ridge: linearRidge – R documentation

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linearRidge

Linear ridge regression.

Description

Fits a linear ridge regression model. Optionally, the ridge regression parameter is chosen automatically using the method proposed by Cule et al (2012).

Usage

linearRidge(formula, data, lambda = "automatic", nPCs = NULL,
scaling = c("corrForm", "scale", "none"), ...)

## S3 method for class 'ridgeLinear'
coef(object, all.coef = FALSE, ...)

## S3 method for class 'ridgeLinear'
plot(x, y = NULL, ...)

## S3 method for class 'ridgeLinear'
predict(object, newdata, na.action = na.pass, all.coef = FALSE, ...)

## S3 method for class 'ridgeLinear'
print(x, all.coef = FALSE, ...)

## S3 method for class 'ridgeLinear'
summary(object, all.coef = FALSE, ...)

## S3 method for class 'summary.ridgeLinear'
print(x, digits = max(3,
getOption("digits") - 3),
signif.stars = getOption("show.signif.stars"), ...)

Arguments

`formula`	a formula expression as for regression models, of the form `response ~ predictors`. See the documentation of `formula` for other details.
`data`	an optional data frame in which to interpret the variables occuring in `formula`.
`lambda`	A ridge regression parameter. May be a vector. If `lambda` is `"automatic"` (the default), then the ridge parameter is chosen automatically using the method of Cule et al (2012).
`nPCs`	The number of principal components to use to choose the ridge regression parameter, following the method of Cule et al (2012). It is not possible to specify both `lambda` and `nPCs`.
`scaling`	The method to be used to scale the predictors. One of `"corrform"`(the default) scales the predictors to correlation form, such that the correlation matrix has unit diagonal. `"scale"`Standardizes the predictors to have mean zero and unit variance. `"none"`No scaling.
`object`	A ridgeLinear object, typically generated by a call to `linearRidge`.
`newdata`	An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`na.action`	function determining what should be done with missing values in `newdata`. The default is to predict `NA`.
`all.coef`	Logical. Should results be returned for all ridge regression penalty parameters (`all.coef = TRUE`), or only for the ridge parameter chosen automatically using the method of Cule et al?
`x`	An object of class `ridgeLinear` (for the `print.ridgeLinear` and `plot.ridgeLinear` functions) or an object of class `summary.ridgeLinear` (for the `print.summary.ridgeLinear` function)
`y`	Dummy argument for compatibility with the default `plot` method. Ignored.
`digits`	minimum number of significant digits to be used for most numbers
`signif.stars`	logical; if `TRUE`, P-values are additionally encoded visually as `significance stars` in order to help scanning of long coefficient tables. It defaults to the `show.signif.stars` slot of `options`.
`...`	Additional arguments to be passed to or from other methods.

Details

If an intercept is present in the model, its coefficient is not penalised. If you want to penalise an intercept, put in your own constant term and remove the intercept.

Value

An object of class "ridgeLinear", with components:

`automatic`	Logical. Was `lambda` chosen automatically?
`call`	The matched call.
`coef`	A named vector of fitted coefficients.
`df`	A vector of degrees of freedom of the model fit, degrees of freedom for variance, and residual degrees of freedom of the fitted model.
`Inter`	Was an intercept included?
`isScaled`	Were the predictors scaled before the model was fitted?
`lambda`	The ridge regression parameter(s).
`scales`	The scales used to standardize the predictors.
`terms`	The `terms` object used.
`x`	The scaled predictor matrix.
`xm`	A vector of means of the predictors.
`y`	The response.
`ym`	The mean of the response.

And optionally the components

`max.nPCs`	The maximum number of principal components for which a ridge regression parameter was computed.
`chosen.nPCs`	The number of principal components used to compute the ridge parameter.

Author(s)

Erika Cule

References

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

Examples

data(GenCont)
mod <- linearRidge(Phenotypes ~ ., data = as.data.frame(GenCont))
summary(mod)

ridge

Ridge Regression with Automatic Selection of the Penalty Parameter

v2.9

GPL-2

Authors

Steffen Moritz [aut, cre] (<https://orcid.org/0000-0002-0085-1804>), Erika Cule [aut], Dan Frankowski [aut]

Initial release

2021-02-03