Nothing
R/class.R
In penfa: Single- And Multiple-Group Penalized Factor Analysis
#########################################
# ---- Functions for setting classes ----
#########################################
# Content:
#
# Set the following classes:
# - "penfaData",
# - "penfaSampleStats"
# - "penfaModel"
# - "penfaPenalty"
# - "penfa"
#
# ------------------------------------------------------------------------------
#' S4 Class for describing the input data
#'
#' @description The \code{penfaData} class gives information on the data set
#' provided in input for analysis. This class is an adaptation of the
#' \code{lavData} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#' @slot ngroups Integer. The number of groups.
#' @slot group Character. The observed variables defining the groups.
#' @slot group.label Character. The group labels, that is, the values of the
#' \code{group} variable, if any.
#' @slot std.ov Logical indicating whether the observed variables should be
#' standardized.
#' @slot nobs List of the effective number of observations in each group.
#' @slot norig List of the original number of observations in each group.
#' @slot ov.names List of the observed variable names in each group.
#' @slot ov List of details at the observed variable level.
#' @slot case.idx List of the case (i.e., observation) indices in each group.
#' @slot X List. Local copy of the input data set split into groups.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Data
#' str(alasso_fit@Data)
#'
#'
setClass("penfaData",
slots = c(
ngroups = "integer",
group = "character",
group.label = "character",
std.ov = "logical",
nobs = "list",
norig = "list",
ov.names = "list",
ov = "list",
case.idx = "list",
X = "list"))
#' S4 Class for describing the sample moments
#'
#' @description The \code{penfaSampleStats} class provides information on the
#' sample moments of the factor analysis model. This
#' class is an adaptation of the \code{lavSampleStats} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#' @slot var List of the variances of the observed variables in every group.
#' @slot cov List of the covariance matrices of the observed variables
#' in every group.
#' @slot mean List of the means of the observed variables in every group.
#' @slot group.w List of group weights.
#' @slot nobs List of the effective number of observations for every group.
#' @slot ntotal Integer. Total number of observations across all groups.
#' @slot ngroups Integer. Number of groups.
#' @slot icov List of the inverse matrices of the covariance matrices of the
#' observed variables in every group.
#' @slot cov.log.det List of the logarithms of the determinants of the
#' covariance matrices of the observed variables for every group.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@SampleStats
#'
setClass("penfaSampleStats",
slots = c(
var = "list",
cov = "list",
mean = "list",
group.w = "list",
nobs = "list",
ntotal = "integer",
ngroups = "integer",
icov = "list",
cov.log.det = "list"))
#' S4 Class for internal representation of a factor model
#'
#' @description The \code{penfaModel} class gives the internal matrix
#' representation of a factor analysis model. Note that this representation
#' summarizes the characteristics of the model itself (e.g., number of items,
#' number of factors, parameter indices, etc), without information on the
#' penalization process (see \code{\linkS4class{penfaPenalty}} for that
#' aspect). This class is an adaptation of the \code{lavModel} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#'
#' @slot GLIST List. The model matrices and vectors: "lambda" for the factor
#' loading matrix, "psi" for the covariance matrix of the unique factors,
#' "phi" for the covariance matrix of the common factors, "tau" for the
#' intercept vector, and "kappa" for the vector of factor means. In case of a
#' multiple-group analysis, the elements of each group are presented
#' sequentially.
#' @slot dimNames List. Dimension names (row names and column names) of every
#' model matrix and vector.
#' @slot isSymmetric Logical vector declaring whether each model matrix/vector
#' is symmetric.
#' @slot mmSize Integer vector specifying the size (unique elements only) of
#' each model matrix/vector.
#' @slot meanstructure Logical. It declares whether the model includes a
#' meanstructure.
#' @slot ngroups Integer. The number of groups.
#' @slot nmat Integer vector specifying the number of model matrices/vectors for
#' each group.
#' @slot nvar Integer vector specifying the number of observed variables in each
#' group.
