lassopv {lassopv}

Estimation of Nonparametric P-Value Estimation for Predictors in Lasso

Description

This function estimates the p-values for predictors x against target variable y in lasso regression, using the regularization strength when each predictor enters the active set of regularization path for the first time as the statistic. This is based on the assumption that predictors (of the same variance) that (first) become active earlier tend to be more significant. Two null distributions are supported: normal and spherical, which are computed separately for each predictor and analytically under approximation, which aims at efficiency and accuracy for small p-values.

Usage

lassopv(x,y,normalize=TRUE,H0=c("spherical","normal"),

log.p=FALSE,max.predictors=NULL,trace = FALSE,Gram,

eps = .Machine$double.eps,max.steps,use.Gram=TRUE) 

Arguments

x

Input matrix of predictor variables.

y

Input vector of target variable.

normalize

Whether every predictor is scaled to unit variance first. Every predictor is forcefully shifted to zero mean regardless of this argument.

H0

The null distribution for each predictor x.

Spherical: uniform distribution on n-1 dimensional sphere S^{n-1}, so the variance is kept the same as sigma_x^2.

Normal: i.i.d N(0,sigma_x^2) in R^n, where sigma_x^2 is the variance of the original predictor x and n is the number of rows in x.

log.p

Whether to output log p-values instead.

max.predictors

The number of top predictors to estimate p-values for. Defaults to all predictors.

trace

Whether traces lasso regression. See lars in package lars.

Gram

Optional Gram used by lasso regression in lars.

eps

Precision for lars function.

max.steps

The optional maximum number steps for lasso regression. See lars in package lars.

use.Gram

Whether to use Gram in lasso regression. See lars in package lars.

Value

Vector of p-values for predictors. Predictors never entered the active set of regularization path within the given max.steps or not within the top (max.predictors) predictors have p-value=1. If log.p is set, output log p-values instead.

References

Lingfei Wang and Tom Michoel, Comparable variable selection with lasso, https://arxiv.org/pdf/1701.07011. 2017, 2018.

Examples

library(lars)
library(lassopv)
data(diabetes)
attach(diabetes)
pv=lassopv(x,y)