lmridge (version 1.2)

infocr.lmridge: Model Selection Criteria for Ridge Regression

Description

The infocr.lmridge function computes model information selection criteria (AIC and BIC), see Akaike, 1974 <https://doi.org/10.1109/TAC.1974.1100705>; Imdad, 2017 and Schwarz, 1978 <https://doi.org/10.1214/aos/1176344136>).

Usage

infocr(object, …)
# S3 method for lmridge
infocr(object, …)

Arguments

object

An object of class "lmridge".

…

Not presently used in this implementation.

Value

It returns a matrix of information criteria, AIC and BIC for each biasing parameter \(K\). Column of matrix indicates model selection criteria AIC and BIC, respectively, while rows indicate value of biasing parameter \(K\) for which model selection criteria are computed.

Details

Model information selection criteria are common way of selecting among model while balancing the competing goals of fit and parsimony. The model selection criteria AIC and BIC are computed by quantifying df in the ridge regression model, using formula (\(df=trace[X(X'X+kI)^{-1}X']\)). It can be helpful for selecting optimal value of biasing parameter \(K\).

References

Akaike, H. (1974). A new look at the Statistical Model Identification. IEEE Transaction on Automatic Control, 9(6), 716-723. Akaike, 1974.

Imdad, M. U. Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan), 2017.

Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461--464. Schwarz, 1978.

See Also

the ridge model fitting lmridge, ridge AIC and BIC plot info.plot

Examples

# NOT RUN {
mod <- lmridge(y~., as.data.frame(Hald), K = seq(0, .2, 0.001))
infocr(mod)

## Vector of AIC values
infocr(mod)[,1]

## vector of BIC values
infocr(mod)[,2]
# }