IsoCheck: An R Package to check Isomorphism for Two-level Factorial Designs with Randomization Restrictions

TL;DR

IsoCheck is an R package that efficiently determines isomorphism among multi-stage 2^n factorial designs with randomization restrictions using projective geometry and bitstring representations.

Contribution

The paper introduces IsoCheck, a novel R package that leverages projective geometry and bitstring methods to quickly identify and compare factorial designs with complex restrictions.

Findings

Efficient identification of isomorphic factorial designs.

Ability to create and rank a catalog of non-isomorphic designs.

Demonstrated use cases with R code examples.

Abstract

Factorial designs are often used in various industrial and sociological experiments to identify significant factors and factor combinations that may affect the process response. In the statistics literature, several studies have investigated the analysis, construction, and isomorphism of factorial and fractional factorial designs. When there are multiple choices for a design, it is helpful to have an easy-to-use tool for identifying which are distinct, and which of those can be efficiently analyzed/has good theoretical properties. For this task, we present an R library called IsoCheck that checks the isomorphism of multi-stage 2^n factorial experiments with randomization restrictions. Through representing the factors and their combinations as a finite projective geometry, IsoCheck recasts the problem of searching over all possible relabelings as a search over collineations, then exploits projective geometric properties of the space to make the search much more efficient. Furthermore, a bitstring representation of the factorial effects is used to characterize all possible rearrangements of designs, thus facilitating quick comparisons after relabeling. We present several examples with R code to illustrate the usage of the main functions in IsoCheck. Besides checking equivalence and isomorphism of 2^n multi-stage factorial designs, we demonstrate how the functions of the package can be used to create a catalog of all non-isomorphic designs, and subsequently rank these designs based on a suitably defined ranking criterion. IsoCheck is free software and distributed under the General Public License and available from the Comprehensive R Archive Network.