blocksdesign-package: Blocks design package

In RNED/blocks_design: Nested and Crossed Block Designs for Factorial, Fractional Factorial and Unstructured Treatment Sets

Description

The blocksdesign package provides functionality for the construction of nested or crossed block designs for factorial or unstructured treatment sets with arbitrary levels of replication and arbitrary depth of nesting.

Details

Block designs aim to group experimental units into homogeneous blocks to provide maximum precision of estimation of treatment effects within blocks. The most basic type of block design is a complete randomized blocks design where every block contains one or more complete replicate sets of treatments. Complete randomized block designs estimate all treatment effects fully within individual blocks and are usually the best choice for small experiments. However, for large experiments, the average variability within complete replicate blocks can be large and then it may be beneficial to sub-divide each complete replicate block into smaller incomplete blocks which give improved precision of comparison on inter-block treatment effects.

Block designs with a single level of nesting are widely used in practical research but sometimes the blocks of large designs with a single set of nested blocks may still be too large to give good control of intra-block variability. In this situation, a second set of incomplete blocks can be nested within the first set to reduce the intra-block variability still further. This process of recursive nesting of blocks can be repeated indefinitely as often as required until the bottom set of blocks are sufficiently small to give good control of intra-block variability.

Sometimes it can also abe advantageous to use a double blocking system in which one set of blocks, usually called row blocks, is crossed with a second set of blocks, usually called column blocks. Double blocking systems can be valuable for controlling block effects in two dimensions simultaneously.

The blocksdesign package provides functionality for the construction of general block designs with simple or crossed blocks that can be nested repeatedly to any feasible depth of nesting. The design algorithm proceeds recursively with each nested set of blocks optimized conditionally within each preceding set of blocks. Block sizes within any nested level are as equal as possible and never differ by more than a single plot. The analysis of incomplete block designs is complex but the availability of modern computers and modern software, for example the R mixed model software package lme4 (Bates et al 2014), makes the analysis of any feasible nested block designs with any depth of nesting practicable.

Currently, the blocksdesign package has two main block design functions:

i) blocks : The blocks function is used to generate block designs for any arbitrary number of unstructured treatments where each treatment can have any arbitrary number of replicates. This function generates arbitrary nested block designs with arbitrary depth of nesting where each succesive set of blocks is optimized within the levels of each preceding set of blocks using a conditional D-optimality design criterion. Special block designs such as lattice designs or latin or Trojan square designs are constructed algebraically. The outputs from the blocks function includes a data frame showing the allocation of treatments to blocks for each plot of the design 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 in the bottom level of the design is also included in the output.

ii) factblocks : The factblocks function is used to generate designs for factorial treatment sets. The factblocks function finds a D-optimal or near D-optimal treatment design of the required size for any required factorial model and then finds a D-optimal or near D-optimal block design for the fitted treatment design using the same algorithm as in the blocks function. The output from factblocks includes 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 blocks. Fractional factorial efficiency factors based on the generalized variance of the complete factorial design are also shown (see the factblocks documentation for details)

Further discussion of designs with repeatedly nested strata can be found in the package vignette at: vignette("blocksdesign")

References

Bates, D., Maechler, M., Bolker, B. and Walker, S. (2014). lme4: Linear mixed-effects models using 'Eigen' and S4. R package version 1.1-12. https://CRAN.R-project.org/package=lme4

RNED/blocks_design documentation built on May 8, 2019, 7:33 a.m.