| Title: | Flexible and Accurate Gaussian Graphical Models |
| Version: | 0.1 |
| Description: | In order to achieve accurate estimation without sparsity assumption on the precision matrix, element-wise inference on the precision matrix, and joint estimation of multiple Gaussian graphical models, a novel method is proposed and efficient algorithm is implemented. FLAG() is the main function given a data matrix, and FlagOneEdge() will be used when one pair of random variables are interested where their indices should be given. Flexible and Accurate Methods for Estimation and Inference of Gaussian Graphical Models with Applications, see Qian Y (2023) <doi:10.14711/thesis-991013223054603412>, Qian Y, Hu X, Yang C (2023) <doi:10.48550/arXiv.2306.17584>. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.1.2 |
| Imports: | stats, MASS |
| URL: | https://github.com/YangLabHKUST/FLAG |
| BugReports: | https://github.com/YangLabHKUST/FLAG/issues |
| NeedsCompilation: | no |
| Packaged: | 2025-04-10 09:36:49 UTC; asus |
| Author: | Yueqi QIAN  [aut,
cre] |
| Maintainer: | Yueqi QIAN <yqianai@connect.ust.hk> |
| Repository: | CRAN |
| Date/Publication: | 2025-04-12 08:10:06 UTC |
FLAG is the main function to fulfill the whole process.
Description
FLAG is the main function to fulfill the whole process.
Usage
FLAG(
data,
scale.var = TRUE,
low.rank = NULL,
infer = "llr",
eps = 1e-07,
crit.loglik = 1e-04
)
Arguments
data |
Matrix, with size n*p. |
scale.var |
Logical, whether to scale the variance of X to 1/p, default to be T(RUE). |
low.rank |
Logical, whether to use low rank update to shrink the time of eigen-decomposition of XX^T, default to be TRUE when sample size larger than 1000. |
infer |
Character, option of different tests of inference where 'llr' for likelihood ratio test and 'wald' for Wald test based on Fisher Information Matrix. |
eps |
Numeric, a small term to avoid numerical problems, default to be 1e-7. |
crit.loglik |
Numeric, the criteria of the change ratio of log likelihood to stop. |
Value
List, the estimated precision matrix, the p-value of precision matrix estimation, the edge existence using Bonferroni correction, the edge existence using false discovery rate, the matrix of estimated eta, the standard error or estimated eta, the matrix of estimated partial correlation rho, the standard error or estimated partial correlation rho, the p-value of partial correlation matrix estimation, the matrix of estimated sigma_a^2, the standard error or estimated sigma_b^2, the execution time.
Examples
N = 20
P = 10
pi = 0.2
Pre = matrix(sample(c(0.2, 0.4), P*P, replace = TRUE) * rbinom(P*P, 1, pi), nrow = P, ncol = P )
Pre[lower.tri(Pre)] = t(Pre)[lower.tri(Pre)]
diag(Pre) = 1
vals <- eigen(Pre)$values
Sigma = solve(Pre)
Z = MASS::mvrnorm(N, rep(0, P), Sigma)
Z.c = scale(Z, center = TRUE, scale = FALSE)
results = FLAG(Z.c)
Use FLAG to infer one edge. Given n*p data matrix, when we only interest in the conditional dependence between i-th and j-th variables.
Description
Use FLAG to infer one edge. Given n*p data matrix, when we only interest in the conditional dependence between i-th and j-th variables.
Usage
FlagOneEdge(data, i, j, scale.var = TRUE, infer = "llr", eps = 1e-07)
Arguments
data |
Matrix, with size n*p. |
i |
integer, the index of one element. |
j |
integer, the index of another element. |
scale.var |
Logical, whether to scale the variance of X to 1/p, default to be T(RUE). |
infer |
Character, option of different tests of inference where 'llr' for likelihood ratio test and 'wald' for Wald test based on Fisher Information Matrix. |
eps |
Numeric, a small term to avoid numerical problems, default to be 1e-7. |
Value
List, the list of log likelihood during iterations, the estimated precision value, the p-value of precision value estimation, the estimated Gamma_beta matrix with size 22, in the random effects model, the estimated Gamma_epsilon matrix with size 22, in the random effects model, the estimated off-diagonal element eta in the matrix Gamma_epsilon, the standard error of eta, the estimated partial correlation rho, the standard error of rho, the p-value of rho, the execution time.
