NP_Graph {PAGE}R Documentation

Estimation of network structure and variable selection in the nonlinear model with measurement errors in responses and covariates.

Description

This function characterizes Y and X by nonlinear models and is designed for detecting network structure and variable selection with measurement error in responses and covariates. Here the components of Y can be continuous, binary, or count. The estimation strategy in this function includes the regression calibration for correcting error-prone responses and covariates, the random forest method for marginally characterizing the response and covariates, and the distance correlation and graphical lasso for detecting the network structure among the responses.

Usage

NP_Graph(
  W,
  Z,
  sigma_eta,
  rho,
  sigma_delta = 0.5,
  r = 0.8,
  lambda = 1,
  pi = 0.8,
  label_name,
  var_thred = 5
)

Arguments

W

A n × m response matrix. The variables can be error-prone or precisely measured, and can include continuous, binary, or count random variables.

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.

rho

A tuning parameter for the graphical lasso.

sigma_delta

The common value in the diagonal covariance matrix of the noise term \delta in the classical measurement error model for continuous components in W. The default value is 0.5.

r

A probability r for misclassification when components in W are binary. The default value is 0.8.

lambda

A parameter \lambda in the Poisson distribution that provides the increasing measurement error effects when components in W are count. The default value is 1.

pi

A parameter \pi in [0,1] for the Binomial distribution that characterizes the decreasing measurement error effects when components in W are count. The default value is 0.8.

label_name

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

var_thred

A positive value used to retain important covariates. That is, covariates will be selected when refitting the model if their importance scores are greater than var_thred. The default value is 5.

Value

W_hat

The n × m matrix of corrected responses determined by regression calibration.

Z_hat

The n × p matrix of corrected covariates determined by regression calibration..

PSE

The Frobenius norm of the residual corresponding to W_hat.

importance_score

A matrix containing importance scores for the covariates.

precision_matrix

An estimated matrix reflecting the network structure of the responses.

graph

An visualization of the estimated network structure by precision_matrix.

Author(s)

Wan-Yi Chang and Li-Pang Chen
Maintainer: Wan-Yi Chang jessica306a@gmail.com

Examples

n <- 100
Z <- matrix(rnorm(n * 10), n, 10)
W <- matrix(rnorm(n * 5), n, 5)
sigma_eta <- diag(0.15, ncol(Z))

NP_Graph(W, Z, sigma_eta, rho = 0.2,
                   sigma_delta = 0.5, r = 0.8,
                   lambda = 1, pi = 0.8,
                   label_name = TRUE, var_thred = 3)


[Package PAGE version 0.1.0 Index]