Nested and Crossed Block Designs for Unstructured Treatment Sets

Nested and Crossed Block Designs for Unstructured and Factorial
Treatment Sets
Constructs randomized nested or crossed block designs for
unstructured treatment sets or for factorial treatments sets. Where the
treatments are factorial, the treatments model can be defined by using the
model formulation defined in the model.matrix {stats} base package. Blocks
are nested hierarchically in successive blocks strata and the blocks
model in any particular stratum can comprise either a simple nested blocks
design or a crossed row-and-column design. Block sizes in any one stratum
are either all equal or differ, at most, by one plot. The design outputs
include a data frame showing the allocation of treatments to blocks, a table
showing block levels, the achieved D-efficiency, the achieved A-efficiency
(unstructured treatments only) and A-efficiency upper bounds, where available,
for each stratum in the design. For designs with simple unstructured treatments,
a plan layout showing the allocation of treatments to blocks or to rows and
columns in the bottom stratum of the design is also given.

Constructs randomized nested row-and-column type block designs
with arbitrary depth of nesting for arbitrary factorial or fractional
factorial treatment designs. The treatment model can be defined
by a models.matrix formula which allows any feasible
combination of quantitative or qualitative model terms.
Any feasible design size can be defined and, where necessary,
a D-optimal swapping routine will find the best fraction for the required
design size. Blocks are nested hierarchically in successive strata and the
blocks model in any particular stratum will comprise either a simple nested blocks
design or a crossed row-and-column blocks design. Block sizes in any one stratum
are either all equal or differ, at most, by one plot. The design outputs
include a data frame showing the allocation of treatments to blocks, a table
showing block levels, the fractional design efficiency,
the achieved D-efficiency, the achieved A-efficiency
(unstructured treatments only) and A-efficiency upper bounds, where available,
for each stratum in the design. For designs with simple unstructured treatments,
a plan layout showing the allocation of treatments to blocks or to rows and
columns in the bottom stratum of the design is also given.