smoothElasticNet {lessSEM}

smoothElasticNet

Description

This function allows for regularization of models built in lavaan with the smooth elastic net penalty. Its elements can be accessed with the "@" operator (see examples).

Usage

smoothElasticNet(
  lavaanModel,
  regularized,
  lambdas = NULL,
  nLambdas = NULL,
  alphas,
  epsilon,
  tau,
  modifyModel = lessSEM::modifyModel(),
  control = lessSEM::controlBFGS()
)

Arguments

lavaanModel

model of class lavaan

regularized

vector with names of parameters which are to be regularized. If you are unsure what these parameters are called, use getLavaanParameters(model) with your lavaan model object

lambdas

numeric vector: values for the tuning parameter lambda

nLambdas

alternative to lambda: If alpha = 1, lessSEM can automatically compute the first lambda value which sets all regularized parameters to zero. It will then generate nLambda values between 0 and the computed lambda.

alphas

numeric vector with values of the tuning parameter alpha. Must be between 0 and 1. 0 = ridge, 1 = lasso.

epsilon

epsilon > 0; controls the smoothness of the approximation. Larger values = smoother

tau

parameters below threshold tau will be seen as zeroed

modifyModel

used to modify the lavaanModel. See ?modifyModel.

control

used to control the optimizer. This element is generated with the controlBFGS function. See ?controlBFGS for more details.

Details

For more details, see:

1. Zou, H., & Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B, 67(2), 301–320. https://doi.org/10.1111/j.1467-9868.2005.00503.x for the details of this regularization technique.

2. Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized Structural Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 23(4), 555–566. https://doi.org/10.1080/10705511.2016.1154793

3. Lee, S.-I., Lee, H., Abbeel, P., & Ng, A. Y. (2006). Efficient L1 Regularized Logistic Regression. Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI-06), 401–408.

Value

Model of class regularizedSEM

Examples

library(lessSEM)

# Identical to regsem, lessSEM builds on the lavaan
# package for model specification. The first step
# therefore is to implement the model in lavaan.

dataset <- simulateExampleData()

lavaanSyntax <- "
f =~ l1*y1 + l2*y2 + l3*y3 + l4*y4 + l5*y5 +
     l6*y6 + l7*y7 + l8*y8 + l9*y9 + l10*y10 +
     l11*y11 + l12*y12 + l13*y13 + l14*y14 + l15*y15
f ~~ 1*f
"

lavaanModel <- lavaan::sem(lavaanSyntax,
                           data = dataset,
                           meanstructure = TRUE,
                           std.lv = TRUE)

# Regularization:

# names of the regularized parameters:
regularized = paste0("l", 6:15)

lsem <- smoothElasticNet(
  # pass the fitted lavaan model
  lavaanModel = lavaanModel,
  regularized = regularized,
  epsilon = 1e-10,
  tau = 1e-4,
  lambdas = seq(0,1,length.out = 5),
  alphas = seq(0,1,length.out = 3))

# the coefficients can be accessed with:
coef(lsem)

# elements of lsem can be accessed with the @ operator:
lsem@parameters[1,]