  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.
