A Bayesian perspective on the analysis of unreplicated factorial experiments using potential outcomes

TY - JOUR

T1 - A Bayesian perspective on the analysis of unreplicated factorial experiments using potential outcomes

AU - Espinosa, Valeria

AU - Dasgupta, Tirthankar

AU - Rubin, Donald B.

N1 - Publisher Copyright: © 2016 American Statistical Association and the American Society for Quality.

PY - 2016/1/2

Y1 - 2016/1/2

N2 - Unreplicated factorial designs have been widely used in scientific and industrial settings, when it is important to distinguish "active" or real factorial effects from "inactive" or noise factorial effects used to estimate residual or "error" terms. We propose a new approach to screen for active factorial effects from such experiments that uses the potential outcomes framework and is based on sequential posterior predictive model checks. One advantage of the proposed method is its ability to broaden the standard definition of active effects and to link their definition to the population of interest. Another important aspect of this approach is its conceptual connection to Fisherian randomization tests. Extensive simulation studies are conducted, which demonstrate the superiority of the proposed approach over existing ones in the situations considered.

AB - Unreplicated factorial designs have been widely used in scientific and industrial settings, when it is important to distinguish "active" or real factorial effects from "inactive" or noise factorial effects used to estimate residual or "error" terms. We propose a new approach to screen for active factorial effects from such experiments that uses the potential outcomes framework and is based on sequential posterior predictive model checks. One advantage of the proposed method is its ability to broaden the standard definition of active effects and to link their definition to the population of interest. Another important aspect of this approach is its conceptual connection to Fisherian randomization tests. Extensive simulation studies are conducted, which demonstrate the superiority of the proposed approach over existing ones in the situations considered.

KW - Causal inference

KW - Posterior predictive check

KW - Randomization tests

KW - Screening experiments

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U2 - https://doi.org/10.1080/00401706.2015.1006337

DO - https://doi.org/10.1080/00401706.2015.1006337

M3 - Article

SN - 0040-1706

VL - 58

SP - 62

EP - 73

JO - Technometrics

JF - Technometrics

IS - 1

ER -