  Factorial designs are widely used in agriculture, engineering, and the social
sciences to study the causal effects of several factors simultaneously on a
response. The objective of such a design is to estimate all factorial effects
of interest, which typically include main effects and interactions among
factors. To estimate factorial effects with high precision when a large number
of pre-treatment covariates are present, balance among covariates across
treatment groups should be ensured. We propose utilizing rerandomization to
ensure covariate balance in factorial designs. Although both factorial designs
and rerandomization have been discussed before, the combination has not. Here,
theoretical properties of rerandomization for factorial designs are
established, and empirical results are explored using an application from the
New York Department of Education.
