PenalisedOpenMx: Penalised Structural Equation Model

Description

Runs penalised Structural Equation Modelling using implementations from OpenMx functions (for PenalisedOpenMx), or using series of penalised regressions with glmnet (for PenalisedLinearSystem). The function PenalisedLinearSystem does not accommodate latent variables. These functions are not using stability.

Usage

PenalisedOpenMx(
  xdata,
  adjacency,
  penalised = NULL,
  residual_covariance = NULL,
  Lambda,
  ...
)
PenalisedLinearSystem(xdata, adjacency, penalised = NULL, Lambda = NULL, ...)

Value

A list with:

selected: matrix of binary selection status. Rows correspond to different regularisation parameters. Columns correspond to different parameters to estimated.
beta_full: matrix of model coefficients. Rows correspond to different regularisation parameters. Columns correspond to different parameters to estimated.

Arguments

xdata: matrix with observations as rows and variables as columns. Column names must be defined and in line with the row and column names of adjacency.
adjacency: binary adjacency matrix of the Directed Acyclic Graph (transpose of the asymmetric matrix A in Reticular Action Model notation). The row and column names of this matrix must be defined.
penalised: optional binary matrix indicating which coefficients are regularised.
residual_covariance: binary and symmetric matrix encoding the nonzero entries in the residual covariance matrix (symmetric matrix S in Reticular Action Model notation). By default, this is the identity matrix (no residual covariance).
Lambda: matrix of parameters controlling the level of sparsity. Only the minimum, maximum and length are used in PenalisedOpenMx.
...: additional parameters passed to OpenMx functions (for PenalisedOpenMx), or glmnet (for PenalisedLinearSystem).

References

RegSEMsharp

Examples

Run this code

# \donttest{
# Data simulation
pk <- c(3, 2, 3)
dag <- LayeredDAG(layers = pk)
theta <- dag
theta[2, 4] <- 0
set.seed(1)
simul <- SimulateStructural(theta = theta, pk = pk, output_matrices = TRUE)

# Running regularised SEM (OpenMx)
if (requireNamespace("OpenMx", quietly = TRUE)) {
  mysem <- PenalisedOpenMx(
    xdata = simul$data, adjacency = dag,
    Lambda = seq(1, 10, 1)
  )
  OpenMxMatrix(vect = mysem$selected[3, ], adjacency = dag)
}

# Running regularised SEM (glmnet)
mysem <- PenalisedLinearSystem(
  xdata = simul$data, adjacency = dag
)
LinearSystemMatrix(vect = mysem$selected[20, ], adjacency = dag)
# }