PCA-Based Weighting Method — pca

Computes indicator weights using Principal Component Analysis (PCA). The method extracts principal components and uses their variance contribution to derive objective weights for indicators. Optionally handles positive/negative directions of indicators, and supports pre-standardized data.

Usage

pca_weight(X, index = NULL, nfs = NULL, varimax = TRUE, method = "abs")

Arguments

X

A numeric data frame or matrix where rows represent samples and columns represent indicators.

index

A character vector indicating the direction of each indicator. Use "+" for positive indicators (higher is better), "-" for negative indicators (lower is better), and NA for already standardized indicators (no standardization will be applied).

         If `index = NULL` (default), all indicators are treated as `NA`,
         meaning no standardization is performed.

nfs

Number of principal components to use; by default, all are used.

varimax

Whether to perform Varimax rotation, default is TRUE.

method

Weighting Method, "abs" (default, |a_ji|) or "squared" (a_ji^2)

Value

A list containing:

w: Numeric vector of normalized weights for each indicator.
s: Numeric vector of scores for each sample.
lambda: Eigenvalues of principal components (explained variance).
varP: Proportion of variance explained by selected PCs.

Examples

# Example: Using PCA to compute indicator weights
ind = c("+","+","-","-")
pca_weight(iris[1:10, 1:4], ind, nfs = 2)
#> $w
#> [1] 0.3653755 0.2576950 0.2288199 0.1481095
#> 
#> $s
#>  [1]  0.603861299 -0.066459291  0.062381683 -0.570617445  0.562358748
#>  [6]  0.304619966 -0.294827855  0.182708247 -0.777385321 -0.006640031
#> 
#> $cum_contrib
#> [1] 0.8454999
#> 
#> $loading
#>                     PC1        PC2
#> Sepal.Length -0.7089283  0.3581971
#> Sepal.Width  -0.5128833 -0.1963096
#> Petal.Length  0.4706905  0.1075345
#> Petal.Width   0.1132333  0.9064181
#> 
#> $lambda
#> [1] 2.7523578 0.6296417
#> 
#> $varP
#> [1] 0.6880895 0.1574104
#>