This package carries out the Robust Subgroup Analysis and Variable Selection simultaneously. It implements the computation in a parallel manner.


You can use devtools to directly install the latest version from Github


If you have trouble connecting to Github, this packages is also hosted on Gitlab.


Note: If you are interested in the original yet unoptimized version of this package used in the simulation of our paper, you can check the simulation_archive branch of this repo.

Note: It’s recommended to read the vignettes on the package’s website. But if you want to build the vignettes locally, you can run

devtools::install_github("fenguoerbian/RSAVS", force = TRUE, build_vignettes = TRUE)

Just keep in mind that this will take some really long time.


Here is a toy example:

n <- 200    # number of observations
q <- 5    # number of active covariates
p <- 50    # number of total covariates
k <- 2    # number of subgroups
# k subgroup effect, centered at 0
group_center <- seq(from = 0, to = 2 * (k - 1), by = 2) - (k - 1)
beta_true <- c(rep(1, q), rep(0, p - q))    # covariate effect vector
alpha_true <- sample(group_center, size = n, replace = T)    # subgroup effect vector

x_mat <- matrix(rnorm(n * p), nrow = n, ncol = p)    # covariate matrix
err_vec <- rnorm(n, sd = 0.5)    # error term
y_vec <- alpha_true + x_mat %*% beta_true + err_vec    # response vector

Then we analyze the generated data with the function RSAVS_LargeN:

res <- RSAVS_LargeN(y_vec = y_vec, x_mat = x_mat, lam1_len = 50, lam2_len = 40, phi = 5)

where phi is the parameter needed by mBIC. By default, this function uses L1 as the loss function with the SCAD penalty for both subgroup identification and variable selection. You can use other losses or penalties, e.g

res_huber <- RSAVS_LargeN(y_vec = y_vec, x_mat = x_mat, l_type = "Huber", l_param = 1.345, 
                          lam1_len = 50, lam2_len = 40, p1_type = "M", p2_type = "L", 
                          phi = 5)

uses Huber loss with parameter 1.345, MCP penalty for subgroup identification and Lasso penalty for variable selection. More details of options can be found in the package documentation.

The function uses the ADMM method to obtain the solution and the result stored in the variable res is a list containing all lam1_len * lam2_len results. And res$best_id corresponds to the solution with the lowest mBIC.

You can do post-selection estimation by

ind <- res$best_ind    # pick an id of the solution
res2 <- RSAVS_Further_Improve(y_vec = y_vec, x_mat = x_mat, 
                              mu_vec = res$mu_improve_mat[ind, ], 
                              beta_vec = res$w_mat[ind, ])

This function carries out ordinary low dimensional estimation(without any penalties) given the parameter structure indicated by mu_vec and beta_vec.

Besides RSAVS_LargeN, there are also RSAVS_Path and RSAVS_Path_PureR which can perform the same task. Furthermore, these two functions use the progress bar framework provided by package progressr.

if(as.numeric(version$major) >= 4){
    # For R >= 4.0, one can enable global handler so that
    #   there is NO need to enclose expression in `with_progress`
    handlers(global = TRUE)
handlers("progress")    # "progress" handlers requires the package `progress`
                        # defualt handler is `txtprogress` from base R

res3 <- RSAVS_Path(y_vec = y_vec, x_mat = x_mat, l_type = "Huber", l_param = 1.345, 
                   lam1_len = 50, lam2_len = 40, p1_type = "M", p2_type = "L", 
                   phi = 5)