ridgeGLMmultiT {porridge}

Multi-targeted ridge estimation of generalized linear models.

Description

Function that evaluates the multi-targeted ridge estimator of the regression parameter of generalized linear models.

Usage

ridgeGLMmultiT(Y, X, U=matrix(ncol=0, nrow=length(Y)), 
               lambdas, targetMat, model="linear", 
               minSuccDiff=10^(-10), maxIter=100)

Arguments

Y

A numeric being the response vector.

X

The design matrix of the penalized covariates. The number of rows should match the number of elements of Y.

U

The design matrix of the unpenalized covariates. The number of rows should match the number of elements of Y.

lambdas

An all-positive numeric, vector of penalty parameters, one per target.

targetMat

A matrix with targets for the regression parameter as columns.

model

A character, either "linear" and "logistic" (a reference to the models currently implemented), indicating which generalized linear model model instance is to be fitted.

minSuccDiff

A numeric, the minimum distance between the loglikelihoods of two successive iterations to be achieved. Used only if model="logistic".

maxIter

A numeric specifying the maximum number of iterations. Used only if model="logistic".

Details

This function finds the maximizer of the following penalized loglikelihood: \mathcal{L}( \mathbf{Y}, \mathbf{X}; \boldsymbol{\beta}) - \frac{1}{2} \sum_{k=1}^K \lambda_k \| \boldsymbol{\beta} - \boldsymbol{\beta}_{k,0} \|_2^2, with loglikelihood \mathcal{L}( \mathbf{Y}, \mathbf{X}; \boldsymbol{\beta}), response \mathbf{Y}, design matrix \mathbf{X}, regression parameter \boldsymbol{\beta}, penalty parameter \lambda, and the k-th shrinkage target \boldsymbol{\beta}_{k,0}. For more details, see van Wieringen, Binder (2020).

Value

The ridge estimate of the regression parameter.

Author(s)

W.N. van Wieringen.

References

van Wieringen, W.N. Binder, H. (2020), "Online learning of regression models from a sequence of datasets by penalized estimation", submitted.

Examples

# set the sample size
n <- 50

# set the true parameter
betas <- (c(0:100) - 50) / 20

# generate covariate data
X <- matrix(rnorm(length(betas)*n), nrow=n)

# sample the response
probs <- exp(tcrossprod(betas, X)[1,]) / (1 + exp(tcrossprod(betas, X)[1,]))
Y     <- numeric()
for (i in 1:n){
    Y <- c(Y, sample(c(0,1), 1, prob=c(1-probs[i], probs[i])))
}

# set the penalty parameter
lambdas <- c(1,3)

# estimate the logistic regression parameter
# bHat <- ridgeGLMmultiT(Y, X, lambdas, model="logistic",
#                       targetMat=cbind(betas/2, rnorm(length(betas))))