regsem {regsem}

Regularized Structural Equation Modeling. Tests a single penalty. For testing multiple penalties, see cv_regsem().

Description

Regularized Structural Equation Modeling. Tests a single penalty. For testing multiple penalties, see cv_regsem().

Usage

regsem(
  model,
  lambda = 0,
  alpha = 0.5,
  gamma = 3.7,
  type = "lasso",
  dual_pen = NULL,
  random.alpha = 0.5,
  data = NULL,
  optMethod = "rsolnp",
  estimator = "ML",
  gradFun = "none",
  hessFun = "none",
  prerun = FALSE,
  parallel = "no",
  Start = "lavaan",
  subOpt = "nlminb",
  longMod = FALSE,
  pars_pen = "regressions",
  diff_par = NULL,
  LB = -Inf,
  UB = Inf,
  par.lim = c(-Inf, Inf),
  block = TRUE,
  full = TRUE,
  calc = "normal",
  max.iter = 500,
  tol = 1e-05,
  round = 3,
  solver = FALSE,
  quasi = FALSE,
  solver.maxit = 5,
  alpha.inc = FALSE,
  line.search = FALSE,
  step = 0.1,
  momentum = FALSE,
  step.ratio = FALSE,
  nlminb.control = list(),
  missing = "listwise"
)

Arguments

model

Lavaan output object. This is a model that was previously run with any of the lavaan main functions: cfa(), lavaan(), sem(), or growth(). It also can be from the efaUnrotate() function from the semTools package. Currently, the parts of the model which cannot be handled in regsem is the use of multiple group models, missing other than listwise, thresholds from categorical variable models, the use of additional estimators other than ML, most notably WLSMV for categorical variables. Note: the model does not have to actually run (use do.fit=FALSE), converge etc... regsem() uses the lavaan object as more of a parser and to get sample covariance matrix.

lambda

Penalty value. Note: higher values will result in additional convergence issues. If using values > 0.1, it is recommended to use mutli_optim() instead. See multi_optim for more detail.

alpha

Mixture for elastic net. 1 = ridge, 0 = lasso

gamma

Additional penalty for MCP and SCAD

type

Penalty type. Options include "none", "lasso", "enet" for the elastic net, "alasso" for the adaptive lasso and "diff_lasso". If ridge penalties are desired, use type="enet" and alpha=1. diff_lasso penalizes the discrepency between parameter estimates and some pre-specified values. The values to take the deviation from are specified in diff_par. Two methods for sparser results than lasso are the smooth clipped absolute deviation, "scad", and the minimum concave penalty, "mcp". Last option is "rlasso" which is the randomised lasso to be used for stability selection.

dual_pen

Two penalties to be used for type="dual", first is lasso, second ridge

random.alpha

Alpha parameter for randomised lasso. Has to be between 0 and 1, with a default of 0.5. Note this is only used for "rlasso", which pairs with stability selection.

data

Optional dataframe. Only required for missing="fiml" which is not currently working.

optMethod

Solver to use. Two main options for use: rsoolnp and coord_desc. Although slightly slower, rsolnp works much better for complex models. coord_desc uses gradient descent with soft thresholding for the type of of penalty. Rsolnp is a nonlinear solver that doesn't rely on gradient information. There is a similar type of solver also available for use, slsqp from the nloptr package. coord_desc can also be used with hessian information, either through the use of quasi=TRUE, or specifying a hess_fun. However, this option is not recommended at this time.

estimator

Whether to use maximum likelihood (ML) or unweighted least squares (ULS) as a base estimator.

gradFun

Gradient function to use. Recommended to use "ram", which refers to the method specified in von Oertzen & Brick (2014). Only for use with optMethod="coord_desc".

hessFun

Hessian function to use. Recommended to use "ram", which refers to the method specified in von Oertzen & Brick (2014). This is currently not recommended.

prerun

Logical. Use rsolnp to first optimize before passing to gradient descent? Only for use with coord_desc.

parallel

Logical. Whether to parallelize the processes?

Start

type of starting values to use. Only recommended to use "default". This sets factor loadings and variances to 0.5. Start = "lavaan" uses the parameter estimates from the lavaan model object. This is not recommended as it can increase the chances in getting stuck at the previous parameter estimates.

subOpt

Type of optimization to use in the optimx package.

longMod

If TRUE, the model is using longitudinal data? This changes the sample covariance used.

pars_pen

Parameter indicators to penalize. There are multiple ways to specify. The default is to penalize all regression parameters ("regressions"). Additionally, one can specify all loadings ("loadings"), or both c("regressions","loadings"). Next, parameter labels can be assigned in the lavaan syntax and passed to pars_pen. See the example.Finally, one can take the parameter numbers from the A or S matrices and pass these directly. See extractMatrices(lav.object)$A.

diff_par

Parameter values to deviate from. Only used when type="diff_lasso".

LB

lower bound vector. Note: This is very important to specify when using regularization. It greatly increases the chances of converging.

UB

Upper bound vector

par.lim

Vector of minimum and maximum parameter estimates. Used to stop optimization and move to new starting values if violated.

block

Whether to use block coordinate descent

full

Whether to do full gradient descent or block

calc

Type of calc function to use with means or not. Not recommended for use.

max.iter

Number of iterations for coordinate descent

tol

Tolerance for coordinate descent

round

Number of digits to round results to

solver

Whether to use solver for coord_desc

quasi

Whether to use quasi-Newton

solver.maxit

Max iterations for solver in coord_desc

alpha.inc

Whether alpha should increase for coord_desc

line.search

Use line search for optimization. Default is no, use fixed step size

step

Step size

momentum

Momentum for step sizes

step.ratio

Ratio of step size between A and S. Logical

nlminb.control

list of control values to pass to nlminb

missing

How to handle missing data. Current options are "listwise" and "fiml". "fiml" is not currently working well.

Value

out List of return values from optimization program

convergence Convergence status. 0 = converged, 1 or 99 means the model did not converge.

par.ret Final parameter estimates

Imp_Cov Final implied covariance matrix

grad Final gradient.

KKT1 Were final gradient values close enough to 0.

KKT2 Was the final Hessian positive definite.

df Final degrees of freedom. Note that df changes with lasso penalties.

npar Final number of free parameters. Note that this can change with lasso penalties.

SampCov Sample covariance matrix.

fit Final F_ml fit. Note this is the final parameter estimates evaluated with the F_ml fit function.

coefficients Final parameter estimates

nvar Number of variables.

N sample size.

nfac Number of factors

baseline.chisq Baseline chi-square.

baseline.df Baseline degrees of freedom.

Examples

# Note that this is not currently recommended. Use cv_regsem() instead
library(lavaan)
# put variables on same scale for regsem
HS <- data.frame(scale(HolzingerSwineford1939[,7:15]))
mod <- '
f =~ 1*x1 + l1*x2 + l2*x3 + l3*x4 + l4*x5 + l5*x6 + l6*x7 + l7*x8 + l8*x9
'
# Recommended to specify meanstructure in lavaan
outt = cfa(mod, HS, meanstructure=TRUE)

fit1 <- regsem(outt, lambda=0.05, type="lasso",
  pars_pen=c("l1", "l2", "l6", "l7", "l8"))
#equivalent to pars_pen=c(1:2, 6:8)
#summary(fit1)