selection.index (version 2.0.0)

estimate_missing_values: Estimate Missing Values in Experimental Data

Description

Estimates and imputes missing values in randomized complete block design (RCBD), Latin square design (LSD), or split plot design (SPD) experimental data.

Uses one of six methods: REML, Yates, Healy, Regression, Mean, or Bartlett.

Usage

estimate_missing_values(
  data,
  genotypes,
  replications,
  columns = NULL,
  main_plots = NULL,
  design = c("RCBD", "LSD", "SPD"),
  method = c("REML", "Yates", "Healy", "Regression", "Mean", "Bartlett"),
  tolerance = 1e-06
)

Value

Matrix of the same dimensions as data with all missing values replaced by estimates.

Arguments

data

Matrix or data.frame with observations (rows) by traits (columns). May contain missing values (NA, NaN, Inf).

genotypes

Vector indicating genotype/treatment for each observation (sub-plot treatments in SPD).

replications

Vector indicating replication/block (RCBD) or row (LSD) for each observation.

columns

Vector indicating column index for each observation (required for Latin Square Design only).

main_plots

Vector indicating main plot treatment for each observation (required for Split Plot Design only).

design

Character string specifying experimental design:

• "RCBD" - Randomized Complete Block Design (default)

• "LSD" - Latin Square Design

• "SPD" - Split Plot Design

method

Character string specifying the estimation method:

• REML - Restricted Maximum Likelihood with BLUP. Most robust for complex missing patterns. (RCBD, LSD only)

• Yates - Traditional iterative formula. Simple and fast. Good for simple missing patterns. (RCBD, LSD only)

• Healy - Healy & Westmacott weighted adjustment method. More stable than Yates for multiple missing values. (RCBD, LSD only)

• Regression - Linear regression with QR decomposition. Non-iterative, fast and stable. (RCBD, LSD only)

• Mean - Mean substitution using treatment and block effects. Non-iterative, fastest. (RCBD, LSD, SPD)

• Bartlett - ANCOVA using other traits as covariates. Best when traits are correlated. (RCBD, LSD only)

tolerance

Numeric convergence criterion for iterative methods. Iteration stops when maximum change in estimated values falls below this threshold. Default: 1e-6.

Details

The function handles missing values by iteratively estimating them based on the experimental design structure:

**RCBD:** 2-way blocking (genotypes × blocks) **LSD:** 3-way blocking (genotypes × rows × columns) **SPD:** Nested structure (blocks > main plots > sub-plots)

Method Availability:

• RCBD: All methods (REML, Yates, Healy, Regression, Mean, Bartlett)

• LSD: All methods (REML, Yates, Healy, Regression, Mean, Bartlett)

• SPD: Mean only (other methods fall back to Mean)

Method Selection Guide:

• Use REML for complex missing patterns or when precision is critical

• Use Yates for balanced designs with few missing values

• Use Healy when multiple values missing from same treatment/block

• Use Regression for fast, deterministic estimation

• Use Mean for quick estimation when precision is less critical

• Use Bartlett when traits are highly correlated

The function uses the centralized design_stats engine for all ANOVA computations, ensuring consistency with gen_varcov(), phen_varcov(), and mean_performance().

References

Yates, F. (1933). The analysis of replicated experiments when the field results are incomplete. Empire Journal of Experimental Agriculture, 1, 129-142.

Healy, M. J. R., & Westmacott, M. (1956). Missing values in experiments analysed on automatic computers. Applied Statistics, 5(3), 203-206.

Bartlett, M. S. (1937). Some examples of statistical methods of research in agriculture and applied biology. Supplement to the Journal of the Royal Statistical Society, 4(2), 137-183.

Examples

# RCBD example with missing values
data(seldata)
test_data <- seldata[, 3:5]
test_data[c(1, 10, 25), 1] <- NA
test_data[c(5, 15), 2] <- NA

# Impute using Yates method
imputed <- estimate_missing_values(test_data, seldata$treat, seldata$rep, method = "Yates")

# Check that no NA remain
anyNA(imputed) # Should be FALSE

if (FALSE) {
# Latin Square Design example
# lsd_data should have genotypes, rows, and columns
imputed_lsd <- estimate_missing_values(
  data = lsd_data[, 3:7],
  genotypes = lsd_data$treat,
  replications = lsd_data$row,
  columns = lsd_data$col,
  design = "LSD",
  method = "REML"
)

# Split Plot Design example
# spd_data should have sub-plots, blocks, and main plots
imputed_spd <- estimate_missing_values(
  data = spd_data[, 3:7],
  genotypes = spd_data$subplot,
  replications = spd_data$block,
  main_plots = spd_data$mainplot,
  design = "SPD",
  method = "Mean"
)
}