GLM statistics for knockoff

Computes the signed maximum statistic $$W_j = \max(Z_j, \tilde{Z}_j) \cdot \mathrm{sgn}(Z_j - \tilde{Z}_j),$$ where \(Z_j\) and \(\tilde{Z}_j\) are the maximum values of \(\lambda\) at which the jth variable and its knockoff, respectively, enter the generalized linear model.

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

Arguments

X

n-by-p matrix of original variables.

X_k

n-by-p matrix of knockoff variables.

y

Response variable vector of length n. Quantitative for family = "gaussian" or "poisson".

  • For family = "binomial", y should be either:

    • a two-level factor,

    • a two-column matrix of counts, or

    • proportions.

  • For family = "multinomial", y can be a factor with at least two levels or a matrix.

  • For family = "cox", y should be a two-column matrix with 'time' and 'status'.

  • For family = "mgaussian", y is a matrix of quantitative responses.

family

response type (see above).

...

additional arguments specific to glmnet (see Details).

Value

A vector of statistics \(W\) of length p.

Details

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

The additional nlambda parameter can be used to control the granularity of the grid of \(\lambda\) values. 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'.

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

Examples

set.seed(2024)
n=80; p=100; k=10; Ac = 1:k; Ic = (k+1):p
X = generate_X(n=n,p=p)
y <- generate_y(X, p_nn=k, a=3)
Xk = create.shrink_Gaussian(X = X, n_ko = 10)
res1 = knockoff.filter(X, y, Xk, statistic = stat.glmnet_lambdasmax,
                       offset = 1, fdr = 0.1)
res1
#> Call:
#> knockoff.filter(X = X, y = y, Xk = Xk, statistic = stat.glmnet_lambdasmax, 
#>     fdr = 0.1, offset = 1)
#> 
#> Selected variables:
#> [1]  1  3  6  7  9 10
#> 
#> Frequency of selected variables from 10 knockoff copys:
#>   [1] 10  0 10  0  0 10  8  0 10 10  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [26]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [51]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
#>  [76]  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1
perf_eval(res1$shat,Ac,Ic)
#> [1] 0.6 0.0