#' @slot num.idx List of the indices of the observed variables in each group.
#' @slot nx.free Integer. The number of parameters of the factor model. This
#' count does not include the fixed parameters, but it does include the
#' parameters that will be penalized (if any) during optimization. (see
#' \code{\linkS4class{penfaPenalty}} for additional details in this respect).
#' @slot nx.user Integer. The total count of the parameters that are being
#' estimated and the ones that have been fixed.
#' @slot m.free.idx List. For each model matrix, the indices of the elements to
#' be estimated (i.e., non-fixed). The counter starts at 1 for every model
#' matrix.
#' @slot x.free.idx List. For each model matrix, the indices of the elements to
#' be estimated (i.e., non-fixed). The counter continues from the previous
#' model matrix.
#' @slot m.user.idx List. Much like \code{m.free.idx}, but it also contains the
#' indices of the parameters that have been fixed by the user.
#' @slot x.user.idx List. Much like \code{x.free.idx}, but it also contains the
#' indices of the parameters that have been fixed by the user.
#' @slot x.free.var.idx Vector of integers denoting the indices corresponding to
#' the unique variances.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Model
#'
setClass("penfaModel",
slots = c(
GLIST = "list",
dimNames = "list",
isSymmetric = "logical",
mmSize = "integer",
meanstructure = "logical",
ngroups = "integer",
nmat = "integer",
nvar = "integer",
num.idx = "list",
nx.free = "integer",
nx.user = "integer",
m.free.idx = "list",
x.free.idx = "list",
m.user.idx = "list",
x.user.idx = "list",
x.free.var.idx = "integer"))
#' S4 Class for describing the penalization process
#'
#' @description The \code{penfaPenalty} class provides information on the
#' penalization process, such as the user-specified penalty functions, the
#' optimal values of the tuning parameters, and the penalty matrices at
#' convergence.
#'
#' @slot strategy Character. The strategy used for the selection of the tuning
#' parameter(s). If \code{strategy = "auto"}, the optimal values of the tuning
#' parameters are determined via the automatic tuning parameter procedure; if
#' \code{strategy = "fixed"}, a penalized factor model with the values of the
#' tuning parameters stored in the option \code{eta} is estimated.
#' @slot penalty List. A list of the user-specified penalty functions for
#' sparsity ("shrink") and parameter equivalence ("diff").
#' @slot tuning List. A named list containing the optimal values of the tuning
#' parameter(s) if \code{strategy = "auto"} or the user-specified fixed
#' values of the tuning parameter(s) if \code{strategy = "fixed"}. The list
#' has two components with names "shrink" and "diff", and refers to the tuning
#' parameters used for shrinkage and group equivalence, respectively. The
#' components of the list are, in turn, the named vectors specifying the type
#' of parameter matrices or vectors that were penalized.
#' @slot pmat List. A named list containing the names of the parameter matrices
#' and vectors that were penalized for sparsity ("shrink") and/or group
#' equivalence ("diff").
#' @slot pen.idx List. A named list with the indices of the parameters that were
#' penalized for sparsity ("shrink") and/or group equivalence ("diff").
#' @slot Sh.info List. A list of the penalization terms, vectors and matrices
#' evaluated at the optimal values of the tuning parameters. In particular,
#' its argument \code{S.h} returns the estimated penalty matrix. If the factor
#' model is penalized only through a shrinkage penalty (i.e.,
#' \code{pen.shrink} is not \code{'none'}), and there is no penalization on
#' the differences (i.e., \code{pen.diff = 'none'}), then \code{S.h} is a
#' diagonal matrix whose elements precisely quantify the extent to which each
#' model parameter has been penalized.
#' @slot extra List. A list possibly containing additional information on the
#' penalization process, such as the hyperparameter values for some penalty
#' functions (e.g., for the alasso, the value of the exponent and the adaptive
#' weights.)
