The estimated s gives information about the consistency between the z scores and LD matrix. A larger \(s\) means there is a strong inconsistency between z scores and LD matrix. The “null-mle” method obtains mle of \(s\) under \(z | R ~ N(0,(1-s)R + s I)\), \(0 < s < 1\). The “null-partialmle” method obtains mle of \(s\) under \(U^T z | R ~ N(0,s I)\), in which \(U\) is a matrix containing the of eigenvectors that span the null space of R; that is, the eigenvectors corresponding to zero eigenvalues of R. The estimated \(s\) from “null-partialmle” could be greater than 1. The “null-pseudomle” method obtains mle of \(s\) under pseudolikelihood \(L(s) = \prod_{j=1}^{p} p(z_j | z_{-j}, s, R)\), \(0 < s < 1\).
estimate_s_rss(z, R, n, r_tol = 1e-08, method = "null-mle")A p-vector of z scores.
A p by p symmetric, positive semidefinite correlation matrix.
The sample size. (Optional, but highly recommended.)
Tolerance level for eigenvalue check of positive semidefinite matrix of R.
a string specifies the method to estimate \(s\).
A number between 0 and 1.
set.seed(1)
n = 500
p = 1000
beta = rep(0,p)
beta[1:4] = 0.01
X = matrix(rnorm(n*p),nrow = n,ncol = p)
X = scale(X,center = TRUE,scale = TRUE)
y = drop(X %*% beta + rnorm(n))
input_ss = compute_suff_stat(X,y,standardize = TRUE)
ss = univariate_regression(X,y)
R = cor(X)
attr(R,"eigen") = eigen(R,symmetric = TRUE)
zhat = with(ss,betahat/sebetahat)
# Estimate s using the unadjusted z-scores.
s0 = estimate_s_rss(zhat,R)
#> WARNING: Providing the sample size (n), or even a rough estimate of n, is highly recommended. Without n, the implicit assumption is n is large (Inf) and the effect sizes are small (close to zero).
# Estimate s using the adjusted z-scores.
s1 = estimate_s_rss(zhat,R,n)