stat.glmnet_lambdadiff: Importance statistics based on a GLM

Description

Fits a generalized linear model via penalized maximum likelihood 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 $\lambda$ at which the jth variable and its knockoff enter the model, respectively.

Usage

stat.glmnet_lambdadiff(X, X_k, y, family = "gaussian", ...)

Value

A vector of statistics $W$ of length p.

Arguments

X: n-by-p matrix of original variables.
X_k: n-by-p matrix of knockoff variables.
y: vector of length n, containing the response variables. Quantitative for family="gaussian", or family="poisson" (non-negative counts). For family="binomial" 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). For family="multinomial", can be a nc>=2 level factor, or a matrix with nc columns of counts or proportions. For either "binomial" or "multinomial", if y is presented as a vector, it will be coerced into a factor. For family="cox", y should be a two-column matrix with columns named 'time' and 'status'. The latter is a binary variable, with '1' indicating death, and '0' indicating right censored. The function Surv() in package survival produces such a matrix. For family="mgaussian", y is a matrix of quantitative responses.
family: response type (see above).
...: additional arguments specific to glmnet (see Details).

Details

This function uses glmnet to compute the regularization path on a fine grid of $\lambda$'s.

The nlambda parameter can be used to control the granularity of the grid of $\lambda$'s. The default value of nlambda is 500.

If the family is 'binomial' and a lambda sequence is not provided by the user, this function generates it on a log-linear scale before calling 'glmnet'.

The default response family is 'gaussian', for a linear regression model. Different response families (e.g. 'binomial') can be specified by passing an optional parameter 'family'.

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

Examples

Run this code

set.seed(2022)
p=200; n=100; 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)
y = X %*% beta + rnorm(n)
knockoffs = function(X) create.gaussian(X, mu, Sigma)

# Basic usage with default arguments
result = knockoff.filter(X, y, knockoffs=knockoffs, 
                           statistic=stat.glmnet_lambdadiff)
print(result$selected)

# Advanced usage with custom arguments
foo = stat.glmnet_lambdadiff
k_stat = function(X, X_k, y) foo(X, X_k, y, nlambda=200)
result = knockoff.filter(X, y, knockoffs=knockoffs, statistic=k_stat)
print(result$selected)