Entire regularization path of non-negative penalized generalized linear model for binomial family using using Multiplicative Iterative Algorithm

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Description

The function computes coefficients of a penalized generalized linear model subject to non-negativity constraints for binomial family using Multiplicative Iterative Algorithm for a sequence of lambda values. The function can also be used to obtain coefficient estimates for a given lambda value. Currently lasso and elastic net penalty are supported.

Usage

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nnlasso.binomial(x,y,lambda=NULL,intercept=TRUE,normalize=TRUE,tau=1,tol=1e-6,
maxiter=1e5,nstep=100,min.lambda=1e-4,eps=1e-6,path=TRUE,SE=FALSE)

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 binomial distribution and y should be a vector of 0 and 1.

lambda

The value of lambda for which coefficients are desired. The value of path must be FALSE in this case.

intercept

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

normalize

If TRUE, columns of x matrix are norma lized 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 ≤ τ ≤ 1 in elastic net penalty λ\{τ\|β\|_1+(1-τ)\|β\|_2^2\}. Default tau = 1 corresponds to LASSO penalty.

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.

eps

A small value below which a coefficient would be considered as zero.

path

Logical. If path=TRUE, entire regularization path will be obtained for a sequence of lambda values which are calculated automatically. To get coefficient estimates for a single lambda value, set path=FALSE with lambda=value. Default is path=TRUE.

SE

logical. If SE=TRUE, standard errors are produced for estimated coefficient at a given lambda. Standard errors are not produced if path=TRUE. Default is SE=FALSE.

Value

An object of class ‘nnlasso’ for which plot, predict and coef method exists. The object has 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 ‘nnlasso’ 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 ‘nnlasso’ object.

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

se

The standard errors of coefficient estimates

Author(s)

Baidya Nath Mandal and Jun Ma

References

Mandal, B.N. and Ma, J. (2016). L1 regularized multiplicative iterative path algorithm for non-negative generalized linear models.

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