Efficiency of a resolvable row-column design

Computes the design criteria of Williams, John and Whitaker (2006) for a resolvable row-column design with complete replicates: the average efficiency factors of the row-column design, the row design and the column design (rows and columns nested within replicates), the spatial average efficiency factor of the two-dimensional linear variance model, $$A = rI - X'(I_r \otimes W_R \otimes W_C)X,$$ with its upper bound \(U = (v - t)/(v - 1)\), \(t = tr(W_R) tr(W_C)\), and treatment neighbour and edge statistics. Optionally, it evaluates the average pairwise variance criterion \(z(X)\) under an assumed autoregressive (AR) model, which is used to compare designs (Section 4 of the paper).

Usage

resolvable_row_column_efficiency(
  design,
  ar = NULL,
  genotype_col = "all_entries",
  replicate_col = "replicate",
  row_col = "row_in_rep",
  col_col = "col_in_rep"
)

Arguments

design

A design object from resolvable_row_column_design() or a data frame with replicate, row, column and treatment columns. Each replicate must be complete (k * s plots, each treatment once; filler plots count as separate treatments).

ar

Optional named list of AR model parameters eta_r, eta_c, psi, rho_r, rho_c (Eq. 4 of the paper).

genotype_col, replicate_col, row_col, col_col

Column names.

Value

A list with efficiency_rc, efficiency_rows, efficiency_cols, efficiency_spatial, upper_bound_spatial, ar_criterion (NA unless ar is given), and neighbours, a tibble with each treatment's number of distinct row and column neighbours and the number of replicates in which it is on an edge or in a corner.

Examples

design <- resolvable_row_column_design(paste0("T", 1:20), 2, 4, 5,
                                       n_starts = 1, n_iter = 500, seed = 1)
eff <- resolvable_row_column_efficiency(design,
  ar = list(eta_r = 35, eta_c = 60, psi = 10, rho_r = 0.5, rho_c = 0.5))
eff[c("efficiency_rc", "efficiency_spatial", "ar_criterion")]
#> $efficiency_rc
#> [1] 0.5496625
#> 
#> $efficiency_spatial
#> [1] 0.8154889
#> 
#> $ar_criterion
#> [1] 4.338679
#>