penfaPenalty-class {penfa}

S4 Class for describing the penalization process

Description

The 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.

Slots

strategy

Character. The strategy used for the selection of the tuning parameter(s). If strategy = "auto", the optimal values of the tuning parameters are determined via the automatic tuning parameter procedure; if strategy = "fixed", a penalized factor model with the values of the tuning parameters stored in the option eta is estimated.

penalty

List. A list of the user-specified penalty functions for sparsity ("shrink") and parameter equivalence ("diff").

tuning

List. A named list containing the optimal values of the tuning parameter(s) if strategy = "auto" or the user-specified fixed values of the tuning parameter(s) if 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.

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").

pen.idx

List. A named list with the indices of the parameters that were penalized for sparsity ("shrink") and/or group equivalence ("diff").

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 S.h returns the estimated penalty matrix. If the factor model is penalized only through a shrinkage penalty (i.e., pen.shrink is not 'none'), and there is no penalization on the differences (i.e., pen.diff = 'none'), then S.h is a diagonal matrix whose elements precisely quantify the extent to which each model parameter has been penalized.

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.)

automatic

List. If 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.

See Also

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)