Type: Package
Title: Predictor-Assisted Graphical Models under Error-in-Variables
Version: 0.1.0
Description: We consider the network structure detection for variables Y with auxiliary variables X accommodated, which are possibly subject to measurement error. The following three functions are designed to address various structures by different methods : one is NP_Graph() that is used for handling the nonlinear relationship between the responses and the covariates, another is Joint_Gaussian() that is used for correction in linear regression models via the Gaussian maximum likelihood, and the other Cond_Gaussian() is for linear regression models via conditional likelihood function.
License: GPL-3
Encoding: UTF-8
Imports: glasso, lars, network, GGally, caret, randomForest, metrica, MASS, stats
Suggests: sna
RoxygenNote: 7.3.2
Author: Wan-Yi Chang [aut, cre], Li-Pang Chen [aut]
Maintainer: Wan-Yi Chang <jessica306a@gmail.com>
NeedsCompilation: yes
Packaged: 2025-07-18 02:25:38 UTC; user
Repository: CRAN
Date/Publication: 2025-07-21 08:42:18 UTC

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
)

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.

Value

B

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.

Author(s)

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

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)

Estimation of network structure and variable selection in the linear model via the Gaussian maximum likelihood.

Description

This function focuses on multivariate linear regression models Y = XB + \epsilon subject to measurement error in the 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 Gaussian maximum likelihood function and uses the conditional expectation to correct for measurement error.

Usage

Joint_Gaussian(
  W,
  Z,
  sigma_eta,
  sigma_delta,
  alpha_1,
  alpha_2,
  alpha_1_list = NULL,
  alpha_2_list = NULL,
  label_name = TRUE
)

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 the parameter B.

alpha_2

A tuning parameter associated with precision matrix C, which is the inverse of the covariance matrix of \epsilon.

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 C. The default value is NULL.

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.

Value

B

An estimator of B.

C

An estimator of C.

graph

A visualization of the estimated network structure by C.

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 C under candidate models alpha_2_list.

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))
sigma_delta <- diag(0.3, ncol(W))

Joint_Gaussian(W, Z, sigma_eta, sigma_delta,
                         alpha_1 = 0.1, alpha_2 = 0.1,
                         alpha_1_list = c(0.1, 0.3),
                         alpha_2_list = c(0.1, 0.3),
                         label_name = TRUE)

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)

Predictor-Assisted Graphical Models under Error-in-Variables

Description

This package has three functions that characterize the multivariate responses and covariates under linear or nonlinear structures. All functions are valid to handle measurement error, detection of network in responses, and selection of informative covariates.

Details

Given the responses and covariates that can be error-prone or precisely measured, NP_graph is a function used to detect the network structure of responses and select important covariates under nonlinear structures. Under linear structures, this package provides two different estimation methods: the function Joint_Gaussian implements the error-corrected Gaussian maximum likelihood method, and the function Cond_Gaussian extends the neighborhood selection strategy to construct the corrected conditional likelihood function. All functions are able to estimate the network strucure of responses and perform variable selection to identify important covariates with measurement error taken into account.

Value

PAGE_package