# Isomorphism Check for Two-level Multi-Stage Factorial Designs with Randomization Restrictions via an R Package: IsoCheck

• Pratishtha Batra
• Neil A. Spencer
• Pritam Ranjan Indian Institute of Management Indore
Keywords: Isomorphism; Spreads; Factorial designs; Design ranking

### Abstract

Factorial designs are often used in various industrial and sociological experiments to identify significant factors and factor combinations that may affect the process re- sponse. In the statistics literature, several studies have investigated the analysis, con- struction, 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 26n 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. This paper presents several detailed examples with R codes that 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 good designs as per a suitably defined ranking criterion.

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Published
2023-08-05
How to Cite
Batra, P., Spencer, N., & Ranjan, P. (2023). Isomorphism Check for Two-level Multi-Stage Factorial Designs with Randomization Restrictions via an R Package: IsoCheck. Statistics, Optimization & Information Computing, 11(4), 892-910. https://doi.org/10.19139/soic-2310-5070-1494
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Research Articles