S4 Class for internal representation of a factor model

Source: R/class.R

The 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 penfaPenalty for that aspect). This class is an adaptation of the lavModel class from the lavaan package.

Slots

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.

dimNames

List. Dimension names (row names and column names) of every model matrix and vector.

isSymmetric

Logical vector declaring whether each model matrix/vector is symmetric.

mmSize

Integer vector specifying the size (unique elements only) of each model matrix/vector.

meanstructure

Logical. It declares whether the model includes a meanstructure.

ngroups

Integer. The number of groups.

nmat

Integer vector specifying the number of model matrices/vectors for each group.

nvar

Integer vector specifying the number of observed variables in each group.

num.idx

List of the indices of the observed variables in each group.

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 penfaPenalty for additional details in this respect).

nx.user

Integer. The total count of the parameters that are being estimated and the ones that have been fixed.

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.

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.

m.user.idx

List. Much like m.free.idx, but it also contains the indices of the parameters that have been fixed by the user.

x.user.idx

List. Much like x.free.idx, but it also contains the indices of the parameters that have been fixed by the user.

x.free.var.idx

Vector of integers denoting the indices corresponding to the unique variances.

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")

#> 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@Model

#> An object of class "penfaModel"
#> Slot "GLIST":
#> $lambda
#>                [,1]          [,2]
#>  [1,]  7.658121e-01  0.000000e+00
#>  [2,]  8.579551e-01 -1.287100e-05
#>  [3,]  7.753391e-01  5.304850e-06
#>  [4,]  9.208458e-01 -4.119937e-02
#>  [5,]  8.096618e-01  5.262033e-02
#>  [6,]  7.820608e-01  1.042524e-01
#>  [7,]  5.230518e-01  3.412021e-01
#>  [8,]  0.000000e+00  8.507219e-01
#>  [9,]  4.013798e-05  8.714683e-01
#> [10,]  2.389271e-05  8.418956e-01
#> [11,]  8.563583e-07  8.429135e-01
#> [12,] -9.202527e-07  8.047512e-01
#> 
#> $psi
#>            [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
#>  [1,] 0.3875064 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [2,] 0.0000000 0.2331226 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [3,] 0.0000000 0.0000000 0.3723067 0.0000000 0.0000000 0.0000000 0.0000000
#>  [4,] 0.0000000 0.0000000 0.0000000 0.1844461 0.0000000 0.0000000 0.0000000
#>  [5,] 0.0000000 0.0000000 0.0000000 0.0000000 0.2349729 0.0000000 0.0000000
#>  [6,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2009585 0.0000000
#>  [7,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2638821
#>  [8,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>  [9,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#> [12,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
#>            [,8]      [,9]     [,10]    [,11]     [,12]
#>  [1,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [2,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [3,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [4,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [5,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [6,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [7,] 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
#>  [8,] 0.2454065 0.0000000 0.0000000 0.000000 0.0000000
#>  [9,] 0.0000000 0.2083625 0.0000000 0.000000 0.0000000
#> [10,] 0.0000000 0.0000000 0.2607043 0.000000 0.0000000
#> [11,] 0.0000000 0.0000000 0.0000000 0.259044 0.0000000
#> [12,] 0.0000000 0.0000000 0.0000000 0.000000 0.3240195
#> 
#> $phi
#>           [,1]      [,2]
#> [1,] 1.0000000 0.8771535
#> [2,] 0.8771535 1.0000000
#> 
#> 
#> Slot "dimNames":
#> [[1]]
#> [[1]][[1]]
#>  [1] "h1" "h2" "h3" "h4" "h5" "h6" "h7" "v1" "v2" "v3" "v4" "v5"
#> 
#> [[1]][[2]]
#> [1] "help"  "voice"
#> 
#> 
#> [[2]]
#> [[2]][[1]]
#>  [1] "h1" "h2" "h3" "h4" "h5" "h6" "h7" "v1" "v2" "v3" "v4" "v5"
#> 
#> [[2]][[2]]
#>  [1] "h1" "h2" "h3" "h4" "h5" "h6" "h7" "v1" "v2" "v3" "v4" "v5"
#> 
#> 
#> [[3]]
#> [[3]][[1]]
#> [1] "help"  "voice"
#> 
#> [[3]][[2]]
#> [1] "help"  "voice"
#> 
#> 
#> 
#> Slot "isSymmetric":
#> [1] FALSE  TRUE  TRUE
#> 
#> Slot "mmSize":
#> [1] 24 78  3
#> 
#> Slot "meanstructure":
#> [1] FALSE
#> 
#> Slot "ngroups":
#> [1] 1
#> 
#> Slot "nmat":
#> [1] 3
#> 
#> Slot "nvar":
#> [1] 12
#> 
#> Slot "num.idx":
#> [[1]]
#>  [1]  1  2  3  4  5  6  7  8  9 10 11 12
#> 
#> 
#> Slot "nx.free":
#> [1] 35
#> 
#> Slot "nx.user":
#> [1] 39
#> 
#> Slot "m.free.idx":
#> [[1]]
#>  [1]  1  2  3  4  5  6  7  9 10 11 12 14 15 16 17 18 19 20 21 22 23 24
#> 
#> [[2]]
#>  [1]   1  14  27  40  53  66  79  92 105 118 131 144
#> 
#> [[3]]
#> [1] 2 3
#> 
#> 
#> Slot "x.free.idx":
#> [[1]]
#>  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22
#> 
#> [[2]]
#>  [1] 23 24 25 26 27 28 29 30 31 32 33 34
#> 
#> [[3]]
#> [1] 35 35
#> 
#> 
#> Slot "m.user.idx":
#> [[1]]
#>  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
#> 
#> [[2]]
#>  [1]   1  14  27  40  53  66  79  92 105 118 131 144
#> 
#> [[3]]
#> [1] 1 2 3 4
#> 
#> 
#> Slot "x.user.idx":
#> [[1]]
#>  [1]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
#> 
#> [[2]]
#>  [1] 25 26 27 28 29 30 31 32 33 34 35 36
#> 
#> [[3]]
#> [1] 37 39 39 38
#> 
#> 
#> Slot "x.free.var.idx":
#>  [1] 23 24 25 26 27 28 29 30 31 32 33 34
#>