Functionality for penalized multivariate analysis ('SPC', 'CCA', 'MultiCCA') objects

These methods extract data from, and attribute new data to, objects of class 'SPC', 'CCA', and 'MultiCCA' from the PMA package.

# S3 method for CCA
as_tbl_ord(x)

# S3 method for CCA
recover_coord(x)

# S3 method for CCA
recover_rows(x)

# S3 method for CCA
recover_cols(x)

# S3 method for CCA
recover_inertia(x)

# S3 method for CCA
recover_conference(x)

# S3 method for CCA
augmentation_rows(x)

# S3 method for CCA
augmentation_cols(x)

# S3 method for CCA
augmentation_coord(x)

Arguments

x

An ordination object.

Details

Witten, Tibshirani, and Hastie (2009) provide a theoretical basis and computational algorithm for penalized matrix decomposition that specializes to sparse PCA and to sparse CCA. Their R package PMA implements these specializations as well as one to sparse multiple CCA.

Note: These draft methods produce the biplot of Greenacre (1984), which are advised against by ter Braak (1990).

References

Witten DM, Tibshirani R, & Hastie T (2009) "A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis". Biostatistics 10(3): 515--534. doi: 10.1093/biostatistics/kxp008

Greenacre MJ (1984) Theory and applications of correspondence analysis. London: Academic Press, ISBN 0-12-299050-1. http://www.carme-n.org/?sec=books5

ter Braak CJF (1990) "Interpreting canonical correlation analysis through biplots of structure correlations and weights". Psychometrika 55(3), 519--531. doi: 10.1007/BF02294765

Examples

# data frame of life-cycle savings across countries
class(LifeCycleSavings)
#> [1] "data.frame"
head(LifeCycleSavings)
#>              sr pop15 pop75     dpi ddpi
#> Australia 11.43 29.35  2.87 2329.68 2.87
#> Austria   12.07 23.32  4.41 1507.99 3.93
#> Belgium   13.17 23.80  4.43 2108.47 3.82
#> Bolivia    5.75 41.89  1.67  189.13 0.22
#> Brazil    12.88 42.19  0.83  728.47 4.56
#> Canada     8.79 31.72  2.85 2982.88 2.43
# canonical correlation analysis of age distributions and financial factors
savings_cca <- PMA::CCA(
  LifeCycleSavings[, c(2L, 3L)],
  LifeCycleSavings[, c(1L, 4L, 5L)],
  K = 2L, penaltyx = .7, penaltyz = .7,
  xnames = names(LifeCycleSavings)[c(2L, 3L)],
  znames = names(LifeCycleSavings)[c(1L, 4L, 5L)]
)
#> 12
#> 12
# wrap as a 'tbl_ord' object
(savings_cca <- as_tbl_ord(savings_cca))
#> # A tbl_ord of class 'CCA': (2 x 2) x (3 x 2)'
#> # 2 coordinates: sCD1 and sCD2
#> # 
#> # Rows (standard): [ 2 x 2 | 0 ]
#>    sCD1  sCD2 | 
#>               | 
#> 1    -1     1 | 
#> 2     0     0 | 
#> # 
#> # Columns (standard): [ 3 x 2 | 0 ]
#>    sCD1    sCD2 | 
#>                 | 
#> 1 0.242 -0.986  | 
#> 2 0.970  0.146  | 
#> 3 0     -0.0801 | 
# summarize ordination
glance(savings_cca)
#> # A tibble: 1 × 7
#>    rank n.row n.col inertia prop.var.1 prop.var.2 class
#>   <int> <int> <int>   <dbl>      <dbl>      <dbl> <chr>
#> 1     2     2     3   0.764      0.845      0.155 CCA  
# recover canonical variates
get_rows(savings_cca)
#>       sCD1 sCD2
#> pop15   -1    1
#> pop75    0    0
get_cols(savings_cca)
#>           sCD1        sCD2
#> sr   0.2422123 -0.98598522
#> dpi  0.9702233  0.14634075
#> ddpi 0.0000000 -0.08010956
# augment canonical variates with variable names
(savings_cca <- augment_ord(savings_cca))
#> # A tbl_ord of class 'CCA': (2 x 2) x (3 x 2)'
#> # 2 coordinates: sCD1 and sCD2
#> # 
#> # Rows (standard): [ 2 x 2 | 1 ]
#>    sCD1  sCD2 |   .name
#>               |   <chr>
#> 1    -1     1 | 1 pop15
#> 2     0     0 | 2 pop75
#> # 
#> # Columns (standard): [ 3 x 2 | 1 ]
#>    sCD1    sCD2 |   .name
#>                 |   <chr>
#> 1 0.242 -0.986  | 1 sr   
#> 2 0.970  0.146  | 2 dpi  
#> 3 0     -0.0801 | 3 ddpi 
# summarize canonical correlations
tidy(savings_cca)
#> # A tibble: 2 × 4
#>   .name .cancor .inertia .prop_var
#>   <fct>   <dbl>    <dbl>     <dbl>
#> 1 sCD1    0.803    0.645     0.845
#> 2 sCD2    0.344    0.119     0.155
# scree plot of canonical correlations
tidy(savings_cca) %>%
  ggplot(aes(x = .name, y = .inertia)) +
  geom_col() +
  labs(x = "", y = "Inertia (squared canonical correlations)")

# fortification binds tibbles of canonical variates
fortify(savings_cca)
#> # A tibble: 5 × 4
#>     sCD1    sCD2 .name .matrix
#>    <dbl>   <dbl> <chr> <chr>  
#> 1 -1      1      pop15 rows   
#> 2  0      0      pop75 rows   
#> 3  0.242 -0.986  sr    cols   
#> 4  0.970  0.146  dpi   cols   
#> 5  0     -0.0801 ddpi  cols   
# column-standard biplot of canonical variates
savings_cca %>%
  confer_inertia("rows") %>%
  ggbiplot(aes(label = .name, color = .matrix)) +
  theme_bw() +
  geom_origin() +
  geom_unit_circle(linetype = "dotted") +
  geom_cols_vector() +
  geom_cols_text_radiate() +
  geom_rows_point() +
  geom_rows_text_repel() +
  expand_limits(x = c(-1, 1), y = c(-1, 1))