Examples
FlagOneEdge(matrix, i, j)
FLAG for one pair of random variables, using random effects model. This is a repeated function for FLAG.
Description
FLAG for one pair of random variables, using random effects model. This is a repeated function for FLAG.
Usage
FlagOnePair(
Y,
X,
Gamma_beta = NULL,
Gamma_e = NULL,
infer = "llr",
fix.eta = FALSE,
eps = 1e-07,
max.iter = 5000,
crit.loglik = 1e-04
)
Arguments
Y |
Matrix, with size n*2. |
X |
Matrix, with size n*(p-2). |
Gamma_beta |
Matrix, with size 2*2. |
Gamma_e |
Matrix, with size 2*2. |
infer |
Character, option of different tests of inference where 'llr' for likelihood ratio test and 'wald' for Wald test based on Fisher Information Matrix. |
fix.eta |
Logical, whether to fix eta, default to be FALSE. |
eps |
Numeric, a small term to avoid numerical problems, default to be 1e-7. |
max.iter |
Integer, the maximum number of iterations, default to be 5000. |
crit.loglik |
Numeric, the criteria of the change ratio of log likelihood to stop. |
Value
List, the list of log likelihood during iterations, the estimated Gamma_beta matrix with size 22, in the random effects model, the estimated Gamma_epsilon matrix with size 22, in the random effects model, the estimated 2*2 submatrix of the precision matrix, the covariance matrix, which is the inverse of the Fisher information matrix, inferred by the Wald test, the estimated off-diagonal element eta in the matrix Gamma_epsilon, the standard error of eta, the p-value of eta, the estimated partial correlation rho, the standard error of rho, the p-value of rho.
Examples
FlagOnePair(Y, X)
FLAG for one pair of random variables fixing eta as zero, using likelihood-ratio test.
Description
FLAG for one pair of random variables fixing eta as zero, using likelihood-ratio test.
Usage
FlagOnePairEta0(
Y,
X,
Gamma_beta,
Gamma_e,
eps = 1e-07,
max.iter = 5000,
crit.loglik = 1e-04
)
Arguments
Y |
Matrix, with size n*2. |
X |
Matrix, with size n*(p-2). |
Gamma_beta |
Matrix, with size 2*2. |
Gamma_e |
Matrix, with size 2*2. |
eps |
Numeric, a small term to avoid numerical problems, default to be 1e-4. |
max.iter |
Integer, the maximum number of iterations, default to be 5000. |
crit.loglik |
Numeric, the criteria of the change ratio of log likelihood to stop. |
Value
List, the list of log likelihood during iterations, Numeric, the log likelihood of the last iterations, the estimated Gamma_beta matrix with size 22, in the random effects model, the estimated Gamma_epsilon matrix with size 22, in the random effects model, the estimated 2*2 submatrix of the precision matrix.
Examples
FlagOnePairEta0(Y, X, Gamma_beta, Gamma_e)
Get the standard error of rho.
Description
Get the standard error of rho.
Usage
GetSeRho(Gamma_e, Gamma_e_cov)
Arguments
Gamma_e |
Matrix, with size 2*2. |
Gamma_e_cov |
Matrix, with size 2*2. |
Value
Numeric.
Examples
GetSeRho(Gamma_e,Gamma_e_cov)
Infer by the Wald test.
Description
Infer by the Wald test.
Usage
InferWald(Omega.inv, n, K, Y.vec, Gamma_e)
Arguments
Omega.inv |
Matrix, with size (2n)*(2n). |
n |
Integer. |
K |
Matrix, with size n*n. |
Y.vec |
Matrix, with size (2*n)*1, the vectorized Y. |
Gamma_e |
Matrix, with size 2*2. |
Value
List, the covariance matrix, which is the inverse of the Fisher information matrix, inferred by the Wald test, the estimated off-diagonal element eta in the matrix Gamma_epsilon, the standard error of eta, the p-value of eta, the estimated partial correlation rho, the standard error of rho, the p-value of rho.
Examples
InferWald(Omega.inv, n, K, Y.vec, Gamma_e)