liureg (version 1.1.2)

infoliu.liu: Model Selection Criteria for Liu Regression

Description

The infoliu.liu computes model selection criteria (AIC and BIC).

Usage

infoliu(object, …)
# S3 method for liu
infoliu(object, …)

Arguments

object

An object of class "liu".

…

Not presently used in this implementation.

Value

It returns a matrix of information criteria, AIC and BIC for each biasing parameter \(d\). Column of matrix indicates model selection criteria AIC and BIC, respectively, while rows indicate value of biasing parameter \(d\) 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 degree of freedom df in the Liu regression model, using formula \(trace(H_d)\), where \(H_d\) is hat matrix from Liu regression. Model selection criteria may be helpful for selecting optimal value of biasing parameter \(d\).

References

Akaike, H. (1974). A new look at the Statistical Model Identification. IEEE Transaction on Automatic Control, 9(6), 716--723. https://doi.org/10.1109/TAC.1974.1100705.

Akdeniz, F. and Kaciranlar, S. (1995). On the Almost Unbiased Generalized Liu Estimators and Unbiased Estimation of the Bias and MSE. Communications in Statistics-Theory and Methods, 24, 1789--1897. http://doi.org/10.1080/03610929508831585.

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

Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232--247.

Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189--196. http://doi.org/10.1080/03610929308831027.

Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461--464. https://projecteuclid.org/euclid.aos/1176344136.

See Also

Testing of Liu coefficient summary.liu

Examples

# NOT RUN {
mod<-liu(y~X1+X2+X3+X4, data = as.data.frame(Hald), d = seq(-5, 5, 0.1), scaling = "centered")

infoliu(mod)

## AIC values
infoliu(mod)[,1]

## BIC values
infoliu(mod)[,2]
# }