Generate a resolvable (spatial) row-column design

Builds a resolvable row-column design for v <= k * s treatments in r replicates, each a k x s array of rows and columns that contains every treatment once (Williams, John and Whitaker, 2006). The design is found by a search over swaps of treatments within replicates:

The average efficiency factor of the resolvable row-column design (rows and columns within replicates), together with the efficiency factors of the component row design and column design, is maximized.
With spatial = TRUE, the spatial average efficiency factor of the two-dimensional linear variance (LV + RC) model is then maximized while keeping the three efficiency factors of step 1 within efficiency_tolerance of their optimized values. This spreads treatments over edge and interior plots and over row and column neighbours, without needing prior values for spatial parameters.

When replicates are contiguous, latinize = TRUE builds a latinized design: no treatment appears twice in the same long column (replicates stacked vertically) or long row (replicates side by side), within every group of latin_t adjacent replicates (t-latinized designs; John and Williams, 1998).

Usage

resolvable_row_column_design(
  treatments,
  n_reps,
  rows_per_rep,
  cols_per_rep,
  spatial = TRUE,
  latinize = FALSE,
  replicate_layout = c("vertical", "horizontal"),
  latin_t = NULL,
  n_starts = 3,
  n_iter = NULL,
  efficiency_tolerance = 0.002,
  plot_type = c("serpentine", "cartesian"),
  seed = NULL,
  output_file = NULL,
  start_design = NULL
)

Arguments

treatments: Character vector of treatment names (v <= k * s).
n_reps: Number of replicates (r).
rows_per_rep: Number of rows in each replicate (k).
cols_per_rep: Number of columns in each replicate (s).
spatial: Logical. If TRUE (default), optimize the spatial efficiency factor in a second stage.
latinize: Logical. If TRUE, build a latinized design for contiguous replicates.
replicate_layout: How replicates are placed in the field: "vertical" (stacked, giving long columns) or "horizontal" (side by side, giving long rows).
latin_t: Optional size of the groups of adjacent replicates within which latinization holds (t-latinized design). Defaults to all replicates.
n_starts: Number of random starting designs.
n_iter: Number of swap proposals per stage and start. Defaults to min(20000, max(3000, 60 * v * r)).
efficiency_tolerance: Largest loss in the row-column, row and column efficiency factors accepted in the spatial stage.
plot_type: Plot numbering order: "serpentine" or "cartesian".
seed: Optional random seed.
output_file: Optional tab-delimited output file for the design.
start_design: Optional existing design to start from (for example one produced by CycDesigN), as a data frame with replicate, row_in_rep, col_in_rep and all_entries columns and complete replicates. The search then improves this design; use n_iter = 1 and spatial = FALSE to keep it essentially as it is and only lay it out.

Value

An object of class resolvable_row_column_design: a list with input, summary (efficiency factors, spatial upper bound, latinization check), design (one row per plot with replicate, row_in_rep, col_in_rep, field row and col, long_row / long_col, all_entries, is_filler), breedbase_design, and efficiency (see resolvable_row_column_efficiency()).

Details

When there are fewer treatments than plots per replicate, the remaining plots are fillers (all_entries = "FILLER", is_filler = 1), placed by the search like an extra treatment.

References

Williams, E. R., John, J. A. and Whitaker, D. (2006). Construction of resolvable spatial row-column designs. Biometrics 62, 103-108. doi:10.1111/j.1541-0420.2005.00393.x

John, J. A. and Williams, E. R. (1998). t-Latinized designs. Australian and New Zealand Journal of Statistics 40, 111-118.

Examples

# Example 2 of Williams, John and Whitaker (2006): 42 treatments in three
# replicates of 6 rows x 7 columns.
design <- resolvable_row_column_design(
  treatments = paste0("T", 1:42),
  n_reps = 3,
  rows_per_rep = 6,
  cols_per_rep = 7,
  n_starts = 1,
  n_iter = 2000,
  seed = 1
)
design$summary
#> # A tibble: 1 × 15
#>   n_treatments n_fillers n_reps rows_per_rep cols_per_rep n_plots efficiency_rc
#>          <int>     <int>  <int>        <int>        <int>   <int>         <dbl>
#> 1           42         0      3            6            7     126         0.684
#> # ℹ 8 more variables: efficiency_rows <dbl>, efficiency_cols <dbl>,
#> #   efficiency_spatial <dbl>, upper_bound_spatial <dbl>, spatial <lgl>,
#> #   latinized <lgl>, latin_ok <lgl>, replicate_layout <chr>