Title: SEM Model Comparison with K-Fold Cross-Validation
Version: 1.0.0
Description: The goal of 'cvsem' is to provide functions that allow for comparing Structural Equation Models (SEM) using cross-validation. Users can specify multiple SEMs using 'lavaan' syntax. 'cvsem' computes the Kullback Leibler (KL) Divergence between 1) the model implied covariance matrix estimated from the training data and 2) the sample covariance matrix estimated from the test data described in Cudeck, Robert & Browne (1983) <doi:10.18637/jss.v048.i02>. The KL Divergence is computed for each of the specified SEMs allowing for the models to be compared based on their prediction errors.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.2.0
Imports: lavaan, stats, Rdpack
RdMacros: Rdpack
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2022-08-10 19:09:46 UTC; annawy
Author: Anna Wysocki [aut, cre], Danielle Siegel [aut], Cameron allen [aut], Philippe Rast [aut]
Maintainer: Anna Wysocki <awysocki@ucdavis.edu>
Repository: CRAN
Date/Publication: 2022-08-13 12:30:05 UTC

Internal function to extract variable names for each tested model This is used to find largest umber of folds K

Description

Internal function to extract variable names for each tested model This is used to find largest umber of folds K

Usage

.lavaan_vars(X, data)

Arguments

X

lavaan model

data

Data

Value

list of variable names

Author(s)

philippe

Compute KL-Divergence on two covariance matrices. KL-Divergence corresponds to the Maximum Wishart Likelihood (MWL) discrepancy described in (Cudeck and Browne 1983).

Description

Compute KL-Divergence on two covariance matrices. KL-Divergence corresponds to the Maximum Wishart Likelihood (MWL) discrepancy described in (Cudeck and Browne 1983).

Usage

KL_divergence(implied_sigma, test_S)

Arguments

implied_sigma

Model implied covariances matrix from training set

test_S

Sample covariance matrix from test set

Value

KL-Divergence index

References

Cudeck R, Browne MW (1983). “Cross-Validation Of Covariance Structures.” Multivariate Behavioral Research, 18, 147–167. doi:10.1207/s15327906mbr1802_2, https://www.tandfonline.com/doi/abs/10.1207/s15327906mbr1802_2.()

Gather lavan model objects into a list

Description

Gather lavaan model objects to be compared via CV. Function returns a named list.

Usage

cvgather(...)

Arguments

...

Names of lavaan model objects

Value

Named list

Author(s)

philippe

Examples


example_data <- lavaan::HolzingerSwineford1939
colnames(example_data) <- c("id", "sex", "ageyr", "agemo", 'school', "grade",
"visualPerception", "cubes", "lozenges", "comprehension",
"sentenceCompletion", "wordMeaning", "speededAddition",
"speededCounting", "speededDiscrimination")

model1 <- 'comprehension ~ sentenceCompletion + wordMeaning'

model2 <- 'comprehension ~ wordMeaning
           sentenceCompletion ~ wordMeaning

           comprehension ~~ 0.5*wordMeaning'

model_list <- cvgather(model1, model2)

Cross-Validation of Structural Equation Models

Description

Do model comparison on SEM models using cross-validation as described in (Cudeck and Browne 1983) and (Browne and Cudeck 1992). Cross-validation is based on the discrepancy between the sample covariance matrix and the model implied matrix. Currently, cvsem supports 'KL-Divergence', Frobenius Distance and Generalized Least Squares 'GLS' as discrepancy metrics.

Usage

cvsem(
  data = NULL,
  Models,
  discrepancyMetric = "KL-Divergence",
  k = 5,
  lavaanFunction = "sem",
  echo = TRUE,
  ...
)

Arguments

data

Data

Models

A collection of models, specified in lavaan syntax. Provide Models with the cvgather() function.

discrepancyMetric

Specify which discrepancy metric to use (one of 'KL-Divergence', 'FD', 'GLS'). Default is KL Divergence.

k

The number of folds. Default is 5.

lavaanFunction

Specify which lavaan function to use. Default is "sem". Other options are "lavaan" and "cfa"

echo

Provide feedback on progress to user, defaults to TRUE. Set to FALSE to suppress.

...

Not used

Value

A list with the prediction error for each model.

References

Browne MW, Cudeck R (1992). “Alternative Ways of Assessing Model Fit.” Sociological Methods & Research, 21, 230–258.

Cudeck R, Browne MW (1983). “Cross-Validation Of Covariance Structures.” Multivariate Behavioral Research, 18, 147–167. doi:10.1207/s15327906mbr1802_2, https://www.tandfonline.com/doi/abs/10.1207/s15327906mbr1802_2.()

Examples


example_data <- lavaan::HolzingerSwineford1939
colnames(example_data) <- c("id", "sex", "ageyr", "agemo", 'school', "grade",
"visualPerception", "cubes", "lozenges", "comprehension",
"sentenceCompletion", "wordMeaning", "speededAddition",
"speededCounting", "speededDiscrimination")

model1 <- 'comprehension ~ meaning

           ## Add some latent variables:
        meaning =~ wordMeaning + sentenceCompletion
        speed =~ speededAddition + speededDiscrimination + speededCounting
        speed ~~ meaning'

model2 <- 'comprehension ~ wordMeaning + speededAddition'
model3 <- 'comprehension ~ wordMeaning + speededAddition'

models <- cvgather(model1, model2, model3)

fit <- cvsem( data = example_data, Models = models, k = 10, discrepancyMetric = "KL-Divergence")

Frobenius Matrix Discrepancy

Description

Frobenius Distance as described in (Biscay et al. 1997) or (Amendola and Storti 2015).

Usage

fd(implied_Sigma, test_S)

Arguments

implied_Sigma

Model implied covariances matrix from training set

test_S

Sample covariance matrix from test set

Value

FD discrepancy

References

Amendola A, Storti G (2015). “Model Uncertainty and Forecast Combination in High-Dimensional Multivariate Volatility Prediction.” Journal of Forecasting, 34, 83–91. doi:10.1002/for.2322.

Biscay R, Rodr\'iguez LM, D\'iaz-Frances E (1997). “Cross-validation of covariance structures using the frobenius matrix distance as a discrepancy function.” Journal of Statistical Computation and Simulation, 58, 195–215. doi:10.1080/00949659708811831, https://www.tandfonline.com/doi/abs/10.1080/00949659708811831.()

Generalized Least Squares Discrepancy Function

Description

Generalized Least Squares (GLS) Discrepancy as defined in (Cudeck and Browne 1983).

Usage

gls(implied_sigma, test_S)

Arguments

implied_sigma

Model implied covariances matrix from training set

test_S

Sample covariance matrix from test set

Value

GLS discrepancy

References

Cudeck R, Browne MW (1983). “Cross-Validation Of Covariance Structures.” Multivariate Behavioral Research, 18, 147–167. doi:10.1207/s15327906mbr1802_2, https://www.tandfonline.com/doi/abs/10.1207/s15327906mbr1802_2.()

Print cvsem object

Description

Return the ordered list of models where the model with the smallest discrepancy metric is listed first.

Usage

## S3 method for class 'cvsem'
print(x, digits = 2, ...)

Arguments

x

cvsem object

digits

Round to (default 2) digits.

...

not used

Value

Formatted cvsem object