press.lmridge: Predicted Residual Sum of Squares

In lmridge: Linear Ridge Regression with Ridge Penalty and Ridge Statistics

Predicted Residual Sum of Squares

Description

The press.lmridge function computes predicted residual sum of squares (PRESS) (see Allen, 1971).

Usage

press(object, ...)
## S3 method for class 'lmridge'
press(object, ...)

Arguments

object	An object of class "lmridge".
...	Not presently used in this implementation.

Details

All of the n leave-one-out predicted residual sum of squares is calculated by fitting full regression model by using, ∑(\hat{e}_{i,k})(1-(1/n)-H_{ii_{R,k}}), where H_{ii_{R,k}} is hat matrix from ridge model fit, \hat{e_{i,k}} is the ith residual at specific value of K.

Value

The press.lmridge produces a vector of PRESS or a matrix of PRESS for scalar or vector values of biasing parameter.

Author(s)

Muhammad Imdad Ullah, Muhammad Aslam

References

Allen, D. M. (1971). Mean Square Error of Prediction as a Criterion for Selecting Variables. Technometrics, 13, 469-475. doi: 10.1080/00401706.1971.10488811.

Allen, D. M. (1974). The Relationship between Variable Selection and Data Augmentation and Method for Prediction. Technometrics, 16, 125-127. doi: 10.1080/00401706.1974.10489157.

Hoerl, A. E., Kennard, R. W., and Baldwin, K. F. (1975). Ridge Regression: Some Simulation. Communication in Statistics, 4, 105-123. doi: 10.1080/03610927508827232.

Hoerl, A. E. and Kennard, R. W., (1970). Ridge Regression: Biased Estimation of Nonorthogonal Problems. Technometrics, 12, 55-67. doi: 10.1080/00401706.1970.10488634.

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.

See Also

The ridge model fitting lmridge, ridge residual residuals, ridge predicted value predict

Examples

mod <- lmridge(y~., as.data.frame(Hald), K = seq(0, 0.5, 0.04))
press(mod)

lmridge documentation built on Jan. 15, 2023, 5:06 p.m.