Causal Inference from Possibly Unbalanced Split-Plot Designs: A\n Randomization-based Perspective

2019/06/19 by Rahul Mukerjee, Mukerjee, Rahul, Tirthankar Dasgupta +1 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Optimal Experimental Design Methods #Economic and Environmental Valuation #Advanced Causal Inference Techniques

paper · pdf · doi:10.48550/arxiv.1906.08420

Abstract

Split-plot designs find wide applicability in multifactor experiments with\nrandomization restrictions. Practical considerations often warrant the use of\nunbalanced designs. This paper investigates randomization based causal\ninference in split-plot designs that are possibly unbalanced. Extension of\nideas from the recently studied balanced case yields an expression for the\nsampling variance of a treatment contrast estimator as well as a conservative\nestimator of the sampling variance. However, the bias of this variance\nestimator does not vanish even when the treatment effects are strictly\nadditive. A careful and involved matrix analysis is employed to overcome this\ndifficulty, resulting in a new variance estimator, which becomes unbiased under\nmilder conditions. A construction procedure that generates such an estimator\nwith minimax bias is proposed.\n

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• Design-based theory for causal inference

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