#' @slot automatic List. If \code{strategy = "auto"}, it contains information on
#' the automatic multiple tuning parameter procedure, such as the optimal
#' values of the tuning parameters, the convergence status, the specified
#' value of the influence factor, the number of necessary iterations, and the
#' tolerance level.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Penalize
#'
#' str(alasso_fit@Penalize)
#'
setClass("penfaPenalty",
slots = c(
strategy = "character",
penalty = "list",
tuning = "list",
pmat = "list",
pen.idx = "list",
Sh.info = "list",
extra = "list",
automatic = "list"))
#' S4 Class for describing a \code{penfa} model
#'
#' @description The \code{penfa} class represents a (fitted) penalized factor
#' analysis model. It contains a description of the model as specified by the
#' user, a summary of the data, an internal matrix representation, the
#' fitting results, and the penalized quantities.
#'
#' @section Objects from the Class:
#'
#' Objects can be created via the \code{\link{penfa}} function.
#'
#' @section Slots:
#'
#' \describe{
#' \item{\code{version}:}{The \code{penfa} package version used to create this object.}
#' \item{\code{call}:}{The function call as returned by \code{match.call()}.}
#' \item{\code{timing}:}{The elapsed time (user + system) for various parts of
#' the program as a list, including the total time.}
#' \item{\code{Options}:}{Named list of options that were provided by the user
#' or filled-in automatically. See \code{\link{penfaOptions}} for additional
#' details.}
#' \item{\code{ParTable}:}{Named list describing the model parameters.
#' Can be coerced to a data.frame. This is also called "parameter table".
#' It includes information on the fixed, free and penalized parameters, their
#' indices, the active penalization strategies ("none", "shrink", "diff", or
#' "shrink + diff"), the starting values, the estimated parameters and the
#' associated standard errors.}
#' \item{\code{pta}:}{Named list containing parameter table attributes, like
#' observed and latent variable names, their indices, and the number of groups.}
#' \item{\code{Data}:}{Object of internal class \code{"penfaData"}; contains
#' information about the data set. See the \code{\linkS4class{penfaData}} class
#' for additional details.}
#' \item{\code{SampleStats}:}{Object of internal class \code{"penfaSampleStats"};
#' contains the sample statistics. See the \code{\linkS4class{penfaSampleStats}}
#' class for additional details.}
#' \item{\code{Model}:}{Object of internal class \code{"penfaModel"}: the internal
#' (matrix) representation of the model. See the \code{\linkS4class{penfaModel}}
#' class for additional details.}
#' \item{\code{Optim}:}{List. Information about the optimization process. This
#' includes the estimated parameters (\code{x}), the number of estimated
#' parameters (\code{npar}), the number of trust-region iterations
#' (\code{iterations}), the value of the penalized objective function
#' (\code{fx.pen}), the value of the unpenalized objective
#' function (\code{fx.unpen}), the penalized log-likelihood (\code{logl.pen};
#' this is equal to \code{fx.pen} multiplied by (-1)), the unpenalized
#' log-likelihood (\code{logl.unpen}; this is equal to \code{fx.unpen} multiplied
#' by (-1)), the penalized gradient (\code{dx.pen}), the penalized Hessian/Fisher
#' information matrix (\code{hessian.pen}), the list of control arguments for
#' the trust-region algorithm (\code{control}), and how many times the
#' objective function became non-positive definite during the estimation
#' process (\code{npd}). If penfa was called with the option \code{verbose =
#' TRUE}, the following additional arguments coming from the trust-region
#' function \code{trust} are reported in the \code{Optim} slot: \code{argpath},
#' \code{argtry}, \code{type}, \code{accept}, \code{radii}, \code{rho},
#' \code{fx.val}, \code{fx.valtry}, \code{change}, \code{stepnorm}. See the
#' manual page of \code{trust} from the \code{trust} package for an overview of
#' these quantities.}
#' \item{\code{Penalize}:}{Object of internal class \code{"penfaPenalty"}; contains
#' information about the penalization. See the \code{\linkS4class{penfaPenalty}} for
#' additional details.}
