blocksdesign (version 3.2)

blocks: Block designs for unstructured treatment sets

Description

Constructs randomized nested block designs for unstructured treatment sets with any feasible depth of nesting.

Usage

blocks(treatments, replicates, blocks = NULL, searches = NULL,
  seed = NULL, jumps = 1)

Arguments

treatments

a partition of the total required number of treatments into equally replicated treatment sets, possibly a complete partition into individual treatments.

replicates

a set of treatment replication numbers with one replication number for each partitioned treatment set, possibly a complete set of treatment replication numbers.

blocks

the number of blocks nested in each preceding block for each level of nesting from the top-level block downwards.

searches

the maximum number of local optima searched for a design optimization. The default number decreases as the design size increases.

seed

an integer initializing the random number generator. The default is a random seed.

jumps

the number of pairwise random treatment swaps used to escape a local maxima. The default is a single swap.

Value

Treatments

A table showing the replication number of each treatment in the design.

Design

Data frame giving the optimized block and treatment design in plot order.

Plan

Data frame showing a plan view of the treatment design in the bottom level of the design.

blocks_model

The D-efficiencies and the A-efficiencies of the blocks in each nested level of the design together with A-efficiency upper-bounds, where available.

seed

Numerical seed used for random number generator.

searches

Maximum number of searches used for each level.

jumps

Number of random treatment swaps used to escape a local maxima.

Details

Constructs randomized nested block designs with arbitrary depth of nesting for arbitrary unstructured treatment sets.

The treatments parameter is a set of numbers that partitions the total number of treatments into equally replicated treatment sets while the replicates parameter is a matching set of numbers that defines the replication of each equally replicated treatment set.

The blocks parameter, if any, defines the number of blocks for each level of nesting from the highest to the lowest. The first number, if any, is the number of nested row blocks in the first-level of nesting, the second number, if any, is the number of nested row blocks in the second-level of nesting and so on down to any required feasible depth of nesting.

Block sizes are as nearly equal as possible and will never differ by more than a single plot for any particular block classification.

Unreplicated treatments are allowed and any simple nested block design can be augmented by any number of single unreplicated treatments to give augmented blocks that never differ in size by more than a single plot. However, it may sometimes be preferable to find an efficient block design for the replicated treatments and then add the unreplicated treatments to the design heuristically.

Square lattice designs are resolvable incomplete block designs for r replicates of p*p treatments arranged in blocks of size p where r < p+2 for prime or prime power p or r < 4 for general p. Square lattice designs are constructed algebraically from Latin squares or MOLS.

Rectangular lattice designs are resolvable incomplete block designs for r replicates of (p-1)*p treatments arranged in blocks of size p-1 where r < p+1 for prime or prime power p. Rectangular lattice designs are constructed algebraically from Latin squares or MOLS.

Designs based on prime-power MOLS require the MOLS package.

All other designs are constructed numerically by optimizing a D-optimality criterion.

Outputs:

• A data frame showing the allocation of treatments to blocks with successive nested strata arranged in standard block order.

• A table showing the replication number of each treatment in the design.

• A table showing the block levels and the achieved D-efficiency and A-efficiency factor for each nested level together with A-efficiency upper bounds, where available.

• A plan showing the allocation of treatments to blocks in the bottom level of the design.

References

Sailer, M. O. (2013). crossdes: Construction of Crossover Designs. R package version 1.1-1. https://CRAN.R-project.org/package=crossdes

Cochran, W.G., and G.M. Cox. 1957. Experimental Designs, 2nd ed., Wiley, New York.

Examples

# NOT RUN {
## The number of searches in the following examples have been limited for fast execution.  
## In practice, the number of searches may need to be increased for optimum results.
## Designs should be rebuilt several times to check that a near-optimum design has been found.  

# 12 treatments x 4 replicates in 4 complete blocks with 4 sub-blocks of size 3
# rectangular lattice see Plan 10.10 Cochran and Cox 1957.
blocks(treatments=12,replicates=4,blocks=c(4,4))

# 3 treatments x 2 replicates + 2 treatments x 4 replicates in two complete randomized blocks
blocks(treatments=c(3,2),replicates=c(2,4),searches=10)

# 50 treatments x 4 replicates with 4 main blocks and 5 nested sub-blocks in each main block
blocks(treatments=50,replicates=4,blocks=c(4,5))

# as above but with 20 additional single replicate treatments, one single treatment per sub-block
blocks(treatments=c(50,20),replicates=c(4,1),blocks=c(4,5))

blocks(treatments=c(12,12),replicates=c(2,1),blocks=c(2,3))

# 6 replicates of 6 treatments in 4 blocks of size 9 (non-binary block design)
blocks(treatments=6,replicates=6,blocks=4)

# 128 treatments x 2 replicates with two main blocks and 3 levels of nesting
 
# }
# NOT RUN {
blocks(128,2,c(2,2,2,2))
# }
# NOT RUN {
#' # 64 treatments x 4 replicates with 4 main blocks nested blocks of size 8 (lattice square)
blocks(64,4,c(4,8)) 

# 100 treatments x 4 replicates with 4 main blocks nested blocks of size 10 (lattice square)
blocks(100,4,c(4,10)) 

# }