n-edf)\) where \(RSS\) is the residual sum of squares and \(edf\) is the effective degree of freedom of the model. k = 2 corresponds to the traditional AIC, using k = log(n) provides Bayesian Information Criterion (BIC) instead. For k=2, the corrected Akaike's Information Criterion (AICc) is obtained by \(AICc = AIC + \frac{2 (n-edf) (n-edf+1)}{(edf-1)}\).

References

Liu, D., Lin, X., and Ghosh, D. (2007). Semiparametric regression of multidimensional genetic pathway data: least squares kernel machines and linear mixed models. Biometrics, 63(4), 1079:1088.

See Also

stepKSPM for variable selection procedure based on AIC.

Examples

# NOT RUN {
x <- 1:15
y <- 3*x + rnorm(15, 0, 2)
fit <- kspm(y, kernel = ~ Kernel(x, kernel.function = "linear"))
extractAIC(fit)

# }