Abstract:
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Factorial designs are widely used in agriculture, engineering, and social sciences to study causal effects of several factors on a response. The objective is to estimate all factorial effects of interest, including main effects and interactions. When a large number of pre-treatment covariates are present, the factorial effects may be confounded with the effects of these covariates, and thus estimation may be a challenging task. To estimate factorial effects with high precision, balance among covariates across treatment groups should be ensured. Achieving such balance with common strategies like blocking is often impossible when the number of covariates is large. We propose utilizing rerandomization for ensuring covariate balance in factorial designs. Although both factorial designs and rerandomization have been discussed since Fisher, rerandomization has not been utilized for factorial designs. We argue that rerandomization increases the precision of estimated factorial effects of interest without sacrificing the precision of other estimates. Theoretical properties of rerandomization for factorial designs are established, and empirical results are explored via extensive simulation.
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