#' \item{\code{Implied}:}{List. Model-implied moments (covariance matrix and
#' mean vector).}
#' \item{\code{Vcov}:}{List. Information about the covariance matrix (vcov) of
#' the model parameters. This slot includes the following quantities: the type
#' of penalized information matrix used in the model (either Hessian or Fisher;
#' \code{information}), the vcov matrix of parameters (\code{vcov}), whether
#' the convergence checks on the penalized gradient and the penalized
#' information matrix were satisfied (\code{solution}), whether the employed
#' information matrix was positive-definite (\code{pdef}), whether the
#' estimated factor solution was admissible (\code{admissibility}), the
#' standard errors computed according to the Bayesian result from the
#' information matrix reported in \code{information} (\code{se}), and the 95%
#' confidence intervals (\code{ci}).}
#' \item{\code{Inference}:}{List. Information on effective degrees of the model
#' and information criteria for model selection. This slot reports the
#' following quantities: effective degree of freedom for each parameter
#' (\code{edf.single}), total edf (\code{edf}), influence matrix
#' (\code{influence.mat}), generalized information criteria (\code{IC}), such
#' as AIC and BIC.}
#' \item{\code{external}:}{List. Empty slot.}
#'}
#'
#' @section Methods:
#'
#' The following methods are available for an object of class
#' \code{\linkS4class{penfa}}:
#'
#' \describe{
#' \item{show}{\code{signature(object = "penfa")}: Prints a short summary of the
#' estimation process, including the optimization method, the specified penalty
#' functions, the convergence status, the number of iterations, the tuning
#' selection strategy, and the effective degrees of freedom. See the manual page of
#' \code{show,penfa-method} for details. } \item{summary}{\code{signature(object
#' = "penfa", header = TRUE, estimates = TRUE, ci = TRUE, level =} \code{ 0.95,
#' nd = 3L, cutoff = 0.05, extra = TRUE)}: Prints a summary of the model
#' parameter estimates, and the optimization process. See the manual page of
#' \code{summary,penfa-method} for details.} \item{coef}{\code{signature(object
#' = "penfa", type = "free", labels = TRUE)}: Returns the estimates of the
#' parameters in the model as a named numeric vector. See the manual page of
#' \code{coef,penfa-method} for details.} \item{fitted}{\code{signature(object =
#' "penfa", labels = TRUE)}: Returns a list of the model-implied moments (per
#' group). See the manual page of \code{fitted,penfa-method} for details.}
#' }
#'
#' @seealso \code{\link{penfa}}, \code{\link{penfaParEstim}}
#'
#'
#' @export
#'
#'
#' @references Geminiani, E., Marra, G., & Moustaki, I. (2021). "Single- and
#' Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach
#' with Integrated Automatic Multiple Tuning Parameter Selection."
#' Psychometrika, 86(1), 65-95. \doi{10.1007/s11336-021-09751-8}
#'
#'
#'
#'
#'
setClass("penfa",
slots = c(
version = "character", # package version
call = "call", # matched call
timing = "list", # timing information
Options = "list", # options
ParTable = "list", # parameter table user-specified model
pta = "list", # parameter table attributes
Data = "penfaData", # full data
SampleStats = "penfaSampleStats", # sample statistics
Model = "penfaModel", # internal model representation
Optim = "list", # optimizer results
Penalize = "penfaPenalty", # information on penalization
Implied = "list", # model-implied moments
Vcov = "list", # vcov, std.err, conf. intervals
Inference = "list", # effective dof, IC and more
external = "list")) # optional empty slot
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#########################################
# ---- Functions for setting classes ----
#########################################
# Content:
#
# Set the following classes:
# - "penfaData",
# - "penfaSampleStats"
# - "penfaModel"
# - "penfaPenalty"
# - "penfa"
#
# ------------------------------------------------------------------------------
#' S4 Class for describing the input data
#'
#' @description The \code{penfaData} class gives information on the data set
#' provided in input for analysis. This class is an adaptation of the
#' \code{lavData} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#' @slot ngroups Integer. The number of groups.
