blocksdesign package provides functionality for the construction of block designs for unstructured
treatment sets with arbitrary levels of replication and arbitrary depth of nesting.Complete randomized blocks are excellent for small designs but for larger designs, the variability within blocks may become large
and then it may become desirable to sub-divide complete blocks into smaller incomplete blocks to give better control of variability.
The analysis of incomplete block designs is complex and requires combination of treatment information from different sources of variation
and before the advent of modern computers the complexity of such an analysis restricted incomplete block designs to a single nested blocks stratum.
Nowadays, however, the availability of modern computers and modern software such as the lme4 mixed model
package (Bates et al 2014) have largely eliminated such restrictions and the routine analysis of multi-stratum nested block designs is now entirely feasible.
The advantage of multi-stratum nesting is that random variability can be captured for
a range of block sizes and this allows for more realistic modelling of block effects compared with single stratum nesting.
The blocksdesign package provides for the construction of general block designs where
treatments can have any feasible number of levels of replication and blocks can be nested repeatedly to any feasible depth of nesting.
The design algorithm optimizes nested blocks hierarchically with each successive set of nested blocks
optimized within the blocks of the preceding set. Block sizes within each stratum are as equal as possible and never differ by more than a single plot.
The main function is blocks which is used to generate the actual required design. The output from
blocks includes a data frame of the block and treatment factors for each plot,
a data frame of the allocation of treatments to plots for each block in the design,
blocks-by-treatments incidence matrices for each stratum in the design and an A-efficiency factor for each stratum in the design,
together with an efficiency upper bound, where available.
The secondary function efficiencies takes the design output from the blocks
function and uses it to construct tables of efficiency factors for each pairwise treatment difference in each stratum, as required.
The subsidiary function upper_bounds estimates
A-efficiency upper bounds for regular block designs with equally replicated treatments and equal block sizes.
Further discussion of multi-stratum nesting can be found in the package vignette at: vignette("blocksdesign")