# MFKnockoffs.stat.lasso_lambda_difference_bin: Penalized logistic regression statistics for MFKnockoffs In MFKnockoffs: Model-Free Knockoff Filter for Controlled Variable Selection

## Description

Fit the lasso path and computes the difference statistic

W_j = Z_j - \tilde{Z}_j

where Z_j and \tilde{Z}_j are the maximum values of the regularization parameter λ at which the jth variable and its knockoff enter the penalized logistic regression model, respectively.

## Usage

 1 MFKnockoffs.stat.lasso_lambda_difference_bin(X, X_k, y, ...) 

## Arguments

 X original design matrix (size n-by-p) X_k knockoff matrix (size n-by-p) y response vector (length n). It should be either a factor with two levels, or a two-column matrix of counts or proportions (the second column is treated as the target class; for a factor, the last level in alphabetical order is the target class). If y is presented as a vector, it will be coerced into a factor. ... additional arguments specific to 'glmnet' (see Details)

## Details

This function uses glmnet to compute the lasso path on a fine grid of λ's.

The nlambda parameter can be used to control the granularity of the grid of λ's. The default value of nlambda is 100.

This function is a wrapper around the more general MFKnockoffs.stat.glmnet_lambda_difference.

For a complete list of the available additional arguments, see glmnet or lars.

## Value

A vector of statistics W (length p)

Other statistics for knockoffs: MFKnockoffs.stat.forward_selection, MFKnockoffs.stat.glmnet_coef_difference, MFKnockoffs.stat.glmnet_lambda_difference, MFKnockoffs.stat.lasso_coef_difference_bin, MFKnockoffs.stat.lasso_coef_difference, MFKnockoffs.stat.lasso_lambda_difference, MFKnockoffs.stat.random_forest, MFKnockoffs.stat.sqrt_lasso, MFKnockoffs.stat.stability_selection
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 p=100; n=200; k=15 mu = rep(0,p); Sigma = diag(p) X = matrix(rnorm(n*p),n) nonzero = sample(p, k) beta = 3.5 * (1:p %in% nonzero) pr = 1/(1+exp(-X %*% beta)) y = rbinom(n,1,pr) knockoffs = function(X) MFKnockoffs.create.gaussian(X, mu, Sigma) # Basic usage with default arguments result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=MFKnockoffs.stat.lasso_lambda_difference_bin) print(result$selected) # Advanced usage with custom arguments foo = MFKnockoffs.stat.lasso_lambda_difference_bin k_stat = function(X, X_k, y) foo(X, X_k, y, nlambda=200) result = MFKnockoffs.filter(X, y, knockoffs=knockoffs, statistic=k_stat) print(result$selected)