blocksdesign-package {blocksdesign}

Blocks design package

Description

The blocksdesign package provides functionality for the construction of block and treatment designs for general linear models.

Details

Randomized complete blocks are the designs of choice for small experiments with few treatments. For large experiments with many treatments, however, a single set of complete blocks may not be adequate and then sub-division into smaller nested blocks may be required. Block designs with a single level of nesting are widely used but a single level of nesting may be inadequate for very large experiments with many treatments. blocksdesign provides for the construction of designs with multiple levels of nesting down to any feasible depth of nesting.

Sometimes block designs for the control of variability in two or more dimensions are required and blocksdesign can also build crossed block designs allowing for both additive and interactive crossed block effects simultaneously.

The blocksdesign package has two main functions:

i) blocks: This is a simple recursive function for nested blocks for unstructured treatments. The function generates designs for treatments with arbitrary levels of replication and with arbitrary depth of nesting where blocks sizes are assumed to be as equal as possible for each level of nesting. Special square and rectangular lattice designs (see Cochran and Cox 1957) are constructed algebraically from mutually orthogonal Latin squares (MOLS). The outputs from the blocks function include a data frame showing the allocation of treatments to blocks and a table showing the achieved D- and A-efficiency factors for each set of nested blocks together with A-efficiency upper bounds, where available. A plan showing the allocation of treatments to blocks for the bottom level of the design is also included in the output.

ii) design: This is a general purpose function for linear models with qualitative or quantitative level treatment factors and qualitative level block factors. The function finds a D-optimal or near D-optimal design for a specified treatment model and then finds a conditional D-optimal or near D-optimal block design for that choice of treatment design. The design algorithm builds the blocks design by sequentially adding blocks factors where each blocks factor is optimized conditional on all previously added blocks factors. The outputs include a data frame of the block and treatment factors for each plot and a table showing the achieved D-efficiency factors for each set of nested or crossed blocks. Fractional factorial efficiency factors based on the generalized variance of the complete factorial design are also shown.

Other available functions are A_bound, which finds upper A-efficiency bounds for regular block designs, MOLS, which constructs sets of mutually orthogonal prime-power Latin squares (MOLS), GraecoLatin, which constructs mutually orthogonal Graeco-Latin squares not necessarily prime-power, isPrime, which tests an integer for primality, isPrimePower, which factorizes prime powers and HCF, which finds the highest common factor (hcf) for a set of positive integer numbers.

For further explanation see Edmondson (2020) and vignette(package = "blocksdesign").

References

Cochran W. G. & Cox G. M. (1957) Experimental Designs 2nd Edition John Wiley & Sons.

Edmondson, R.N. Multi-level Block Designs for Comparative Experiments. JABES 25, 500–522 (2020).