smoothAdaptiveLasso

This function allows for regularization of models built in lavaan with the smooth adaptive lasso penalty. The returned object is an S4 class; its elements can be accessed with the "@" operator (see examples).

Usage

smoothAdaptiveLasso(
  lavaanModel,
  regularized,
  weights = NULL,
  lambdas,
  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

weights

labeled vector with weights for each of the parameters in the model. If you are unsure what these parameters are called, use getLavaanParameters(model) with your lavaan model object. If set to NULL, the default weights will be used: the inverse of the absolute values of the unregularized parameter estimates

lambdas

numeric vector: values for the tuning parameter lambda

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.

Value

Model of class regularizedSEM

Details

For more details, see:

1. Zou, H. (2006). The Adaptive Lasso and Its Oracle Properties. Journal of the American Statistical Association, 101(476), 1418–1429. https://doi.org/10.1198/016214506000000735

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.

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)

# define adaptive lasso weights:
# We use the inverse of the absolute unregularized parameters
# (this is the default in adaptiveLasso and can also specified
# by setting weights = NULL)
weights <- 1/abs(getLavaanParameters(lavaanModel))
weights[!names(weights) %in% regularized] <- 0

lsem <- smoothAdaptiveLasso(
  # pass the fitted lavaan model
  lavaanModel = lavaanModel,
  regularized = regularized,
  weights = weights,
  epsilon = 1e-10,
  tau = 1e-4,
  lambdas = seq(0,1,length.out = 50))

# use the plot-function to plot the regularized parameters:
plot(lsem)

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

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

# AIC and BIC:
AIC(lsem)
BIC(lsem)

# The best parameters can also be extracted with:
coef(lsem, criterion = "AIC")
coef(lsem, criterion = "BIC")