Reduce Parametric Covariates with PCA

Applies a Principal Component Analysis (PCA) to the covariates matrix V and replaces it with a lower dimensional representation. This function is intended for parametric workflows and requires a valid V matrix.

PCA(
  object = NULL,
  X = NULL,
  W = NULL,
  V = NULL,
  json_path = NULL,
  components = NULL,
  sd_threshold = NULL,
  center = TRUE,
  scale = TRUE
)

Arguments

object: An object of class eim, which can be created using the eim function.
X: A (b x c) matrix representing candidate votes per ballot box.
W: A (b x g) matrix representing group votes per ballot box.
V: A (b x a) matrix with parametric covariates.
json_path: A path to a JSON file containing X, W, and V fields.
components: Integer specifying the number of principal components to keep.
sd_threshold: Numeric in (0, 1] indicating the minimum cumulative proportion of variance explained by the retained components.
center: Logical indicating whether to center the columns of V before PCA.
scale: Logical indicating whether to scale the columns of V before PCA.

Value

Returns an eim object with the V matrix replaced by its PCA scores. The columns of V are renamed as PCA 1, PCA 2, ..., up to the chosen number of components.

Examples

sim <- simulate_election(
    num_ballots = 50,
    num_candidates = 3,
    num_groups = 2,
    ballot_voters = 40,
    num_covariates = 10,
    num_districts = 2,
    seed = 1
)

sim_pca <- PCA(sim, components = 2)
sim_pca$V
#>           PCA 1        PCA 2
#>  [1,] -3.531675 9.389463e-16
#>  [2,]  2.774887 8.533705e-16
#>  [3,]  2.774887 8.533705e-16
#>  [4,] -3.531675 9.389463e-16
#>  [5,]  2.774887 8.533705e-16
#>  [6,]  2.774887 8.533705e-16
#>  [7,] -3.531675 9.389463e-16
#>  [8,] -3.531675 9.389463e-16
#>  [9,]  2.774887 8.533705e-16
#> [10,]  2.774887 8.533705e-16
#> [11,]  2.774887 8.533705e-16
#> [12,] -3.531675 9.389463e-16
#> [13,] -3.531675 9.389463e-16
#> [14,]  2.774887 8.533705e-16
#> [15,]  2.774887 8.533705e-16
#> [16,]  2.774887 8.533705e-16
#> [17,]  2.774887 8.533705e-16
#> [18,]  2.774887 8.533705e-16
#> [19,]  2.774887 8.533705e-16
#> [20,] -3.531675 9.389463e-16
#> [21,]  2.774887 8.533705e-16
#> [22,]  2.774887 8.533705e-16
#> [23,]  2.774887 8.533705e-16
#> [24,]  2.774887 8.533705e-16
#> [25,] -3.531675 9.389463e-16
#> [26,] -3.531675 9.389463e-16
#> [27,] -3.531675 9.389463e-16
#> [28,]  2.774887 8.533705e-16
#> [29,]  2.774887 8.533705e-16
#> [30,] -3.531675 9.389463e-16
#> [31,] -3.531675 9.389463e-16
#> [32,]  2.774887 8.533705e-16
#> [33,]  2.774887 8.533705e-16
#> [34,]  2.774887 8.533705e-16
#> [35,] -3.531675 9.389463e-16
#> [36,] -3.531675 9.389463e-16
#> [37,] -3.531675 9.389463e-16
#> [38,]  2.774887 8.533705e-16
#> [39,] -3.531675 9.389463e-16
#> [40,]  2.774887 8.533705e-16
#> [41,] -3.531675 9.389463e-16
#> [42,]  2.774887 8.533705e-16
#> [43,] -3.531675 9.389463e-16
#> [44,] -3.531675 9.389463e-16
#> [45,]  2.774887 8.533705e-16
#> [46,]  2.774887 8.533705e-16
#> [47,] -3.531675 9.389463e-16
#> [48,] -3.531675 9.389463e-16
#> [49,] -3.531675 9.389463e-16
#> [50,]  2.774887 8.533705e-16