# Robust Subgroup Analysis and Variable Selection

# RSAVS

This package carries out the **R**obust **S**ubgroup **A**nalysis and **V**ariable **S**election simultaneously. It implements the computation in a parallel manner.

## Installation

You can use `devtools`

to directly install from github

```
#install.packages("devtools")
devtools::install_github("fenguoerbian/RSAVS")
```

## Example

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_length = 50, lam2_length = 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_length = 50, lam2_length = 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_length`

* `lam2_length`

results. And `res$best_id`

corresponds to the solution with the lowest mBIC.

You can do post-selection estimation by

```
ind <- res$best_id # pick an id of the solution
res2 <- RSAVS_Further_Improve(y_vec = y_vec, x_mat = x_mat,
mu_vec = res$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`

.