rstats1.lmridge {lmridge}

Ordinary Ridge Regression Statistics 1

Description

The rstats1 function computes the ordinary ridge related statistics such as variance, squared bias, MSE, R-squared and condition number (CN), etc. (see Lee, 1979; Kalivas and Palmer, 2014 <doi:10.1002/cem.2555>)

Usage

   rstats1(x, ...)
   ## S3 method for class 'lmridge'
rstats1(x, ...)
   ## S3 method for class 'rstats1'
print(x, digits = max(5,getOption("digits") - 5), ...)

Arguments

x

An object of class "lmridge" (for the rstats1 or print.rstats1.lmridge)

digits

Minimum number of significant digits to be used for most numbers.

...

Not presently used in this implementation.

Details

The rstats1 function computes the ordinary ridge regression related statistics which may help in selecting optimal value of biasing parameter K. If value of K is zero then these statistics are equivalent to the relevant OLS statistics.

Value

Following are the ridge related statistics computed for given scalar or vector value of biasing parameter K provided as argument to lmridge or lmridgeEst function.

var

Variance of ridge regression for given biasing parameter K.

bias2

Squared bias of ridge regression for given biasing parameter K.

mse

Total MSE value for given biasing parameter K.

Fv

F-statistics value for testing of the significance of the ordinary ridge regression estimator computed for given biasing parameter K.

rfact

Shrinkage factor \frac{\lambda_j}{\lambda_j+K} for given biasing parameter K.

R2

R-squared for given biasing parameter K.

adjR2

Adjusted R-squared for given biasing parameter K.

eigval

Eigenvalue of X'X matrix for K=0.

CN

Condition number after addition of biasing parameter in X'X matrix.

Author(s)

Muhammad Imdad Ullah, Muhammad Aslam

References

Cule, E. and De lorio, M. (2012). A semi-Automatic method to guide the choice of ridge parameter in ridge regression. arXiv:1205.0686v1 [stat.AP].

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.

Kalivas, J. H., and Palmer, J. (2014). Characterizing multivariate calibration tradeoffs (bias, variance, selectivity, and sensitivity) to select model tuning parameters. Journal of Chemometrics, 28(5), 347–357. doi:10.1002/cem.2555.

See Also

Ridge related statistics rstats2, the ridge model fitting lmridge, ridge var-cov matrix vcov

Examples

data(Hald)
mod <- lmridge(y~., data = as.data.frame(Hald), K = seq(0,0.2, 0.005) )

rstats1(mod)

## Getting only Ridge MSE
rstats1(mod)[3]

rstats1(mod)$mse