Showing papers by "Rahul Mukerjee published in 2018"

Using Standard Tools From Finite Population Sampling to Improve Causal Inference for Complex Experiments

Abstract: This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are “milder” than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatm...

Randomization-based causal inference from split-plot designs

Abstract: Author(s): Zhao, A; Ding, P; Mukerjee, R; Dasgupta, T | Abstract: Under the potential outcomes framework, we propose a randomization based estimation procedure for causal inference from split-plot designs, with special emphasis on 22 designs that naturally arise in many social, behavioral and biomedical experiments. Point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between- and within-group covariances of the potential outcomes. Results are compared to those under complete randomization as measures of design efficiency. Conservative estimators of these sampling variances are proposed. Connection of the randomization-based approach to inference based on the linear mixed effects model is explored. Results on sampling variances of point estimators and their estimators are extended to general split-plot designs. The superiority over existing model-based alternatives in frequency coverage properties is reported under a variety of simulation settings for both binary and continuous outcomes.

Optimal designs with string property under asymmetric errors and SLS estimation

Abstract: We consider the optimal design problem when the design space consists of binary vectors with a string property, i.e., a single stretch of ones. This is done in the framework of second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. Analytical as well as computational results on optimal design measures, under the D- and A-criteria, are obtained. The issue of robustness to the unknown skewness parameter of the error distribution is also explored. Finally, we present several procedures which entail N-run designs that are highly efficient, if not optimal.

Causal Inference from Strip-Plot Designs in a Potential Outcomes Framework

Abstract: Strip-plot designs are very useful when the treatments have a factorial structure and the factors levels are hard-to-change. We develop a randomization-based theory of causal inference from such designs in a potential outcomes framework. For any treatment contrast, an unbiased estimator is proposed, an expression for its sampling variance is worked out, and a conservative estimator of the sampling variance is obtained. This conservative estimator has a nonnegative bias, and becomes unbiased under between-block additivity, a condition milder than Neymannian strict additivity. A minimaxity property of this variance estimator is also established. Simulation results on the coverage of resulting confidence intervals lend support to theoretical considerations.

Design of Order-of-Addition Experiments

Abstract: In an order-of-addition experiment, each treatment is a permutation of m components. It is often unaffordable to test all the m! treatments, and the design problem arises. We consider a model that incorporates the order of each pair of components and can also account for the distance between the two components in every such pair. Under this model, the optimality of the uniform design measure is established, via the approximate theory, for a broad range of criteria. Coupled with an eigen-analysis, this result serves as a benchmark that paves the way for assessing the efficiency and robustness of any exact design. The closed-form construction of a class of robust optimal fractional designs is then explored and illustrated.