Transform compositional data using Helmert matrix — helmert

Transform n-dimension compositional data (all values sum to 1) into an (n-1)-dimensional Euclidean space using the Helmert matrix. This dimension reduction is the geometric basis for plotting points within the simplex.

Usage

helmert_transform(data, items = dplyr::everything(), append = FALSE)

Arguments

data: A data frame or matrix containing the compositional data.
items: <tidy-select> Columns representing the components of the composition. Default is tidyselect::everything(), which selects all columns. Must select at least 3 columns.
append: (Optional) A logical value indicating whether the transformed data should be appended to the original data frame. Default is FALSE.

Value

A data frame containing the Helmert-transformed coordinates, named x1, x2, ..., x(n-1), where n is the number of items. If append = TRUE, these columns are added to the input data.

Examples

# Example 1: Transform a matrix (all columns)
comp_mat <- matrix(c(0.5, 0.3, 0.2,
                     0.4, 0.4, 0.2,
                     0.6, 0.2, 0.2),
                   ncol = 3, byrow = TRUE)
helmert_transform(comp_mat)
#> New names:
#> • `` -> `...1`
#> • `` -> `...2`
#> • `` -> `...3`
#> # A tibble: 3 × 2
#>         x1    x2
#>      <dbl> <dbl>
#> 1 1.41e- 1 0.163
#> 2 2.67e-18 0.163
#> 3 2.83e- 1 0.163

# Example 2: Transform specific columns in a data frame
df <- data.frame(
  electorate = c("A", "B", "C"),
  ALP = c(0.5, 0.4, 0.6),
  LNP = c(0.3, 0.4, 0.2),
  Other = c(0.2, 0.2, 0.2)
)
helmert_transform(df, items = c(ALP, LNP, Other))
#> # A tibble: 3 × 2
#>         x1    x2
#>      <dbl> <dbl>
#> 1 1.41e- 1 0.163
#> 2 2.67e-18 0.163
#> 3 2.83e- 1 0.163