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Select Minimum Data Set (MDS) Using PCA

Source: R/pca_mds.R
pca_select_mds.Rd

Performs Principal Component Analysis (PCA) on soil property data and selects a minimum data set (MDS) of indicators based on variance and loading thresholds. This function implements the PCA-based MDS selection methodology commonly used in soil quality assessment.

Usage

pca_select_mds(data, var_threshold = 0.05, loading_threshold = 0.5)

Arguments

data

A data frame containing standardized soil property measurements. All columns should be numeric. It is recommended to standardize the data using standardize_numeric before applying PCA.

var_threshold

Numeric value specifying the minimum proportion of variance a principal component must explain to be retained. Components with variance below this threshold are excluded from MDS selection. Default is 0.05 (5%).

loading_threshold

Numeric value specifying the minimum absolute loading value for a variable to be considered for selection within a principal component. Variables with absolute loadings below this threshold are not selected. Default is 0.5.

Value

A list with the following components:

mds

Character vector of selected variable names representing the minimum data set.

pca

The PCA object returned by stats::prcomp, containing the full PCA results including rotation matrix, scores, and other components.

loadings

Numeric matrix of variable loadings (rotation matrix) for all principal components.

var_exp

Numeric vector containing the proportion of variance explained by each principal component.

Details

The MDS selection algorithm follows these steps:

  1. Perform PCA using stats::prcomp with scaling disabled (data should be pre-standardized).

  2. Calculate the proportion of variance explained by each PC.

  3. Identify PCs that explain variance greater than var_threshold.

  4. For each retained PC, identify the variable with the maximum absolute loading that exceeds loading_threshold.

  5. Return the unique set of selected variables as the MDS.

If no variables meet the selection criteria, an empty character vector is returned for the MDS component.

See also

standardize_numeric for data standardization

Examples

# Create example soil data
soil_data <- data.frame(
  Sand = c(45, 50, 42, 48, 52, 38, 44, 49),
  Silt = c(30, 28, 35, 32, 25, 40, 33, 29),
  Clay = c(25, 22, 23, 20, 23, 22, 23, 22),
  pH = c(6.5, 7.0, 6.8, 7.2, 6.9, 6.7, 7.1, 6.6),
  OM = c(3.2, 2.8, 3.5, 3.0, 2.9, 3.3, 3.1, 3.4)
)

# Standardize the data first
soil_std <- standardize_numeric(soil_data)

# Select MDS using PCA
result <- pca_select_mds(soil_std)

# View selected indicators
print(result$mds)
#> [1] "Sand" "Clay"

# View variance explained
print(result$var_exp)
#> [1] 5.364949e-01 3.191878e-01 1.052890e-01 3.902825e-02 2.001949e-33

# Use custom thresholds
result2 <- pca_select_mds(soil_std,
                          var_threshold = 0.10,
                          loading_threshold = 0.6)