lm.ridge: Ridge Regression

Description Usage Arguments Details Value References See Also Examples

View source: R/lm.ridge.R

Description

Fit a linear model by ridge regression.

Usage

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lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
         x = FALSE, y = FALSE, contrasts = NULL, ...)

Arguments

formula

a formula expression as for regression models, of the form response ~ predictors. See the documentation of formula for other details. offset terms are allowed.

data

an optional data frame, list or environment in which to interpret the variables occurring in formula.

subset

expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.

na.action

a function to filter missing data.

lambda

A scalar or vector of ridge constants.

model

should the model frame be returned? Not implemented.

x

should the design matrix be returned? Not implemented.

y

should the response be returned? Not implemented.

contrasts

a list of contrasts to be used for some or all of factor terms in the formula. See the contrasts.arg of model.matrix.default.

...

additional arguments to lm.fit.

Details

If an intercept is present in the model, its coefficient is not penalized. (If you want to penalize an intercept, put in your own constant term and remove the intercept.)

Value

A list with components

coef

matrix of coefficients, one row for each value of lambda. Note that these are not on the original scale and are for use by the coef method.

scales

scalings used on the X matrix.

Inter

was intercept included?

lambda

vector of lambda values

ym

mean of y

xm

column means of x matrix

GCV

vector of GCV values

kHKB

HKB estimate of the ridge constant.

kLW

L-W estimate of the ridge constant.

References

Brown, P. J. (1994) Measurement, Regression and Calibration Oxford.

See Also

lm

Examples

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longley # not the same as the S-PLUS dataset
names(longley)[1] <- "y"
lm.ridge(y ~ ., longley)
plot(lm.ridge(y ~ ., longley,
              lambda = seq(0,0.1,0.001)))
select(lm.ridge(y ~ ., longley,
               lambda = seq(0,0.1,0.0001)))

Example output

     GNP.deflator     GNP Unemployed Armed.Forces Population Year Employed
1947         83.0 234.289      235.6        159.0    107.608 1947   60.323
1948         88.5 259.426      232.5        145.6    108.632 1948   61.122
1949         88.2 258.054      368.2        161.6    109.773 1949   60.171
1950         89.5 284.599      335.1        165.0    110.929 1950   61.187
1951         96.2 328.975      209.9        309.9    112.075 1951   63.221
1952         98.1 346.999      193.2        359.4    113.270 1952   63.639
1953         99.0 365.385      187.0        354.7    115.094 1953   64.989
1954        100.0 363.112      357.8        335.0    116.219 1954   63.761
1955        101.2 397.469      290.4        304.8    117.388 1955   66.019
1956        104.6 419.180      282.2        285.7    118.734 1956   67.857
1957        108.4 442.769      293.6        279.8    120.445 1957   68.169
1958        110.8 444.546      468.1        263.7    121.950 1958   66.513
1959        112.6 482.704      381.3        255.2    123.366 1959   68.655
1960        114.2 502.601      393.1        251.4    125.368 1960   69.564
1961        115.7 518.173      480.6        257.2    127.852 1961   69.331
1962        116.9 554.894      400.7        282.7    130.081 1962   70.551
                        GNP    Unemployed  Armed.Forces    Population 
2946.85636017    0.26352725    0.03648291    0.01116105   -1.73702984 
         Year      Employed 
  -1.41879853    0.23128785 
modified HKB estimator is 0.006836982 
modified L-W estimator is 0.05267247 
smallest value of GCV  at 0.0057 

MASS documentation built on May 3, 2021, 5:08 p.m.

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