#' @slot group Character. The observed variables defining the groups.
#' @slot group.label Character. The group labels, that is, the values of the
#' \code{group} variable, if any.
#' @slot std.ov Logical indicating whether the observed variables should be
#' standardized.
#' @slot nobs List of the effective number of observations in each group.
#' @slot norig List of the original number of observations in each group.
#' @slot ov.names List of the observed variable names in each group.
#' @slot ov List of details at the observed variable level.
#' @slot case.idx List of the case (i.e., observation) indices in each group.
#' @slot X List. Local copy of the input data set split into groups.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Data
#' str(alasso_fit@Data)
#'
#'
setClass("penfaData",
slots = c(
ngroups = "integer",
group = "character",
group.label = "character",
std.ov = "logical",
nobs = "list",
norig = "list",
ov.names = "list",
ov = "list",
case.idx = "list",
X = "list"))
#' S4 Class for describing the sample moments
#'
#' @description The \code{penfaSampleStats} class provides information on the
#' sample moments of the factor analysis model. This
#' class is an adaptation of the \code{lavSampleStats} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#' @slot var List of the variances of the observed variables in every group.
#' @slot cov List of the covariance matrices of the observed variables
#' in every group.
#' @slot mean List of the means of the observed variables in every group.
#' @slot group.w List of group weights.
#' @slot nobs List of the effective number of observations for every group.
#' @slot ntotal Integer. Total number of observations across all groups.
#' @slot ngroups Integer. Number of groups.
#' @slot icov List of the inverse matrices of the covariance matrices of the
#' observed variables in every group.
#' @slot cov.log.det List of the logarithms of the determinants of the
#' covariance matrices of the observed variables for every group.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@SampleStats
#'
setClass("penfaSampleStats",
slots = c(
var = "list",
cov = "list",
mean = "list",
group.w = "list",
nobs = "list",
ntotal = "integer",
ngroups = "integer",
icov = "list",
cov.log.det = "list"))
#' S4 Class for internal representation of a factor model
#'
#' @description The \code{penfaModel} class gives the internal matrix
#' representation of a factor analysis model. Note that this representation
#' summarizes the characteristics of the model itself (e.g., number of items,
#' number of factors, parameter indices, etc), without information on the
#' penalization process (see \code{\linkS4class{penfaPenalty}} for that
#' aspect). This class is an adaptation of the \code{lavModel} class from the
#' [lavaan](https://CRAN.R-project.org/package=lavaan) package.
#'
#'
#' @slot GLIST List. The model matrices and vectors: "lambda" for the factor
#' loading matrix, "psi" for the covariance matrix of the unique factors,
#' "phi" for the covariance matrix of the common factors, "tau" for the
#' intercept vector, and "kappa" for the vector of factor means. In case of a
#' multiple-group analysis, the elements of each group are presented
#' sequentially.
#' @slot dimNames List. Dimension names (row names and column names) of every
#' model matrix and vector.
#' @slot isSymmetric Logical vector declaring whether each model matrix/vector
#' is symmetric.
#' @slot mmSize Integer vector specifying the size (unique elements only) of
#' each model matrix/vector.
#' @slot meanstructure Logical. It declares whether the model includes a
#' meanstructure.
#' @slot ngroups Integer. The number of groups.
#' @slot nmat Integer vector specifying the number of model matrices/vectors for
#' each group.
#' @slot nvar Integer vector specifying the number of observed variables in each
#' group.
#' @slot num.idx List of the indices of the observed variables in each group.
#' @slot nx.free Integer. The number of parameters of the factor model. This
#' count does not include the fixed parameters, but it does include the
#' parameters that will be penalized (if any) during optimization. (see
#' \code{\linkS4class{penfaPenalty}} for additional details in this respect).
#' @slot nx.user Integer. The total count of the parameters that are being
#' estimated and the ones that have been fixed.
