The genridge package introduces generalizations of the standard univariate ridge trace plot used in ridge regression and related methods (Friendly, 2012). These graphical methods show both bias (actually, shrinkage) and precision, by plotting the covariance ellipsoids of the estimated coefficients, rather than just the estimates themselves. 2D and 3D plotting methods are provided, both in the space of the predictor variables and in the transformed space of the PCA/SVD of the predictors.
Details
This package provides computational support for the
graphical methods described in Friendly (2013). Ridge regression models may
be fit using the function ridge, which incorporates features
of lm.ridge. In particular, the shrinkage factors in
ridge regression may be specified either in terms of the constant added to
the diagonal of \(X^T X\) matrix (lambda), or the equivalent number
of degrees of freedom.
More importantly, the ridge function also calculates and
returns the associated covariance matrices of each of the ridge estimates,
allowing precision to be studied and displayed graphically.
This provides the support for the main plotting functions in the package:
plot.ridge: Bivariate ridge trace plots
pairs.ridge: All pairwise bivariate ridge trace plots
plot3d.ridge: 3D ridge trace plots
traceplot: Traditional univariate ridge trace plots
In addition, the function pca.ridge transforms the
coefficients and covariance matrices of a ridge object from predictor
space to the equivalent, but more interesting space of the PCA of \(X^T
X\) or the SVD of X. The main plotting functions also work for these
objects, of class c("ridge", "pcaridge").
Finally, the functions precision and vif.ridge
provide other useful measures and plots.
References
Friendly, M. (2013). The Generalized Ridge Trace Plot: Visualizing Bias and Precision. Journal of Computational and Graphical Statistics, 22(1), 50-68, doi:10.1080/10618600.2012.681237, https://www.datavis.ca/papers/genridge-jcgs.pdf
Arthur E. Hoerl and Robert W. Kennard (1970). Ridge Regression: Biased Estimation for Nonorthogonal Problems, Technometrics, 12(1), pp. 55-67.
Arthur E. Hoerl and Robert W. Kennard (1970). Ridge Regression: Applications to Nonorthogonal Problems Technometrics, 12(1), pp. 69-82.