Determine an optimal lambda penalty value through cross-validation

This function can be used to determine an optimal lambda value for the lavPredictY function. based on cross-validation.

lavPredictY_cv(object, data = NULL,
              xnames = lavNames(object, "ov.x"),
              ynames = lavNames(object, "ov.y"),
              n.folds = 10L,
              lambda.seq = seq(0, 1, 0.1))

Arguments

object

An object of class lavaan.

data

A data.frame, containing the same variables as the data.frame that was used when fitting the model in object.

xnames

The names of the observed variables that should be treated as the x-variables. Can also be a list to allow for a separate set of variable names per group (or block).

ynames

The names of the observed variables that should be treated as the y-variables. It is for these variables that the function will predict the (model-based) values for each observation. Can also be a list to allow for a separate set of variable names per group (or block).

n.folds

Integer. The number of folds to be used during cross-validation.

lambda.seq

An R seq() containing the range of lambda penalty values to be tested during cross-validation.

Details

This function is used to generate an optimal lambda value for lavPredictY predictions to improve prediction accuracy.

See also

lavPredictY to predict the values of (observed) y-variables given the values of (observed) x-variables in a structural equation model.

References

de Rooij, M., Karch, J.D., Fokkema, M., Bakk, Z., Pratiwi, B.C, and Kelderman, H. (2022) SEM-Based Out-of-Sample Predictions, Structural Equation Modeling: A Multidisciplinary Journal. DOI:10.1080/10705511.2022.2061494

Molina, M. D., Molina, L., & Zappaterra, M. W. (2024). Aspects of Higher Consciousness: A Psychometric Validation and Analysis of a New Model of Mystical Experience. doi:10.31219/osf.io/cgb6e

Examples

colnames(PoliticalDemocracy) <- c("z1", "z2", "z3", "z4", 
                                  "y1", "y2", "y3", "y4", 
                                  "x1", "x2", "x3")

model <- '
  # latent variable definitions
  ind60 =~ x1 + x2 + x3
  dem60 =~ z1 + z2 + z3 + z4
  dem65 =~ y1 + y2 + y3 + y4
  # regressions
  dem60 ~ ind60
  dem65 ~ ind60 + dem60
  # residual correlations
  z1 ~~ y1
  z2 ~~ z4 + y2
  z3 ~~ y3
  z4 ~~ y4
  y2 ~~ y4
'
fit <- sem(model, data = PoliticalDemocracy, meanstructure = TRUE)
#> Warning: lavaan->lav_model_vcov():  
#>    The variance-covariance matrix of the estimated parameters (vcov) does not 
#>    appear to be positive definite! The smallest eigenvalue (= -1.239244e+00) 
#>    is smaller than zero. This may be a symptom that the model is not 
#>    identified.

percent <- 0.5
nobs <- lavInspect(fit, "ntotal")
idx <- sort(sample(x = nobs, size = floor(percent*nobs)))

xnames = c("z1", "z2", "z3", "z4", "x1", "x2", "x3")
ynames = c("y1", "y2", "y3", "y4")

reg.results <- lavPredictY_cv(
    fit,
    PoliticalDemocracy[-idx, ],
    xnames = xnames,
    ynames = ynames,
    n.folds = 10L,
    lambda.seq = seq(from = .6, to = 2.5, by = .1)
)
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 1
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 2
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 3
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 4
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 5
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 6
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 7
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 8
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 9
#> Warning: lavaan->lavPredictY_cv():  
#>    failed fit in fold %s 10
lam <- reg.results$lambda.min

lavPredictY(fit, newdata = PoliticalDemocracy[idx,],
                 ynames  = ynames,
                 xnames  = xnames,
                 lambda  = lam)
#>       y1 y2 y3 y4
#>  [1,] NA NA NA NA
#>  [2,] NA NA NA NA
#>  [3,] NA NA NA NA
#>  [4,] NA NA NA NA
#>  [5,] NA NA NA NA
#>  [6,] NA NA NA NA
#>  [7,] NA NA NA NA
#>  [8,] NA NA NA NA
#>  [9,] NA NA NA NA
#> [10,] NA NA NA NA
#> [11,] NA NA NA NA
#> [12,] NA NA NA NA
#> [13,] NA NA NA NA
#> [14,] NA NA NA NA
#> [15,] NA NA NA NA
#> [16,] NA NA NA NA
#> [17,] NA NA NA NA
#> [18,] NA NA NA NA
#> [19,] NA NA NA NA
#> [20,] NA NA NA NA
#> [21,] NA NA NA NA
#> [22,] NA NA NA NA
#> [23,] NA NA NA NA
#> [24,] NA NA NA NA
#> [25,] NA NA NA NA
#> [26,] NA NA NA NA
#> [27,] NA NA NA NA
#> [28,] NA NA NA NA
#> [29,] NA NA NA NA
#> [30,] NA NA NA NA
#> [31,] NA NA NA NA
#> [32,] NA NA NA NA
#> [33,] NA NA NA NA
#> [34,] NA NA NA NA
#> [35,] NA NA NA NA
#> [36,] NA NA NA NA
#> [37,] NA NA NA NA