#' @slot m.free.idx List. For each model matrix, the indices of the elements to
#' be estimated (i.e., non-fixed). The counter starts at 1 for every model
#' matrix.
#' @slot x.free.idx List. For each model matrix, the indices of the elements to
#' be estimated (i.e., non-fixed). The counter continues from the previous
#' model matrix.
#' @slot m.user.idx List. Much like \code{m.free.idx}, but it also contains the
#' indices of the parameters that have been fixed by the user.
#' @slot x.user.idx List. Much like \code{x.free.idx}, but it also contains the
#' indices of the parameters that have been fixed by the user.
#' @slot x.free.var.idx Vector of integers denoting the indices corresponding to
#' the unique variances.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Model
#'
setClass("penfaModel",
slots = c(
GLIST = "list",
dimNames = "list",
isSymmetric = "logical",
mmSize = "integer",
meanstructure = "logical",
ngroups = "integer",
nmat = "integer",
nvar = "integer",
num.idx = "list",
nx.free = "integer",
nx.user = "integer",
m.free.idx = "list",
x.free.idx = "list",
m.user.idx = "list",
x.user.idx = "list",
x.free.var.idx = "integer"))
#' S4 Class for describing the penalization process
#'
#' @description The \code{penfaPenalty} class provides information on the
#' penalization process, such as the user-specified penalty functions, the
#' optimal values of the tuning parameters, and the penalty matrices at
#' convergence.
#'
#' @slot strategy Character. The strategy used for the selection of the tuning
#' parameter(s). If \code{strategy = "auto"}, the optimal values of the tuning
#' parameters are determined via the automatic tuning parameter procedure; if
#' \code{strategy = "fixed"}, a penalized factor model with the values of the
#' tuning parameters stored in the option \code{eta} is estimated.
#' @slot penalty List. A list of the user-specified penalty functions for
#' sparsity ("shrink") and parameter equivalence ("diff").
#' @slot tuning List. A named list containing the optimal values of the tuning
#' parameter(s) if \code{strategy = "auto"} or the user-specified fixed
#' values of the tuning parameter(s) if \code{strategy = "fixed"}. The list
#' has two components with names "shrink" and "diff", and refers to the tuning
#' parameters used for shrinkage and group equivalence, respectively. The
#' components of the list are, in turn, the named vectors specifying the type
#' of parameter matrices or vectors that were penalized.
#' @slot pmat List. A named list containing the names of the parameter matrices
#' and vectors that were penalized for sparsity ("shrink") and/or group
#' equivalence ("diff").
#' @slot pen.idx List. A named list with the indices of the parameters that were
#' penalized for sparsity ("shrink") and/or group equivalence ("diff").
#' @slot Sh.info List. A list of the penalization terms, vectors and matrices
#' evaluated at the optimal values of the tuning parameters. In particular,
#' its argument \code{S.h} returns the estimated penalty matrix. If the factor
#' model is penalized only through a shrinkage penalty (i.e.,
#' \code{pen.shrink} is not \code{'none'}), and there is no penalization on
#' the differences (i.e., \code{pen.diff = 'none'}), then \code{S.h} is a
#' diagonal matrix whose elements precisely quantify the extent to which each
#' model parameter has been penalized.
#' @slot extra List. A list possibly containing additional information on the
#' penalization process, such as the hyperparameter values for some penalty
#' functions (e.g., for the alasso, the value of the exponent and the adaptive
#' weights.)
#' @slot automatic List. If \code{strategy = "auto"}, it contains information on
#' the automatic multiple tuning parameter procedure, such as the optimal
#' values of the tuning parameters, the convergence status, the specified
#' value of the influence factor, the number of necessary iterations, and the
#' tolerance level.
