lmridge (version 1.2.2)

bias.plot: Bias Variance and MSE Trade-off Plot

Description

Trade-off between bias, variance and MSE of the linear ridge regression against vector or scalar value of biasing parameter \(K\) (see Kalivas and Palmer, 2014 <tools:::Rd_expr_doi("10.1002/cem.2555")>).

Usage

bias.plot(x, abline = TRUE, ...)

Value

Nothing returned

Arguments

x

An object of class "lmridge".

abline

Horizontal and vertical lines show the minimum value of the ridge MSE at certain value of biasing parameter \(K\).

...

Not presently used in this implementation.

Author

Muhammad Imdad Ullah, Muhammad Aslam

Details

The effect of multicollinearity on the coefficient estimates can be identified using different graphical display. One of them is plot of bias, variance and MSE. A little addition of bias lead to a substantial decrease in variance, and MSE. Therefore, a trade-off is made between bias and variance to have acceptable MSE. The bias.plot can be helpful for selection of optimal value of biasing parameter \(K\).

References

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. tools:::Rd_expr_doi("10.1002/cem.2555").

See Also

The ridge model fitting lmridge, ridge CV and GCV plots cv.plot, ridge AIC and BIC plots info.plot, m-scale and isrm plots isrm.plot, ridge and VIF trace plot.lmridge, miscellaneous ridge plots rplots.plot

Examples

mod <- lmridge(y~., as.data.frame(Hald), K = seq(0, 0.3, 0.002))
## for indication vertical line (biasing parameter k) and
## horizontal line (minimum minimum ridge MSE values corresponding to vertical line)
bias.plot(mod)

## without Horizontal and vertical line as set \code{abline = FALSE}
bias.plot(mod, abline=FALSE)