Randomization-Based Covariate Adjustment for Randomized Block 2 K Factorial Experiments With Missing Baselines

This paper develops a covariate adjustment framework for randomized block $2^K$ factorial experiments that accommodates high-dimensional covariates and missing baseline measurements. We propose three Lasso-based regression adjustment procedures. Under a randomization-based finite-population framework that allows model misspecification, we show that the resulting Lasso-adjusted estimators are consistent and jointly asymptotically normal. We also provide Neyman-type covariance estimators that support asymptotically valid conservative inference. For the first projection adjustment, the asymptotic variance of each factorial-effect estimator is no larger than that of the corresponding unadjusted estimator. For the joint projection and stratum-specific adjustments, the differences between the asymptotic covariance matrices of the unadjusted and adjusted estimators are positive semidefinite. We also study, within a design-based framework, three strategies for handling missing covariates and provide practical guidance. Efficiency comparisons among these strategies require the linear spaces used in their sparse population projections to be nested. Under this nesting condition, when missingness indicators are informative about potential outcomes, incorporating them as additional adjustment variables can further improve efficiency. None of the three strategies requires specifying parametric outcome or missingness models. Inference is based on randomization and the stated regularity conditions. Single imputation and the missingness-indicator method additionally require treatment-invariant baseline missingness. Simulation studies and an empirical application corroborate the theoretical findings.