Nested and Crossed Block Designs for Factorial, Fractional
Factorial and Unstructured Treatment Sets
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 and the block model
for any particular level of nesting can comprise either a simple nested blocks
design or a crossed row-and-column blocks design. Block sizes
are either all equal or differ, at most, by one plot within any particular row
or column classification and any particular level of nesting. 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.

The 'blocksdesign' package constructs nested block and
D-optimal factorial designs for any unstructured or factorial
treatment model of any size. The nested block designs can have
repeated nesting down to any required depth of nesting with
either a simple set of nested blocks or a crossed
row-and-column blocks design at each level of nesting.
The block design at each level of nesting is optimized for
D-efficiency within the blocks of each preceding set of blocks.
The block sizes in any particular block classification are
always as nearly equal as possible and never differ by more
than a single plot. Outputs include a table showing the
allocation of treatments to blocks, a plan layout showing
the allocation of treatments within blocks (unstructured
treatment designs only) the achieved D-efficiency and
A-efficiency factors for the block and treatment design
(factorial treatment designs only) and,
where feasible, an A-efficiency upper bound for
the block design (unstructured treatment designs only).