Row-Column Design

Resolvable Row-Column Design

It randomly generates a resolvable row-column design.The design is optimized in both rows and columns blocking factors. The randomization can be done across multiple locations.

Overview

row_column() optimizes both the row and the column blocking factors, and the strategy is selected with the method argument. By default (method = "onestage") the rows and columns are optimized jointly in a single step with blocksdesign::design(). The historical alternative, method = "twostage", reproduces the designs generated by earlier versions of FielDHub: the first step constructs the blocking factor Columns using Incomplete Block Units from an incomplete block design that sets the number of incomplete blocks as the number of Columns in the design, each of which has a dimension equal to the number of Rows. Once this design is generated, the Rows are used as the Row blocking factor that is optimized for A-Efficiency, but levels within the original Columns are fixed. To optimize the Rows while maintaining the current optimized Columns, a heuristic algorithm swaps at random treatment positions within a given Column (Block) also selected at random, keeping a swap only when it does not decrease the A-Efficiency; this iterative process is repeated, by default, 1000 times.

1. Using the FielDHub Shiny App

To generate a Row-Column Design using the FielDHub app:

First, go to Other Designs > Resolvable Row-Column Design (RRCD)

Then, follow the following steps where we will show how to generate a Row-Column Design with 45 treatments, 5 rows and 3 reps.

Inputs

1. Import entries’ list? Choose whether to import a list with entry numbers and names for genotypes or treatments.

   • If the selection is No, that means the app is going to generate synthetic data for entries and names of the treatment based on the user inputs.

   • If the selection is Yes, the entries list must fulfill a specific format and must be a .csv file. The file must have the columns ENTRY and NAME. The ENTRY column must have a unique entry integer number for each treatment. The column NAME must have a unique name that identifies each treatment. Both ENTRY and NAME must be unique, duplicates are not allowed. In the following table, we show an example of the entries list format. This example has an entry list with 12 treatments.

2. Input the number of treatments in the Input # of Treatments box. We will enter 45 for our sample experiment.

3. Set the number of plots in each incomplete block with the Input # of Plots per IBlock box. In this examples, set it to 5.

4. Select the number of replications of these treatments with the Input # of Full Reps box. In this examples, set it to 3.

5. Enter the number of locations in Input # of Locations. We will run this experiment over a single location, so set it to 1.

6. Select serpentine or cartesian in the Plot Order Layout. For this example we will use the default serpentine layout.

7. Enter the starting plot number in the Starting Plot Number box. If the experiment has multiple locations, you must enter a comma separated list of numbers the length of the number of locations for the input to be valid. Set it to 101.

8. Enter a name for the location of the experiment in the Input Location box. If there are multiple locations, each name must be in a comma separated list. For this example, set it to "FARGO".

9. To ensure that randomizations are consistent across sessions, we can set a random seed in the box labeled random seed. In this example, we will set it to 1244.

10. Once we have entered the information for our experiment on the left side panel, click the Run! button to run the design.

Outputs

After you run a row-column design in FielDHub, there are several ways to display the information contained in the field book.

2. Using the FielDHub function: row_column()

You can run the same design with a function in the FielDHub package, row_column().

First, you need to load the FielDHub package by typing

library(FielDHub)

Then, you can enter the information describing the above design like this:

rcd <- row_column(
  t = 45,
  nrows = 5,
  r = 3,
  l = 1, 
  plotNumber = 101, 
  locationNames = "FARGO",
  iterations = 20,
  seed = 1244
)

print(rcd)

Resolvable Row-Column Design (One-Step Optimization) 

Efficiency of design: 
          Level Blocks D-Efficiency A-Efficiency   A-Bound
1           Rep      3    1.0000000    1.0000000 1.0000000
2           Row     15    0.8945848    0.8781404 0.8842892
3        Column     27    0.7903339    0.7593720 0.7674419
4 Row-by-Column     NA    0.6987567    0.6695097        NA

Information on the design parameters: 
List of 8
 $ rows          : num 5
 $ columns       : num 9
 $ reps          : num 3
 $ treatments    : num 45
 $ locations     : num 1
 $ location_names: chr "FARGO"
 $ seed          : num 1244
 $ optimization  : chr "onestage"

