EMSHS (version 1.0.0)

EMSHS: EM Estimator for Bayesian Shrinkage approach with Structural Information incorporated

Description

EMSHS implements the EM algorithm for Bayesian shrinkage approach that incorporates structural information. Users are referred to Chang et al (2018).

Usage

EMSHS(y, X, mus, nu, E = NULL, a_sigma = 1, b_sigma = 1, a_omega = 2,
  b_omega = 1, w = 1, eps = 1e-05)

Arguments

y

An n by 1 response vector

X

An n by p design matrix

mus

A vector of shrinkage parameters

nu

The adaptivity parameter

E

An e by 2 matrix with edges. Edges must be sorted by the first column and then the second column. A single edge (j,k) must be duplicated with (k,j) in E. NULL if no edge.

a_sigma

The shape parameter of the prior for residual variance.

b_sigma

The rate parameter of the prior for residual variance.

a_omega

The shape parameter of the prior for nonzero omega values.

b_omega

The rate parameter of the prior for nonzero omega values.

w

A weight vector for samples.

eps

The algorithm stops if relative improvement goes below eps.

Value

A list that contains the number of EM iterations (niter), the estimated coefficients (beta), the estimated residual variance (sigma), the estimated shrinkage parameter (lambda), and the imputed correlations for the shrinkage parameter (omega) is returned.

References

chang2018EMSHS

Examples

# NOT RUN {
 # Example with no edges for a high-dimensional data
 # with n = 25 observations and p = 50 predictors

 set.seed(100)

 X <- matrix(rnorm(25*50), ncol = 50)
 B <- matrix(c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0), ncol = 1)
 e <- matrix(rnorm(25*1), ncol = 1)
 y <- matrix(X %*% B + e, ncol = 1)
 mus <- 2.3
 nu <- 0.3


 em_no_edge <- EMSHS(y, X, mus, nu, E = NULL,
                     a_sigma = 1, b_sigma = 1, a_omega = 2, b_omega = 1,
                     w = 1, eps = 1e-5)


 # Example with user-defined set of sorted, undirected
 # edges (E) for a high-dimensional data with n = 25
 # and p = 50

 X <- matrix(rnorm(25*50), ncol = 50)
 B <- matrix(c(1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0,0,0,0,0,0,0), ncol = 1)
 e <- matrix(rnorm(25*1), ncol = 1)
 y <- matrix(X %*% B + e, ncol = 1)
 mus <- 2.3
 nu <- 0.3
EE <- matrix(c(1,4,
              4,1,
              1,2,
              2,1,
              1,5,
              5,1,
              2,3,
              3,2,
              3,5,
              5,3,
              10,11,
              11,10,
              19,11,
              11,19,
              36,35,
              35,36,
              31,35,
              35,31,
              31,22,
              22,31,
              22,45,
              45,22,
              45,32,
              32,45,
              22,21,
              21,22,
              31,21,
              21,31,
              21,25,
              25,21,
              21,18,
              18,21,
              18,49,
              49,18,
              49,47,
              47,49,
              47,37,
              37,47,
              37,21,
              21,37,
              18,25,
              25,18), nrow = 42, ncol = 2, byrow = TRUE)

 # Sort edges by first column then second column

 E <- EE[do.call(order, lapply(1:ncol(EE), function(i) EE[,i])),]

 em_edge <- EMSHS(y, X, mus, nu, E,
                  a_sigma = 1, b_sigma = 1, a_omega = 2, b_omega = 1,
                  w = 1, eps = 1e-5)
# }