extlasso {extlasso}

Entire regularization path of penalized generalized linear model for normal/binomial/poisson family using modified Jacobi Algorithm

Description

The function computes coefficients of a penalized generalized linear model for normal/binomial/poisson family using modified Jacobi Algorithm for a sequence of lambda values. Currently lasso and elastic net penalty are supported.

Usage

extlasso(x,y,family=c("normal","binomial","poisson"),intercept=TRUE, 
normalize=TRUE,tau=1,alpha=1e-12,eps=1e-6,tol=1e-6,maxiter=1e5, nstep=100,min.lambda=1e-4)

Arguments

x

x is matrix of order n x p where n is number of observations and p is number of predictor variables. Rows should represent observations and columns should represent predictor variables.

y

y is a vector of response variable of order n x 1. y should follow either normal/binomial/poisson distribution.

family

family should be one of these: "normal","binomial","poisson"

intercept

If TRUE, model includes intercept, else the model does not have intercept.

normalize

If TRUE, columns of x matrix are normalized with mean 0 and norm 1 prior to fitting the model. The coefficients at end are returned on the original scale. Default is normalize = TRUE.

tau

Elastic net parameter, 0 \le \tau \le 1 in elastic net penalty \lambda{\tau||\beta||_1+(1-\tau)||\beta||_2^2}. Default tau = 1 corresponds to LASSO penalty.

alpha

The quantity in approximating |\beta_j| = \sqrt(\beta_j^2+\alpha) Default is alpha = 1e-12.

eps

A value which is used to set a coefficient to zero if coefficients value is within - eps to + eps. Default is eps = 1e-6.

tol

Tolerance criteria for convergence of solutions. Default is tol = 1e-6.

maxiter

Maximum number of iterations permissible for solving optimization problem for a particular lambda. Default is 10000. Rarely you need to change this to higher value.

nstep

Number of steps from maximum value of lambda to minimum value of lambda. Default is nstep = 100.

min.lambda

Minimum value of lambda. Default is min.lambda=1e-4.

Value

An object of class ‘extlasso’ with following components:

beta0

A vector of order nstep of intercept estimates. Each value denote an estimate for a particular lambda. Corresponding lambda values are available in ‘lambdas’ element of the ‘extlasso’ object.

coef

A matrix of order nstep x p of slope estimates. Each row denotes solution for a particular lambda. Corresponding lambda values are available in ‘lambdas’ element of the ‘extlasso’ object. Here p is number of predictor variables.

lambdas

Sequence of lambda values for which coefficients are obtained

L1norm

L1norm of the coefficients

norm.frac

Fractions of norm computed as L1 norm at current lambda divided by maximum L1 norm

lambda.iter

Number of iterations used for different lambdas

of.value

Objective function values

normx

Norm of x variables

Author(s)

B N Mandal and Jun Ma

References

Mandal, B.N. and Jun Ma, (2014). A Jacobi-Armijo Algorithm for LASSO and its Extensions.

Examples

#LASSO
x=matrix(rnorm(100*30),100,30)
y=rnorm(100)
g1=extlasso(x,y,family="normal")
plot(g1)
plot(g1,xvar="lambda")

#Elastic net
g2=extlasso(x,y,family="normal",tau=0.6)
plot(g2)
plot(g2,xvar="lambda")

#Ridge regression
g3=extlasso(x,y,family="normal",tau=0)
plot(g3)
plot(g3,xvar="lambda")

#L1 penalized GLM for binomial family
x=matrix(rnorm(100*30),100,30)
y=sample(c(0,1),100,replace=TRUE)
g1=extlasso(x,y,family="binomial")
plot(g1)
plot(g1,xvar="lambda")

#Elastic net with GLM with binomial family
g2=extlasso(x,y,family="binomial",tau=0.8)
plot(g2)
plot(g2,xvar="lambda")