# extlasso.binomial: Entire regularization path of penalized generalized linear... In extlasso: Maximum Penalized Likelihood Estimation with Extended Lasso Penalty

 extlasso.binomial R Documentation

## Entire regularization path of penalized generalized linear model for binomial family using modified Jacobi Algorithm

### Description

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

### Usage

```extlasso.binomial(x,y,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 binomial distribution and y should be a vector of 0 and 1. `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. `alpha` The quantity in approximating |β| = √(β^2+α) 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’ 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 ‘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. `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

```x=matrix(rnorm(100*30),100,30)
y=sample(c(0,1),100,replace=TRUE)
g1=extlasso.binomial(x,y)
plot(g1)
plot(g1,xvar="lambda")
g1\$of.value
```

extlasso documentation built on May 13, 2022, 9:08 a.m.