#'
#' @seealso \code{\link{penfa}}
#'
#'
#'
#' @examples
#'
#' data(ccdata)
#'
#' syntax = 'help =~ h1 + h2 + h3 + h4 + h5 + h6 + h7 + 0*v1 + v2 + v3 + v4 + v5
#' voice =~ 0*h1 + h2 + h3 + h4 + h5 + h6 + h7 + v1 + v2 + v3 + v4 + v5'
#'
#' alasso_fit <- penfa(## factor model
#' model = syntax,
#' data = ccdata,
#' std.lv = TRUE,
#' ## penalization
#' pen.shrink = "alasso",
#' eta = list(shrink = c("lambda" = 0.01), diff = c("none" = 0)),
#' ## automatic procedure
#' strategy = "auto")
#'
#' alasso_fit@Penalize
#'
#' str(alasso_fit@Penalize)
#'
setClass("penfaPenalty",
slots = c(
strategy = "character",
penalty = "list",
tuning = "list",
pmat = "list",
pen.idx = "list",
Sh.info = "list",
extra = "list",
automatic = "list"))
#' S4 Class for describing a \code{penfa} model
#'
#' @description The \code{penfa} class represents a (fitted) penalized factor
#' analysis model. It contains a description of the model as specified by the
#' user, a summary of the data, an internal matrix representation, the
#' fitting results, and the penalized quantities.
#'
#' @section Objects from the Class:
#'
#' Objects can be created via the \code{\link{penfa}} function.
#'
#' @section Slots:
#'
#' \describe{
#' \item{\code{version}:}{The \code{penfa} package version used to create this object.}
#' \item{\code{call}:}{The function call as returned by \code{match.call()}.}
#' \item{\code{timing}:}{The elapsed time (user + system) for various parts of
#' the program as a list, including the total time.}
#' \item{\code{Options}:}{Named list of options that were provided by the user
#' or filled-in automatically. See \code{\link{penfaOptions}} for additional
#' details.}
#' \item{\code{ParTable}:}{Named list describing the model parameters.
#' Can be coerced to a data.frame. This is also called "parameter table".
#' It includes information on the fixed, free and penalized parameters, their
#' indices, the active penalization strategies ("none", "shrink", "diff", or
#' "shrink + diff"), the starting values, the estimated parameters and the
#' associated standard errors.}
#' \item{\code{pta}:}{Named list containing parameter table attributes, like
#' observed and latent variable names, their indices, and the number of groups.}
#' \item{\code{Data}:}{Object of internal class \code{"penfaData"}; contains
#' information about the data set. See the \code{\linkS4class{penfaData}} class
#' for additional details.}
#' \item{\code{SampleStats}:}{Object of internal class \code{"penfaSampleStats"};
#' contains the sample statistics. See the \code{\linkS4class{penfaSampleStats}}
#' class for additional details.}
#' \item{\code{Model}:}{Object of internal class \code{"penfaModel"}: the internal
#' (matrix) representation of the model. See the \code{\linkS4class{penfaModel}}
#' class for additional details.}
#' \item{\code{Optim}:}{List. Information about the optimization process. This
#' includes the estimated parameters (\code{x}), the number of estimated
#' parameters (\code{npar}), the number of trust-region iterations
#' (\code{iterations}), the value of the penalized objective function
#' (\code{fx.pen}), the value of the unpenalized objective
#' function (\code{fx.unpen}), the penalized log-likelihood (\code{logl.pen};
#' this is equal to \code{fx.pen} multiplied by (-1)), the unpenalized
#' log-likelihood (\code{logl.unpen}; this is equal to \code{fx.unpen} multiplied
#' by (-1)), the penalized gradient (\code{dx.pen}), the penalized Hessian/Fisher
#' information matrix (\code{hessian.pen}), the list of control arguments for
#' the trust-region algorithm (\code{control}), and how many times the
#' objective function became non-positive definite during the estimation
#' process (\code{npd}). If penfa was called with the option \code{verbose =
#' TRUE}, the following additional arguments coming from the trust-region
#' function \code{trust} are reported in the \code{Optim} slot: \code{argpath},
#' \code{argtry}, \code{type}, \code{accept}, \code{radii}, \code{rho},
