Nothing
R/cvRegularizeSmoothSEMInterface.R
In lessSEM: Non-Smooth Regularization for Structural Equation Models
Defines functions
cvSmoothElasticNet
cvRidgeBfgs
cvSmoothAdaptiveLasso
cvSmoothLasso
Documented in
cvRidgeBfgs
cvSmoothAdaptiveLasso
cvSmoothElasticNet
cvSmoothLasso
#' cvSmoothLasso
#'
#' Implements cross-validated smooth lasso regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \lambda \sqrt{(x_j + \epsilon)^2}}
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Lasso regularization:
#'
#' * Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical
#' Society. Series B (Methodological), 58(1), 267–288.
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothLasso(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,.1),
#' k = 5, # number of cross-validation folds
#' epsilon = 1e-8,
#' standardize = TRUE) # automatic standardization
#'
#' # use the plot-function to plot the cross-validation fit:
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # The best parameters can also be extracted with:
#' coef(lsem)
#' @export
cvSmoothLasso <- function(lavaanModel,
regularized,
lambdas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
tuningParameters <- data.frame(lambda = lambdas,
alpha = 1)
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "lasso",
k = k,
epsilon = epsilon,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
weights = regularized,
tuningParameters = tuningParameters,
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvSmoothAdaptiveLasso
#'
#' Implements cross-validated smooth adaptive lasso regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = p( x_j) = \frac{1}{w_j}\lambda\sqrt{(x_j + \epsilon)^2}}
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Adaptive lasso regularization:
#'
#' * 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
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothAdaptiveLasso(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,.1),
#' epsilon = 1e-8)
#'
#' # use the plot-function to plot the cross-validation fit
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # The best parameters can also be extracted with:
#' coef(lsem)
#' @export
cvSmoothAdaptiveLasso <- function(lavaanModel,
regularized,
weights = NULL,
lambdas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
tuningParameters <- data.frame(lambda = lambdas,
alpha = 1)
if(is.null(weights)) weights <- regularized
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "adaptiveLasso",
weights = weights,
epsilon = epsilon,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = tuningParameters,
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvRidgeBfgs
#'
#' Implements cross-validated ridge regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \lambda x_j^2}
#' Note that ridge regularization will not set any of the parameters to zero
#' but result in a shrinkage towards zero.
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Ridge regularization:
#'
#' * Hoerl, A. E., & Kennard, R. W. (1970). Ridge Regression: Biased Estimation
#' for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
#' https://doi.org/10.1080/00401706.1970.10488634
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS
#' for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvRidgeBfgs(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,length.out = 20))
#'
#' # use the plot-function to plot the cross-validation fit:
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' @export
cvRidgeBfgs <- function(lavaanModel,
regularized,
lambdas,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "ridge",
weights = regularized,
epsilon = 0,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = data.frame(lambda = lambdas,
alpha = 0),
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvSmoothElasticNet
#'
#' Implements cross-validated smooth elastic net regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \alpha\lambda\sqrt{(x_j + \epsilon)^2} + (1-\alpha)\lambda x_j^2}
#' Note that the smooth elastic net combines ridge and smooth lasso regularization. If \eqn{\alpha = 0},
#' the elastic net reduces to ridge regularization. If \eqn{\alpha = 1} it reduces
#' to smooth lasso regularization. In between, elastic net is a compromise between the shrinkage of
#' the lasso and the ridge penalty.
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Elastic net regularization:
#'
#' * 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
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param alphas numeric vector with values of the tuning parameter alpha. Must be
#' between 0 and 1. 0 = ridge, 1 = lasso.
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS
#' for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothElasticNet(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' epsilon = 1e-8,
#' lambdas = seq(0,1,length.out = 5),
#' alphas = .3)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # optional: plotting the cross-validation fit requires installation of plotly
#' # plot(lsem)
#' @export
cvSmoothElasticNet <- function(lavaanModel,
regularized,
lambdas,
alphas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
if(any(alphas < 0) || any(alphas > 1))
stop("alpha must be between 0 and 1.")
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "elasticNet",
weights = regularized,
epsilon = epsilon,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = expand.grid(lambda = lambdas,
alpha = alphas),
modifyModel = modifyModel,
control = control
)
return(result)
}
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Defines functions cvSmoothElasticNet cvRidgeBfgs cvSmoothAdaptiveLasso cvSmoothLasso
Documented in cvRidgeBfgs cvSmoothAdaptiveLasso cvSmoothElasticNet cvSmoothLasso
#' cvSmoothLasso
#'
#' Implements cross-validated smooth lasso regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \lambda \sqrt{(x_j + \epsilon)^2}}
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Lasso regularization:
#'
#' * Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical
#' Society. Series B (Methodological), 58(1), 267–288.
