S4 Class for describing the penalization process

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.

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")
#> Computing weights for alasso (ML estimates)... done.
#> 
#> Automatic procedure: 
#> Iteration  1 : 0.00298271 
#> Iteration  2 : 0.00452604 
#> 
#> Largest absolute gradient value: 12.76355181
#> Fisher information matrix is positive definite
#> Eigenvalue range: [180.2917, 9189645]
#> Trust region iterations: 15 
#> Factor solution: admissible 
#> Effective degrees of freedom: 27.12936  

alasso_fit@Penalize
#>   Strategy                                                 auto
#>   Influence factor                                            4
#>   Number of two-steps (automatic)                             2
#>                                                                
#>   Penalty function:                                            
#>     Sparsity                                             alasso
#>                                                                
#>   Additional tuning parameter                                  
#>     alasso                                                    1
#>                                                                
#>   Optimal tuning parameter:                                    
#>     Sparsity                                                   
#>      - Factor loadings                                    0.005
#>                                                                

str(alasso_fit@Penalize)
#> Formal class 'penfaPenalty' [package "penfa"] with 8 slots
#>   ..@ strategy : chr "auto"
#>   ..@ penalty  :List of 2
#>   .. ..$ shrink: chr "alasso"
#>   .. ..$ diff  : chr "none"
#>   ..@ tuning   :List of 2
#>   .. ..$ shrink: Named num 0.00453
#>   .. .. ..- attr(*, "names")= chr "lambda"
#>   .. ..$ diff  : Named num 0
#>   .. .. ..- attr(*, "names")= chr "none"
#>   ..@ pmat     :List of 2
#>   .. ..$ shrink: chr "lambda"
#>   .. ..$ diff  : chr "none"
#>   ..@ pen.idx  :List of 2
#>   .. ..$ shrink:List of 1
#>   .. .. ..$ lambda: int [1:22] 1 2 3 4 5 6 7 8 9 10 ...
#>   .. ..$ diff  : list()
#>   ..@ Sh.info  :List of 5
#>   .. ..$ S.h1     : num [1, 1] 25.4
#>   .. ..$ S.h2     : num [1:35, 1] 4.44 3.84 4.46 3.52 4.43 ...
#>   .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. .. .. ..$ : NULL
#>   .. ..$ S.h      : 'penfaPenMat' num [1:35, 1:35] 5.8 0 0 0 0 ...
#>   .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. ..$ SS.shrink:List of 1
#>   .. .. ..$ lambda: 'penfaPenMat' num [1:35, 1:35] 5.8 0 0 0 0 ...
#>   .. .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. ..$ SS.diff  :List of 1
#>   .. .. ..$ none: 'penfaPenMat' num [1:35, 1:35] 0 0 0 0 0 0 0 0 0 0 ...
#>   .. .. .. ..- attr(*, "dimnames")=List of 2
#>   .. .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   .. .. .. .. ..$ : chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   ..@ extra    :List of 2
#>   .. ..$ a.alasso: num 1
#>   .. ..$ weights : Named num [1:35] 0.782 0.905 0.779 0.986 0.783 ...
#>   .. .. ..- attr(*, "names")= chr [1:35] "help=~h1" "help=~h2" "help=~h3" "help=~h4" ...
#>   ..@ automatic:List of 8
#>   .. ..$ optimal.eta: num 0.00453
#>   .. ..$ conv       : logi TRUE
#>   .. ..$ gamma      : num 4
#>   .. ..$ iter       : num 2
#>   .. ..$ iter.inner : num 43
#>   .. ..$ iterlim    : num 50
#>   .. ..$ tol        : num 1e-07
#>   .. ..$ R          : num [1:35, 1:35] -1.392 -1.033 -0.601 -0.106 0.522 ...

S4 Class for describing the penalization process

Slots

See also

Examples