#' \code{fx.val}, \code{fx.valtry}, \code{change}, \code{stepnorm}. See the
#' manual page of \code{trust} from the \code{trust} package for an overview of
#' these quantities.}
#' \item{\code{Penalize}:}{Object of internal class \code{"penfaPenalty"}; contains
#' information about the penalization. See the \code{\linkS4class{penfaPenalty}} for
#' additional details.}
#' \item{\code{Implied}:}{List. Model-implied moments (covariance matrix and
#' mean vector).}
#' \item{\code{Vcov}:}{List. Information about the covariance matrix (vcov) of
#' the model parameters. This slot includes the following quantities: the type
#' of penalized information matrix used in the model (either Hessian or Fisher;
#' \code{information}), the vcov matrix of parameters (\code{vcov}), whether
#' the convergence checks on the penalized gradient and the penalized
#' information matrix were satisfied (\code{solution}), whether the employed
#' information matrix was positive-definite (\code{pdef}), whether the
#' estimated factor solution was admissible (\code{admissibility}), the
#' standard errors computed according to the Bayesian result from the
#' information matrix reported in \code{information} (\code{se}), and the 95%
#' confidence intervals (\code{ci}).}
#' \item{\code{Inference}:}{List. Information on effective degrees of the model
#' and information criteria for model selection. This slot reports the
#' following quantities: effective degree of freedom for each parameter
#' (\code{edf.single}), total edf (\code{edf}), influence matrix
#' (\code{influence.mat}), generalized information criteria (\code{IC}), such
#' as AIC and BIC.}
#' \item{\code{external}:}{List. Empty slot.}
#'}
#'
#' @section Methods:
#'
#' The following methods are available for an object of class
#' \code{\linkS4class{penfa}}:
#'
#' \describe{
#' \item{show}{\code{signature(object = "penfa")}: Prints a short summary of the
#' estimation process, including the optimization method, the specified penalty
#' functions, the convergence status, the number of iterations, the tuning
#' selection strategy, and the effective degrees of freedom. See the manual page of
#' \code{show,penfa-method} for details. } \item{summary}{\code{signature(object
#' = "penfa", header = TRUE, estimates = TRUE, ci = TRUE, level =} \code{ 0.95,
#' nd = 3L, cutoff = 0.05, extra = TRUE)}: Prints a summary of the model
#' parameter estimates, and the optimization process. See the manual page of
#' \code{summary,penfa-method} for details.} \item{coef}{\code{signature(object
#' = "penfa", type = "free", labels = TRUE)}: Returns the estimates of the
#' parameters in the model as a named numeric vector. See the manual page of
#' \code{coef,penfa-method} for details.} \item{fitted}{\code{signature(object =
#' "penfa", labels = TRUE)}: Returns a list of the model-implied moments (per
#' group). See the manual page of \code{fitted,penfa-method} for details.}
#' }
#'
#' @seealso \code{\link{penfa}}, \code{\link{penfaParEstim}}
#'
#'
#' @export
#'
#'
#' @references Geminiani, E., Marra, G., & Moustaki, I. (2021). "Single- and
#' Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach
#' with Integrated Automatic Multiple Tuning Parameter Selection."
#' Psychometrika, 86(1), 65-95. \doi{10.1007/s11336-021-09751-8}
#'
#'
#'
#'
#'
setClass("penfa",
slots = c(
version = "character", # package version
call = "call", # matched call
timing = "list", # timing information
Options = "list", # options
ParTable = "list", # parameter table user-specified model
pta = "list", # parameter table attributes
Data = "penfaData", # full data
SampleStats = "penfaSampleStats", # sample statistics
Model = "penfaModel", # internal model representation
Optim = "list", # optimizer results
Penalize = "penfaPenalty", # information on penalization
Implied = "list", # model-implied moments
Vcov = "list", # vcov, std.err, conf. intervals
Inference = "list", # effective dof, IC and more
external = "list")) # optional empty slot
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