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Handle Zeros and Censored Data in Compositional Data

gc_handle_zeros.Rd

Process compositional data containing zeros or below-detection-limit (censored) values using log-ratio imputation. Imputation is critical for compositional data analysis because the geometric mean of zeros is undefined, making standard covariance analysis unstable. This function provides three strategies: multiplicative zero imputation, additive zero imputation, or probabilistic imputation using the EM algorithm.

Usage

gc_handle_zeros(comp_data, method = "mzero", dl = NULL, tolerance = 1e-10)

Arguments

comp_data

A data frame with columns representing compositional parts (e.g., sand, silt, clay). Rows with at least one zero or negative value are candidates for imputation.

method

Character string specifying imputation approach:

  • "mzero" (default): Multiplicative zero imputation using zCompositions::multLRM()

  • "azero": Additive zero imputation using zCompositions::addLRM()

  • "lrem": Log-ratio expectation-maximization using zCompositions::lrEM()

Recommended: Use "lrem" for data with many zeros; use "mzero" for sparse zeros. Both are log-ratio based and preserve compositional geometry.

dl

Numeric vector of detection limits (one per column) for handling censored data. Default NULL treats all positive values as observed. If provided, values below dl[i] are treated as left-censored in column i. Only used if method = "lrem".

tolerance

Numeric tolerance for identifying zeros (default 1e-10). Values with absolute value below this threshold are treated as zeros.

Value

A list containing:

  • imputed_data: Data frame with imputed compositional values

  • n_zeros_imputed: Integer count of zero/censored values imputed

  • imputation_rate: Proportion of values imputed (n_zeros / total_values)

  • method_used: Character string with imputation method name

  • row_status: Factor indicating which rows were modified:

    • "observed": No imputation needed (no zeros/negative values)

    • "imputed": At least one zero/censored value replaced

    • "failed": Imputation failed (row excluded from analysis)

Details

Zero Imputation Strategies:

Multiplicative Zero Replacement (mzero): Replaces zeros with a small multiple of the detection limit, then applies log-ratio closure. Fast, appropriate for few isolated zeros.

Additive Zero Replacement (azero): Adds a small constant to all values before closure. Conservative and robust, but can distort low-abundance components.

Log-Ratio EM (lrem): Probabilistic imputation using expectation-maximization on log-ratio transformed data. Respects compositional geometry while honoring censoring patterns. Most theoretically sound but slower than replacement methods.

Detection Limits: If dl is provided and method = "lrem", values below their detection limit are treated as left-censored (uncertainty in exact value). EM iterates to estimate most likely imputed values consistent with the censoring pattern and covariance structure.

Examples

if (FALSE) { # \dontrun{
# Example: Soil texture data with some zeros or missing detections
soil_samples <- data.frame(
  sand = c(40, 35, 0, 42, 38),
  silt = c(35, 40, 45, 36, 40),
  clay = c(25, 25, 55, 22, 22)
)

# Check for zeros before imputation
has_zeros <- rowSums(soil_samples == 0) > 0
print(paste("Rows with zeros:", sum(has_zeros)))

# Impute using multiplicative zero replacement
result_mzero <- gc_handle_zeros(soil_samples, method = "mzero")
print(result_mzero$imputed_data)
print(paste("Imputation rate:", result_mzero$imputation_rate))

# Impute using log-ratio EM (more principled)
result_lrem <- gc_handle_zeros(soil_samples, method = "lrem")
print(result_lrem$imputed_data)

# With detection limits (censored measurements)
detection_limits <- c(sand = 1, silt = 1, clay = 1)
result_dl <- gc_handle_zeros(soil_samples, method = "lrem", dl = detection_limits)
} # }