Using BFI in SAS

Install R

Download and install R from the official R website (https://www.r-project.org/). Follow the installation instructions provided for your operating system.

Install SAS/IML Interface to R

The SAS/IML Interface to R allows you to call R functions from within PROC IML (Interactive Matrix Language). Check if the interface is installed by running the following code within SAS:

proc options option=R_HOME;
run;

If the path to your R installation directory is displayed, the SAS/IML Interface to R is installed. If not, you may need to install or reinstall it.

Installing R packages from CRAN and GitHub in SAS:

To install an R package from CRAN and GitHub, you can use the base, stats and remotes packages, respectively. It can be done in R or in SAS. Here’s how you can do it within SAS:

proc iml;

  rsubmit;

    /* First install and load 'base', 'stats' and 'BFI'from CRAN */
    install.packages("base")
    install.packages("stats")
    install.packages("BFI")  /* To install BFI from CRAN */
    library(base)
    library(stats)
    library(BFI)
  
    /* To install BFI from GitHub (if nessecary) */
    /* install.packages("remotes") */
    /* library(remotes) */
    /* remotes::install_github("hassanpazira/BFI", force = TRUE) */

  endrsubmit;

quit;

Now that you have the BFI package installed and configured, let’s explore its functionality through the following example.

Simulate data for two local centers

First generate 30 samples randomly from Gaussian distribution N(0, 1) with p=3 covariates:

proc iml;

    /****************************************************************/
    /* Center 1: Data simulation for local center 1 with 30 samples */
    /****************************************************************/

    p     = 3;   /* Number of variables */
    n1    = 30;  /* Number of samples for center 1 */
    theta = {1, 2, 2, 2, 1.5}; /* Define theta values directly */

    X1  = j(n1, p); /* Initialize matrix X1 */
    mu1 = j(n1, 1); /* Initialize vector mu1 */
    y1  = j(n1, 1); /* Initialize vector y1 */

    /* Generate data for center 1 */
    call randseed(1123);
    X1  = randfun(n1 || p, "Normal", 0, 1);
    mu1 = theta[1] + X1 * theta[2:4];
    y1  = randfun(n1 || 1, "Normal", mu1, sqrt(theta[5]));

    /* Create dataset for center 1 */
    create y1 var {"y1"};
    append;
    close y1;

    create X1 from X1[colname={"X1_1" "X1_2" "X1_3"}];
    append from X1;
    close X1;

    call ExportMatrixToR(X1, "X1");
    call ExportMatrixToR(y1, "y1");

quit;

Now generate 50 samples randomly from N(0, 1) with 3 covariates:

proc iml;

    /****************************************************************/
    /* Center 2: Data simulation for local center 2 with 50 samples */
    /****************************************************************/
    p     = 3;   /* Number of variables */
    n2    = 50;   /* Number of samples for center 2 */
    theta = {1, 2, 2, 2, 1.5}; /* Define theta values directly */
  
    X2  = j(n2, p);
    mu2 = j(n2, 1);
    y2  = j(n2, 1);

    /* Generate data for center 2 */
    call randseed(1123);
    X2  = randfun(n2 || p, "Normal", 0, 1);
    mu2 = theta[1] + X2 * theta[2:4];
    y2  = randfun(n2 || 1, "Normal", mu2, sqrt(theta[5]));

    /* Create dataset for center 1 */
    create y2 var {"y2"};
    append;
    close y2;

    create X2 from X2[colname={"X2_1" "X2_2" "X2_3"}];
    append from X2;
    close X2;

    call ExportMatrixToR(X2, "X2");
    call ExportMatrixToR(y2, "y2");

quit;

We have transferred SAS data to the R session and are currently initiating an analysis using the BFI method in R. All communications with R are facilitated through SAS’s PROC IML. It’s important to note that capitalization matters in R, and character variables are automatically converted into factors.

MAP estimates at the local centers

The following compute the Maximum A Posterior (MAP) estimators of the parameters for center 1:

proc iml;
  
  rsubmit;

    #---------------------------
    # Inverse Covariance Matrix
    #---------------------------
    # Creating the inverse covariance matrix for the Gaussian prior distribution:
    Lambda <- inv.prior.cov(X1, lambda=0.05, family=gaussian)

    #--------------------------
    # MAP estimates at center 1
    #--------------------------
    fit1       <- MAP.estimation(y1, X1, family=gaussian, Lambda)
    theta_hat1 <- fit1$theta_hat # intercept and coefficient estimates
    A_hat1     <- fit1$A_hat     # minus the curvature matrix
    summary(fit1, cur_mat=TRUE)

  endrsubmit;

quit;

Obtaining the MAP estimators of the parameters for center 2 using the following:

proc iml;

  rsubmit;
    
    # Creating the inverse covariance matrix for the Gaussian prior distribution:
    Lambda <- inv.prior.cov(X2, lambda=0.05, family=gaussian)

    #--------------------------
    # MAP estimates at center 2
    #--------------------------
    fit2       <- MAP.estimation(y2, X2, family=gaussian, Lambda)
    theta_hat2 <- fit2$theta_hat
    A_hat2     <- fit2$A_hat
    summary(fit2, cur_mat=TRUE)

  endrsubmit;

quit;

BFI at central center

Now, you can utilize the primary function bfi() to acquire the BFI estimates:

proc iml;

  rsubmit;
  
    # Creating the inverse covariance matrix for central server:
    Lambda <- inv.prior.cov(X1, lambda=0.05, family=gaussian) # the same as other centers
  
    #----------------------
    # BFI at central center
    #----------------------
    A_hats     <- list(A_hat1, A_hat2)
    theta_hats <- list(theta_hat1, theta_hat2)
    bfi        <- bfi(theta_hats, A_hats, Lambda)
    summary(bfi, cur_mat=TRUE)

  endrsubmit;

  call ImportMatrixFromR(bfi, "bfi");
  
quit;