PAGE (version 0.4.0)

Cond_Gaussian: Estimation of network structure and variable selection in the linear model via the conditional likelihood function.

Description

This function focuses on multivariate linear regression models Y = XB + \(\epsilon\) subject to measurement error in responses and covariates, where with B is a matrix of parameters and \(\epsilon\) is a noise term with zero expectation. We aim to detect the network structure of responses and select informative covaraites. The estimation method is motivated by the conditional likelihood function and uses the conditional expectation to correct for measurement error.

Usage

Cond_Gaussian(
  W,
  Z,
  sigma_eta,
  sigma_delta,
  alpha_1,
  alpha_2,
  alpha_1_list = NULL,
  alpha_2_list = NULL,
  max_iter = 30,
  tol = 1e-06,
  label_name = TRUE,
  symmetry = "NULL"
)

Value

Beta

An estimator of B.

gamma

An estimator of the network in Y.

graph

A visualization of the estimated network structure by gamma.

Beta_BICs

A vector of Bayesian Information Criterion (BIC) weights for the model averaging estimator of B under candidate models alpha_1_list.

Gamma_BICs

A vector of Bayesian Information Criterion (BIC) weights for the model averaging estimator of \(\Gamma\) under candidate models alpha_2_list.

Arguments

W

A n × m response matrix, the variables can be error-prone or precisely measured.

Z

A n × p matrix of continuous covariates. The variables can be error-prone or precisely measured.

sigma_eta

A p × p covariance matrix of the noise term \(\eta\) in the classical measurement error model Z = X + \(\eta\), where X is the unobserved version of Z.

sigma_delta

A m × m covariance matrix of the noise term \(\delta\) in the classical measurement error model W = Y + \(\delta\), where Y is the unobserved version of W.

alpha_1

A tuning parameter associated with parameter B.

alpha_2

A tuning parameter associated with parameter, denoted as \(\Gamma\), that reflects the network in Y.

alpha_1_list

A list of tuning parameters for the model averaging estimator of B. The default value is NULL.

alpha_2_list

A list of tuning parameters for the model averaging estimator of \(\Gamma\). The default value is NULL.

max_iter

A maximum number for iterations for updated values of B and \(\Gamma\). The default value is 30.

tol

A prespecified tolerance \(\zeta\) for iterations for updated values of B and \(\Gamma\). The default value is \(10^{-6}\).

label_name

The name of the response variables. The default value is TRUE, which reflects the labels from the input data. Else, users can input the required labels manually.

symmetry

An argument makes the matrix gamma symmetric. 'AND' sets entries (s,t) and (t,s) to zero only if both original values are zero; `OR' sets entries (s,t) and (t,s) to zero if either original value is zero; `ave' replaces entries (s,t) and (t,s) with the average of the two original values; and `NULL' leaves the matrix unchanged.

Author

Wan-Yi Chang and Li-Pang Chen
Maintainer: Wan-Yi Chang

Examples

n <- 100
Z <- matrix(rnorm(n * 5), n, 5)
W <- matrix(rnorm(n * 5), n, 5)
sigma_eta <- diag(0.15, ncol(Z))
sigma_delta <- diag(0.3, ncol(W))

Cond_Gaussian(W, Z, sigma_eta, sigma_delta,
                        alpha_1 = 0.1, alpha_2 = 0.1,
                        alpha_1_list = NULL,
                        alpha_2_list = NULL,
                        max_iter = 1, tol = 1e-6, label_name = TRUE, symmetry = 'NULL')