STRENGTH OF FACTORS IN [3.sup.3] FACTORIAL DESIGNS USING BAYESIAN ANALYSIS

The study proposes to consider factorial design at three levels and identify all significant factors based on its inherent strength. The methodology considers full, fractional, and reduced factorial designs with three factors each at three levels, to examine the effectiveness of factors in these models through simulation and employing real data. By identifying and quantifying the Bayes factors through simulated datasets, the true strength of the main/interaction effects in these three designs were discovered. Finally, the study concludes that reduced factorial design produces better results than traditional one-third fractional factorial designs when there are no other constraints to adding more factors to the model for analysis. Keywords: [3.sup.3] factorial design; Zellner's g prior; Jeffreys-Zellner-Siow prior; Hyper- g priors; strength of factors