IWLSridge {multiridge}

Iterative weighted least squares algorithm for linear and logistic ridge regression.

Description

Iterative weighted least squares algorithm for linear and logistic ridge regression. Updates the weights and linear predictors until convergence.

Usage

IWLSridge(XXT, Y, X1 = NULL, intercept = TRUE, frac1 = NULL, eps = 1e-07,
maxItr = 25, trace = FALSE, model = NULL, E0 = NULL)

Arguments

XXT

Matrix. Dimensions nxn. Sample cross-product from penalized variables, usually computed by SigmaFromBlocks.

Y

Response vector: numeric, binary, or two-class factor

X1

Matrix. Dimension n x p_0, p_0 < n, representing unpenalized covariates.

intercept

Boolean. Should an intercept be included?

frac1

Scalar. Prior fraction of cases. Only relevant for model="logistic".

eps

Scalar. Numerical bound for IWLS convergence.

maxItr

Integer. Maximum number of iterations used in IWLS.

trace

Boolean. Should the output of the IWLS algorithm be traced?

model

Character. Any of c("linear", "logistic"). Is inferred from Y when NULL. Note that the cox model for survival is covered by the function IWLSCoxridge.

E0

Numerical vector or NULL. Optional initial values for linear predictor. Same length as Y. Usually NULL, which initializes linear predictor with 0.

Details

An (unpenalized) intercept is included by default. To keep the function computationally efficient it returns the linear predictors (which suffice for predictions), instead of parameter estimates. These may be obtained by applying the betasout function to the output of this function.

Value

List, containing:

etas

Numerical vector: Final linear predictors

Ypred

Predicted survival

convergence

Boolean: has IWLS converged?

nIt

Number of iterations

Hres

Auxiliary list object. Passed on to other functions

linearized

Linearized predictions

unpen

Boolean: are there any unpenalized covariates involved? Passed on to other functions

intercept

Boolean: Is an intercept included?

eta0

Numerical vector: Initial linear predictors

X1

Matrix: design matrix unpenalized variables

References

Mark A. van de Wiel, Mirrelijn van Nee, Armin Rauschenberger (2021). Fast cross-validation for high-dimensional ridge regression. J Comp Graph Stat

See Also

IWLSCoxridge for Cox ridge. betasout for obtaining parameter estimates. predictIWLS for predictions on new samples. A full demo and data are available from:
https://drive.google.com/open?id=1NUfeOtN8-KZ8A2HZzveG506nBwgW64e4

Examples

data(dataXXmirmeth)
resp <- dataXXmirmeth[[1]]
XXmirmeth <- dataXXmirmeth[[2]]
lambdas <- c(100,1000)

# Prepare fitting for the specified penalties.
XXT <- SigmaFromBlocks(XXmirmeth,penalties=lambdas)

# Fit. fit$etas contains the n linear predictors
fit <- IWLSridge(XXT,Y=resp)