# nnlasso.normal: Entire regularization path of non-negative penalized... In nnlasso: Non-Negative Lasso and Elastic Net Penalized Generalized Linear Models

## Description

The function computes coefficients of a penalized generalized linear model subject to non-negativity constraint for normal family using Multiplicative Iterative Algorithm for a sequence of lambda values or alternatively for a single lambda value. Currently lasso and elastic net penalty are supported.

## Usage

 ```1 2``` ```nnlasso.normal(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 normal distribution. `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 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 ≤ 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. Each row denotes solution for a particular lambda. Corresponding lambda values are available in ‘lambdas’ element of the ‘nnlasso’ 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 `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.

nnlasso documentation built on May 2, 2019, 8:19 a.m.