stabilitySelection

Provides rudimentary stability selection for regularized SEM. Stability selection has been proposed by Meinshausen & Bühlmann (2010) and was extended to SEM by Li & Jacobucci (2021). The problem that stabiltiy selection tries to solve is the instability of regularization procedures: Small changes in the data set may result in different parameters being selected. To address this issue, stability selection uses random subsamples from the initial data set and fits models in these subsamples. For each parameter, we can now check how often it is included in the model for a given set of tuning parameters. Plotting these probabilities can provide an overview over which of the parameters are often removed and which remain in the model most of the time. To get a final selection, a threshold t can be defined: If a parameter is in the model t% of the time, it is retained.

Usage

stabilitySelection(
  modelSpecification,
  subsampleSize,
  numberOfSubsamples = 100,
  threshold = 70,
  maxTries = 10 * numberOfSubsamples
)

Arguments

modelSpecification

a call to one of the penalty functions in lessSEM. See examples for details

subsampleSize

number of subjects in each subsample. Must be smaller than the number of subjects in the original data set

numberOfSubsamples

number of times the procedure should subsample and recompute the model. According to Meinshausen & Bühlmann (2010), 100 seems to work quite well and is also the default in regsem

threshold

percentage of models, where the parameter should be contained in order to be in the final model

maxTries

fitting models in a subset may fail. maxTries sets the maximal number of subsets to try.

Value

estimates for each subsample and aggregated percentages for each parameter

References

• Li, X., & Jacobucci, R. (2021). Regularized structural equation modeling with stability selection. Psychological Methods, 27(4), 497–518. https://doi.org/10.1037/met0000389

• Meinshausen, N., & Bühlmann, P. (2010). Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(4), 417–473. https://doi.org/10.1111/j.1467-9868.2010.00740.x

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)

# Stability selection
stabSel <- stabilitySelection(
  # IMPORTANT: Wrap your call to the penalty function in an rlang::expr-Block:
  modelSpecification = 
    rlang::expr(
      lasso(
        # pass the fitted lavaan model
        lavaanModel = lavaanModel,
        # names of the regularized parameters:
        regularized = paste0("l", 6:15),
        # in case of lasso and adaptive lasso, we can specify the number of lambda
        # values to use. lessSEM will automatically find lambda_max and fit
        # models for nLambda values between 0 and lambda_max. For the other
        # penalty functions, lambdas must be specified explicitly
        nLambdas = 50)
    ),
  subsampleSize = 80,
  numberOfSubsamples = 5, # should be set to a much higher number (e.g., 100)
  threshold = 70
)
stabSel
plot(stabSel)