m_step_regression {probe}

Function for fitting the initial part of the M-step

Description

A wrapper function providing the quantities related to the M-step for \alpha_0 and \sigma^2.

Usage

m_step_regression(Y, W, W2, Z = NULL, a = -3/2, Int = TRUE)

Arguments

Y

A matrix containing the outcome Y

W

Quantity E(W_0) as outlined in citation, output from W_update_fun

W2

Quantity E(W^2_0) as outlined in citation, output from W_update_fun

Z

A matrix or dataframe of other predictors to account for

a

(optional) parameter for changing the hyperparameter a (default, a=-3/2 uses n-2 as denominator for MAP of \sigma^2)

Int

(optional) Logical - should an intercept be used?

Value

A list including

coef the MAP estimates of the \alpha_0 parameters sigma2_est the MAP estimate of \sigma^2 VCV posterior variance covariance matrix of \alpha_0, res_data dataframe containing MAP estimates, posterior variances, t-test statistics and associated p-values for \alpha_0

References

McLain, A. C., Zgodic, A., & Bondell, H. (2022). Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm. arXiv preprint arXiv:2209.08139.