press.lmridge {lmridge}

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, \sum\frac{\hat{e}_{i,k}}{1-\frac{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)