singleModalityAdmm {HDMAADMM}

High-dimensional Single Modality Mediation Models

Description

High-dimensional Single Modality Mediation Models

Usage

singleModalityAdmm(
  X,
  Y,
  M1,
  rho = 1,
  lambda1a,
  lambda1b,
  lambda1g,
  lambda2a,
  lambda2b,
  penalty = "ElasticNet",
  penaltyParameterList = list(),
  SIS = FALSE,
  SISThreshold = 2,
  maxIter = 3000L,
  tol = 0.001,
  verbose = FALSE,
  verboseOptions = list(numIter = 10L, numAlpha = 1L, numBeta = 1L, numGamma = 1L)
)

Arguments

X

The matrix of independent variables (exposure/treatment/group).

Y

The vector of dependent variable (outcome response).

M1

The single-modality mediator.

rho

The augmented Lagrangian parameter for ADMM.

lambda1a

The L1-norm penalty for the effect between mediator and independent variables.

lambda1b

The L1-norm penalty for the effect between mediator and dependent variable.

lambda1g

The L1-norm penalty for the direct effect. Default is 10 to adress overestimate issue.

lambda2a

The L2-norm penalty for the effect between mediator and independent variables. It's not used when Penalty is PathwayLasso.

lambda2b

The L2-norm penalty for the effect between mediator and dependent variable. It's not used when Penalty is PathwayLasso.

penalty

A string to specify the penalty. Default is ElasticNet. Possible methods are Elastic Net (ElasticNet), Pathway Lasso (PathywayLasso), and Network-constrained Penalty (Network).

penaltyParameterList

• Penalty=PathwayLasso needs two parameters.

  • kappa The L1-norm penalty for pathway Lasso.

  • nu The L2-norm penalty for pathway Lasso.

• Penalty=Network needs one parameter.

  • laplacianMatrix The Laplacian matrix applied on network penalty.

• Penalty=ElasticNet don't need other parameters.

SIS

A logical value to specify whether to perform sure independence screening (SIS).

SISThreshold

The threshold value for the target reduced dimension for mediators. The default is "2," which reduces the dimension to 2*n/log(n).

maxIter

The maximum iterations. Default is 3000.

tol

The tolerence of convergence threshold. Default is 1e-3.

verbose

A logical value to specify whether to print the iteration process.

verboseOptions

A list of values:

• numIter: The number of iterations to print.

• numAlpha: The number of alpha to print.

• numBeta: The number of beta to print.

• numGamma: The number of gamma to print.

Value

A object, SingleModalityAdmm, with three elements.

• gamma: estimated direct effect.

• alpha: estimate effect between mediator and independent variables.

• beta : estimate effect between mediator and dependent variable.

Examples

## Generate Empirical Data
simuData <- modalityMediationDataGen(seed = 20231201, generateLaplacianMatrix = TRUE)

## Parameter Estimation for ElasticNet penalty
modelElasticNet <- singleModalityAdmm(
  X = simuData$MediData$X, Y = simuData$MediData$Y, M1 = simuData$MediData$M1,
  rho = 1, lambda1a = 1, lambda1b = 0.1, lambda1g = 2, lambda2a = 1, lambda2b = 1,
  penalty = "ElasticNet"
)

# fitted & predict
fitted(modelElasticNet)
predict(modelElasticNet, matrix(c(0, 1), ncol=1))

## Parameter Estimation for Pathway Lasso penalty
modelPathwayLasso <- singleModalityAdmm(
  X = simuData$MediData$X, Y = simuData$MediData$Y, M1 = simuData$MediData$M1,
  rho = 1, lambda1a = 1, lambda1b = 0.1, lambda1g = 2, lambda2a = 1, lambda2b = 1,
  penalty = "PathwayLasso", penaltyParameterList = list(kappa = 1, nu = 2)
)

## Parameter Estimation for Network penalty
modelNetwork <- singleModalityAdmm(
  X = simuData$MediData$X, Y = simuData$MediData$Y, M1 = simuData$MediData$M1,
  rho = 1, lambda1a = 1, lambda1b = 0.1, lambda1g = 2, lambda2a = 1, lambda2b = 1,
  penalty = "Network", penaltyParameterList = list(laplacianMatrix = simuData$Info$laplacianMatrix)
)

## Parameter Estimation for Network penalty with a customized Laplacian matrix
set.seed(20231201)
p <- ncol(simuData$MediData$M1)
W <- matrix(0, nrow = p, ncol = p)
W[lower.tri(W)] <- runif(p*(p-1)/2, 0, 1)
W[upper.tri(W)] <- t(W)[upper.tri(W)]
diag(W) <- 1
L <- weightToLaplacian(W)
modelNetwork <- singleModalityAdmm(
  X = simuData$MediData$X, Y = simuData$MediData$Y, M1 = simuData$MediData$M1,
  rho = 1, lambda1a = 1, lambda1b = 0.1, lambda1g = 2, lambda2a = 1, lambda2b = 1,
  penalty = "Network", penaltyParameterList = list(laplacianMatrix = L)
)

## With sure independence screening
## Generate Empirical Data
simuData <- modalityMediationDataGen(n = 50, p = 1000, seed = 20231201)

## Parameter Estimation for ElasticNet penalty
modelElasticNetSIS <- singleModalityAdmm(
  X = simuData$MediData$X, Y = simuData$MediData$Y, M1 = simuData$MediData$M1,
  rho = 1, lambda1a = 1, lambda1b = 0.1, lambda1g = 2, lambda2a = 1, lambda2b = 1,
  penalty = "ElasticNet", SIS = TRUE
)
fitted(modelElasticNetSIS)
predict(modelElasticNetSIS, matrix(c(0, 1), ncol=1))