Fit a linear model by ridge regression, returning an object of class "ridge".
ridge(formula, data, subset, lambda = 1.0, method = "GCV", ngrid = 200, tol = 1e-07,
maxiter = 50, na.action, x = FALSE, y = FALSE, contrasts = NULL, ...)A list with the following components:
dimensions of model matrix.
a named vector of coefficients.
a named vector of coefficients.
the fitted mean values.
the residuals, that is response minus fitted values.
the residual sum of squares.
the effective number of parameters.
vector (if method = "grid") of GCV values.
HKB estimate of the ridge constant.
LW estimate of the ridge constant.
vector (if method = "grid") of lambda values; otherwise, for
methods method = "none", "GCV" or "MSE", the value of ridge
parameter used by the algorithm.
value of lambda with the minimum GCV (only relevant if method = "grid").
number of iterations performed by the algorithm (only relevant if method = "MSE").
the matched call.
the terms object used.
(only where relevant) the contrasts used.
if requested, the response used.
if requested, the model matrix used.
if requested, the model frame used.
an object of class "formula" (or one that
can be coerced to that class): a symbolic description of the model to
be fitted.
an optional data frame, list or environment (or object coercible
by as.data.frame to a data frame) containing the variables in
the model. If not found in data, the variables are taken from
environment(formula), typically the environment from which ridge
is called.
an optional vector specifying a subset of observations to be used in the fitting process.
a function which indicates what should happen when the data
contain NAs. The default is set by the na.action setting of
options, and is na.fail if that is unset.
a scalar or vector of ridge constants. A value of 0 corresponds to ordinary least squares.
the method for choosing the ridge parameter lambda. If method = "none",
then lambda is 'fixed'. If method = "GCV" (the default) then the ridge
parameter is chosen automatically using the generalized cross validation (GCV) criterion.
For method = "grid", optimal value of lambda is selected computing the GCV
criterion over a grid. If method = "MSE" the optimal ridge parameter is selected
minimizing the mean squared estimation error criterion, this is the ORPS1
subroutine by Lee (1987).
number of elements in the grid used to compute the GCV criterion.
Only required if method = "grid" and lambda is a scalar.
tolerance for the optimization of the GCV criterion. Default is 1e-7.
maximum number of iterations. The default is 50.
logicals. If TRUE the corresponding components of
the fit (the model matrix, the response) are returned.
an optional list. See the contrasts.arg of
model.matrix.default.
additional arguments to be passed to the low level regression fitting functions (not implemented).
ridge function fits in linear ridge regression without scaling or centering
the regressors and the response. In addition, If an intercept is present in the model, its
coefficient is penalized.)
Golub, G.H., Heath, M., Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215-223.
Hoerl, A.E., Kennard, R.W., Baldwin, K.F. (1975). Ridge regression: Some simulations. Communication in Statistics 4, 105-123.
Hoerl, A.E., Kennard, R.W. (1970). Ridge regression: Biased estimation of nonorthogonal problems. Technometrics 12, 55-67.
Lawless, J.F., Wang, P. (1976). A simulation study of ridge and other regression estimators. Communications in Statistics 5, 307-323.
Lee, T.S (1987). Algorithm AS 223: Optimum ridge parameter selection. Applied Statistics 36, 112-118.
lm, ols
z <- ridge(GNP.deflator ~ ., data = longley, lambda = 4, method = "grid")
z # ridge regression on a grid over seq(0, 4, length = 200)
z <- ridge(GNP.deflator ~ ., data = longley)
z # ridge parameter selected using GCV (default)
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