Latent variable graphical LASSO

Description

The lvglasso algorithm to estimate network structures containing latent variables, as proposed by Yuan (2012). Uses the glasso package (Friedman, Hastie and Tibshirani, 2014) and mimics input and output of the glasso function.

Usage

1
lvglasso(S, nLatents, rho = 0, thr = 1e-04, maxit = 10000, lambda)

Arguments

S

Sample variance-covariance matrix

nLatents

Number of latent variables.

rho

The LASSO tuning parameter

thr

The threshold to use for convergence

maxit

Maximum number of iterations

lambda

The lambda argument containing factor loadings, only used for starting values!

Value

A list of class lvglasso containing the following elements:

w

The estimated variance-covariance matrix of both observed and latent variables

wi

The estimated inverse variance-covariance matrix of both observed and latent variables

pcor

Estimated partial correlation matrix of both observed and latent variables

observed

Logical vector indicating which elements of w, wi and pcor are observed

niter

The number of iterations used

lambda

The estimated lambda matrix, when result is transformed to EFA model

theta

The estimated theta matrix

omega_theta

The estimated omega_theta matrix

psi

The estimated psi matrix

Author(s)

Sacha Epskamp <mail@sachaepskamp.com>

References

Yuan, M. (2012). Discussion: Latent variable graphical model selection via convex optimization.The Annals of Statistics,40, 1968-1972.

Jerome Friedman, Trevor Hastie and Rob Tibshirani (2014). glasso: Graphical lasso-estimation of Gaussian graphical models. R package version 1.8. http://CRAN.R-project.org/package=glasso