Functionality for factor analysis ('factanal') objects

Source: R/methods-stats-factanal.r

These methods extract data from, and attribute new data to, objects of class "factanal" as returned by stats::factanal().

# S3 method for factanal
as_tbl_ord(x)

# S3 method for factanal
recover_rows(x)

# S3 method for factanal
recover_cols(x)

# S3 method for factanal
recover_inertia(x)

# S3 method for factanal
recover_coord(x)

# S3 method for factanal
recover_conference(x)

# S3 method for factanal
recover_supp_rows(x)

# S3 method for factanal
recover_aug_rows(x)

# S3 method for factanal
recover_aug_cols(x)

# S3 method for factanal
recover_aug_coord(x)

Arguments

x

An ordination object.

Value

The recovery generics recover_*() return core model components, distribution of inertia, supplementary elements, and intrinsic metadata; but they require methods for each model class to tell them what these components are.

The generic as_tbl_ord() returns its input wrapped in the 'tbl_ord' class. Its methods determine what model classes it is allowed to wrap. It then provides 'tbl_ord' methods with access to the recoverers and hence to the model components.

Details

Factor analysis of a data matrix relies on an an eigendecomposition of its correlation matrix, whose eigenvectors (up to weighting) comprise the variable loadings. For this reason, both row and column recoverers retrieve the loadings and inertia is evenly distributed between them. When computed and returned by stats::factanal(), the case scores are accessible as supplementary elements. Redistribution of inertia commutes through both score calculations.

See also

Other methods for eigen-decomposition-based techniques: methods-cmds, methods-eigen

Other models from the stats package: methods-cancor, methods-cmds, methods-kmeans, methods-lm, methods-prcomp, methods-princomp

Examples

# data frame of Swiss fertility and socioeconomic indicators
class(swiss)
#> [1] "data.frame"
head(swiss)
#>              Fertility Agriculture Examination Education Catholic
#> Courtelary        80.2        17.0          15        12     9.96
#> Delemont          83.1        45.1           6         9    84.84
#> Franches-Mnt      92.5        39.7           5         5    93.40
#> Moutier           85.8        36.5          12         7    33.77
#> Neuveville        76.9        43.5          17        15     5.16
#> Porrentruy        76.1        35.3           9         7    90.57
#>              Infant.Mortality
#> Courtelary               22.2
#> Delemont                 22.2
#> Franches-Mnt             20.2
#> Moutier                  20.3
#> Neuveville               20.6
#> Porrentruy               26.6
# perform factor analysis
swiss_fa <- factanal(~ ., factors = 2L, data = swiss, scores = "regression")

# wrap as a 'tbl_ord' object
(swiss_fa <- as_tbl_ord(swiss_fa))
#> # A tbl_ord of class 'factanal': (53 x 2) x (6 x 2)'
#> # 2 coordinates: Factor1 and Factor2
#> # 
#> # Rows (symmetric): [ 53 x 2 | 0 ]
#>   Factor1 Factor2 | 
#>                   | 
#> 1  -0.652  0.393  | 
#> 2  -0.631  0.333  | 
#> 3   0.685 -0.510  | 
#> 4   0.997 -0.0313 | 
#> 5  -0.124  0.961  | 
#> 
#> # 
#> # Columns (symmetric): [ 6 x 2 | 0 ]
#>   Factor1 Factor2 | 
#>                   | 
#> 1 -0.652   0.393  | 
#> 2 -0.631   0.333  | 
#> 3  0.685  -0.510  | 
#> 4  0.997  -0.0313 | 
#> 5 -0.124   0.961  | 
#> 6 -0.0947  0.175  | 

# recover loadings
get_rows(swiss_fa, elements = "active")
#>                      Factor1     Factor2
#> Fertility        -0.65238512  0.39335226
#> Agriculture      -0.63054439  0.33275063
#> Examination       0.68498141 -0.51036433
#> Education         0.99700850 -0.03128268
#> Catholic         -0.12417831  0.96118093
#> Infant.Mortality -0.09466294  0.17483734
get_cols(swiss_fa)
#>                      Factor1     Factor2
#> Fertility        -0.65238512  0.39335226
#> Agriculture      -0.63054439  0.33275063
#> Examination       0.68498141 -0.51036433
#> Education         0.99700850 -0.03128268
#> Catholic         -0.12417831  0.96118093
#> Infant.Mortality -0.09466294  0.17483734
# recover scores
head(get_rows(swiss_fa, elements = "score"))
#>                  Factor1    Factor2
#> Courtelary    0.07912746 -0.6344915
#> Delemont     -0.17926953  1.0783941
#> Franches-Mnt -0.58784929  1.2004233
#> Moutier      -0.42433417 -0.1583409
#> Neuveville    0.38211185 -0.6682790
#> Porrentruy   -0.37286722  1.0884740

# augment column loadings with uniquenesses
(swiss_fa <- augment_ord(swiss_fa))
#> # A tbl_ord of class 'factanal': (53 x 2) x (6 x 2)'
#> # 2 coordinates: Factor1 and Factor2
#> # 
#> # Rows (symmetric): [ 53 x 2 | 2 ]
#>   Factor1 Factor2 |   name        .element
#>                   |   <chr>       <chr>   
#> 1  -0.652  0.393  | 1 Fertility   active  
#> 2  -0.631  0.333  | 2 Agriculture active  
#> 3   0.685 -0.510  | 3 Examination active  
#> 4   0.997 -0.0313 | 4 Education   active  
#> 5  -0.124  0.961  | 5 Catholic    active  
#> # … with 48 more rows
#> # 
#> # Columns (symmetric): [ 6 x 2 | 3 ]
#>   Factor1 Factor2 |   name             uniquen…¹ .elem…²
#>                   |   <chr>                <dbl> <chr>  
#> 1 -0.652   0.393  | 1 Fertility           0.420  active 
#> 2 -0.631   0.333  | 2 Agriculture         0.492  active 
#> 3  0.685  -0.510  | 3 Examination         0.270  active 
#> 4  0.997  -0.0313 | 4 Education           0.005  active 
#> 5 -0.124   0.961  | 5 Catholic            0.0607 active 
#> 6 -0.0947  0.175  | 6 Infant.Mortality    0.960  active 
#> # … with abbreviated variable names
#> #   ¹​uniqueness, ²​.element

# symmetric biplot
swiss_fa %>%
  ggbiplot() +
  theme_bw() +
  geom_cols_vector(aes(color = uniqueness)) +
  geom_cols_text_radiate(aes(label = name)) +
  expand_limits(x = c(-2, 2.5), y = c(-1.5, 2))