 10 First observations of the data frame with the row_column field book: 
   ID LOCATION PLOT REP ROW COLUMN ENTRY TREATMENT
1   1    FARGO  101   1   1      1    30      G-30
2   2    FARGO  102   1   1      2    27      G-27
3   3    FARGO  103   1   1      3     9       G-9
4   4    FARGO  104   1   1      4    15      G-15
5   5    FARGO  105   1   1      5    21      G-21
6   6    FARGO  106   1   1      6    31      G-31
7   7    FARGO  107   1   1      7    25      G-25
8   8    FARGO  108   1   1      8    16      G-16
9   9    FARGO  109   1   1      9    22      G-22
10 10    FARGO  110   1   2      1    40      G-40

field_book <- rcd$fieldBook
head(rcd$fieldBook, 10)

   ID LOCATION PLOT REP ROW COLUMN ENTRY TREATMENT
1   1    FARGO  101   1   1      1    30      G-30
2   2    FARGO  102   1   1      2    27      G-27
3   3    FARGO  103   1   1      3     9       G-9
4   4    FARGO  104   1   1      4    15      G-15
5   5    FARGO  105   1   1      5    21      G-21
6   6    FARGO  106   1   1      6    31      G-31
7   7    FARGO  107   1   1      7    25      G-25
8   8    FARGO  108   1   1      8    16      G-16
9   9    FARGO  109   1   1      9    22      G-22
10 10    FARGO  110   1   2      1    40      G-40

plot(rcd)

Optimization method and latinization

By default, row_column() optimizes the rows and columns jointly in a single step using blocksdesign::design() (method = "onestage"); the iterations argument is then passed to blocksdesign::design() as its number of searches, and a small value already captures most of the gain. The historical alternative method = "twostage" constructs the columns first and then improves the rows with a greedy search while the columns are kept fixed, reproducing the designs generated by earlier versions of FielDHub.

The per-factor (marginal) Row and Column A-Efficiencies reported by both methods are usually already close to optimal and change little between the methods. The advantage of method = "onestage" shows up in the joint row-by-column A-Efficiency of the standard resolvable row-column analysis model, which the efficiency report now includes as the Row-by-Column row of blocksModel. The default one-stage design above reports:

rcd$blocksModel[[1]]
          Level Blocks D-Efficiency A-Efficiency   A-Bound
1           Rep      3    1.0000000    1.0000000 1.0000000
2           Row     15    0.8945848    0.8781404 0.8842892
3        Column     27    0.7903339    0.7593720 0.7674419
4 Row-by-Column     NA    0.6987567    0.6695097        NA

while the historical two-stage method typically reports a lower joint Row-by-Column A-Efficiency:

rcd_twostage <- row_column(
  t = 45,
  nrows = 5,
  r = 3,
  l = 1,
  plotNumber = 101,
  locationNames = "FARGO",
  iterations = 100,
  method = "twostage",
  seed = 1244
)
rcd_twostage$blocksModel[[1]]
          Level Blocks D-Efficiency A-Efficiency   A-Bound
1           Rep      3    1.0000000    1.0000000 1.0000000
2           Row     15    0.8932037    0.8745335 0.8842892
3        Column     27    0.7912510    0.7624863 0.7674419
4 Row-by-Column     NA    0.6824940    0.6311251        NA

Setting latinize = TRUE (only available with method = "onestage") optimizes the rows and columns as crossed factors that are shared across the replicates, so that a treatment tends to occupy different rows and different columns in the different replicates. This is useful when a field trend runs along the rows or columns across the whole trial rather than within individual replicates.

rcd_latinized <- row_column(
  t = 45,
  nrows = 5,
  r = 3,
  l = 1,
  plotNumber = 101,
  locationNames = "FARGO",
  iterations = 20,
  method = "onestage",
  latinize = TRUE,
  seed = 1244
)
rcd_latinized$blocksModel[[1]]
          Level Blocks D-Efficiency A-Efficiency   A-Bound
1           Rep      3    1.0000000    1.0000000 1.0000000
2           Row      5    0.9835497    0.9821140 0.9821140
3        Column      9    0.9488372    0.9423564 0.9425511
4 Row-by-Column     NA    0.9330012    0.9259216        NA

Because a latinized design optimizes the rows and columns as crossed factors shared across the replicates, its Row-by-Column efficiency is computed on that crossed model and is therefore not directly comparable with the nested-model efficiencies reported above.