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothLasso(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,.1),
#' k = 5, # number of cross-validation folds
#' epsilon = 1e-8,
#' standardize = TRUE) # automatic standardization
#'
#' # use the plot-function to plot the cross-validation fit:
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # The best parameters can also be extracted with:
#' coef(lsem)
#' @export
cvSmoothLasso <- function(lavaanModel,
regularized,
lambdas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
tuningParameters <- data.frame(lambda = lambdas,
alpha = 1)
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "lasso",
k = k,
epsilon = epsilon,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
weights = regularized,
tuningParameters = tuningParameters,
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvSmoothAdaptiveLasso
#'
#' Implements cross-validated smooth adaptive lasso regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = p( x_j) = \frac{1}{w_j}\lambda\sqrt{(x_j + \epsilon)^2}}
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Adaptive lasso regularization:
#'
#' * 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
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothAdaptiveLasso(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,.1),
#' epsilon = 1e-8)
#'
#' # use the plot-function to plot the cross-validation fit
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # The best parameters can also be extracted with:
#' coef(lsem)
#' @export
cvSmoothAdaptiveLasso <- function(lavaanModel,
regularized,
weights = NULL,
lambdas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
tuningParameters <- data.frame(lambda = lambdas,
alpha = 1)
if(is.null(weights)) weights <- regularized
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "adaptiveLasso",
weights = weights,
epsilon = epsilon,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = tuningParameters,
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvRidgeBfgs
#'
#' Implements cross-validated ridge regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \lambda x_j^2}
#' Note that ridge regularization will not set any of the parameters to zero
#' but result in a shrinkage towards zero.
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Ridge regularization:
#'
#' * Hoerl, A. E., & Kennard, R. W. (1970). Ridge Regression: Biased Estimation
#' for Nonorthogonal Problems. Technometrics, 12(1), 55–67.
#' https://doi.org/10.1080/00401706.1970.10488634
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS
#' for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvRidgeBfgs(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' lambdas = seq(0,1,length.out = 20))
#'
#' # use the plot-function to plot the cross-validation fit:
#' plot(lsem)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' @export
cvRidgeBfgs <- function(lavaanModel,
regularized,
lambdas,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "ridge",
weights = regularized,
epsilon = 0,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = data.frame(lambda = lambdas,
alpha = 0),
modifyModel = modifyModel,
control = control
)
return(result)
}
#' cvSmoothElasticNet
#'
#' Implements cross-validated smooth elastic net regularization for structural equation models.
#' The penalty function is given by:
#' \deqn{p( x_j) = \alpha\lambda\sqrt{(x_j + \epsilon)^2} + (1-\alpha)\lambda x_j^2}
#' Note that the smooth elastic net combines ridge and smooth lasso regularization. If \eqn{\alpha = 0},
#' the elastic net reduces to ridge regularization. If \eqn{\alpha = 1} it reduces
#' to smooth lasso regularization. In between, elastic net is a compromise between the shrinkage of
#' the lasso and the ridge penalty.
#'
#' Identical to \pkg{regsem}, models are specified using \pkg{lavaan}. Currently,
#' most standard SEM are supported. \pkg{lessSEM} also provides full information
#' maximum likelihood for missing data. To use this functionality,
#' fit your \pkg{lavaan} model with the argument `sem(..., missing = 'ml')`.
#' \pkg{lessSEM} will then automatically switch to full information maximum likelihood
#' as well.
#'
#' Elastic net regularization:
#'
#' * 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
#'
#' Regularized SEM
#'
#' * Huang, P.-H., Chen, H., & Weng, L.-J. (2017). A Penalized Likelihood Method for Structural Equation Modeling. Psychometrika, 82(2), 329–354. https://doi.org/10.1007/s11336-017-9566-9
#' * 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
#'
#' @param lavaanModel model of class lavaan
#' @param 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
#' @param lambdas numeric vector: values for the tuning parameter lambda
#' @param alphas numeric vector with values of the tuning parameter alpha. Must be
#' between 0 and 1. 0 = ridge, 1 = lasso.
#' @param epsilon epsilon > 0; controls the smoothness of the approximation. Larger values = smoother
#' @param k the number of cross-validation folds. Alternatively, you can pass
#' a matrix with booleans (TRUE, FALSE) which indicates for each person which subset
#' it belongs to. See ?lessSEM::createSubsets for an example of how this matrix should look like.
#' @param standardize Standardizing your data prior to the analysis can undermine the cross-
#' validation. Set standardize=TRUE to automatically standardize the data.
#' @param returnSubsetParameters set to TRUE to return the parameters for each training set
#' @param modifyModel used to modify the lavaanModel. See ?modifyModel.
#' @param control used to control the optimizer. This element is generated with
#' the controlBFGS function. See ?controlBFGS
#' for more details.
#' @returns model of class cvRegularizedSEM
#' @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:
#'
#' lsem <- cvSmoothElasticNet(
#' # pass the fitted lavaan model
#' lavaanModel = lavaanModel,
#' # names of the regularized parameters:
#' regularized = paste0("l", 6:15),
#' epsilon = 1e-8,
#' lambdas = seq(0,1,length.out = 5),
#' alphas = .3)
#'
#' # the coefficients can be accessed with:
#' coef(lsem)
#'
#' # elements of lsem can be accessed with the @ operator:
#' lsem@parameters
#'
#' # optional: plotting the cross-validation fit requires installation of plotly
#' # plot(lsem)
#' @export
cvSmoothElasticNet <- function(lavaanModel,
regularized,
lambdas,
alphas,
epsilon,
k = 5,
standardize = FALSE,
returnSubsetParameters = FALSE,
modifyModel = lessSEM::modifyModel(),
control = lessSEM::controlBFGS()){
if(any(alphas < 0) || any(alphas > 1))
stop("alpha must be between 0 and 1.")
result <- .cvRegularizeSmoothSEMInternal(
lavaanModel = lavaanModel,
penalty = "elasticNet",
weights = regularized,
epsilon = epsilon,
k = k,
standardize = standardize,
returnSubsetParameters = returnSubsetParameters,
tuningParameters = expand.grid(lambda = lambdas,
alpha = alphas),
modifyModel = modifyModel,
control = control
)
return(result)
}
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